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- Growth: High School Integrated Math 2 (2020)
Growth: High School Integrated Math 2 (2020)
1: Number Sense, Properties, and Number Theory
1.1: Number Sense: Real Numbers
1.1.1: Exponents
1.1.1.1: [RIT 221 - 233] Represents a whole number as a power of a whole number
![Screenshot of Finding Factors with Area Models](/Assets/img/blank.gif)
Finding Factors with Area Models
Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview
1.1.2: Absolute Value: Concepts/Properties
1.1.2.1: [RIT 227 - 228] Evaluates the absolute value of a number
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.2.3: [RIT 241 - 245] Interprets the absolute value of rational numbers in terms of their relative position to 0 in a given real-world situation
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.3: Properties and Relationships of Operations
1.1.3.1: [RIT 209 - 217] Understands that a number and its opposite are the same distance from 0 on a number line
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.4: Real/Complex Numbers: Concepts/Properties
1.1.4.3: [RIT 231 - 275] Compares and orders real numbers
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.5: Rational Numbers: Equivalence
1.1.5.2: [RIT 227 - 233] Converts between decimals and fractions with a denominator of 3
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
1.1.6: Rational Numbers: Compare/Order
1.1.6.3: [RIT 201 - 235] Compares integers that represent quantities in a real-world context
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.6.5: [RIT 207 - 214] Justifies a comparison of two rational numbers using a number line
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.6.6: [RIT 207 - 211] Compares two rational numbers shown on a number line
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.6.7: [RIT 209 - 239] Compares integers given the meaning of zero within a real-world situation
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.6.8: [RIT 211 - 211] Compares integers
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.6.9: [RIT 213 - 230] Compares two rational numbers using a number line
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.6.10: [RIT 218 - 255] Orders positive and negative rational numbers
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.6.11: [RIT 224 - 230] Compares positive rational numbers represented in multiple forms
![Screenshot of Ordering Percents, Fractions, and Decimals Greater Than 1](/Assets/img/blank.gif)
Ordering Percents, Fractions, and Decimals Greater Than 1
Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview
1.1.6.12: [RIT 230 - 230] Orders positive rational numbers represented in multiple forms
![Screenshot of Ordering Percents, Fractions, and Decimals Greater Than 1](/Assets/img/blank.gif)
Ordering Percents, Fractions, and Decimals Greater Than 1
Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview
1.1.7: Rational Numbers: Represent/Model
1.1.7.1: [RIT 191 - 219] Understands positive and negative numbers in terms of real-world situations
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.7.2: [RIT 200 - 218] Locates integers on a number line
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.7.3: [RIT 204 - 204] Locates positive and negative rational numbers on a number line
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.7.4: [RIT 214 - 232] Locates negative rational numbers on a number line
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.7.5: [RIT 233 - 233] Locates the opposite of a negative rational number on a number line
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
1.1.7.6: [RIT 237 - 237] Identifies values that are a given distance from a point on a number line
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.1.8: Scientific Notation
1.1.8.1: [RIT 224 - 230] Converts a number from scientific notation to standard form
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
1.1.8.2: [RIT 229 - 250] Converts a number from standard form to scientific notation
![Screenshot of Number Systems](/Assets/img/blank.gif)
Number Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
1.2: Properties of Real Numbers
1.2.1: Properties and Relationships of Operations
1.2.1.1: [RIT 184 - 214] Identifies the missing value in an equation to show that a number and its opposite have a sum of 0
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
1.2.1.3: [RIT 221 - 253] Understands that the product of a negative number and a positive number is negative
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
1.2.1.4: [RIT 222 - 231] Locates the additive inverse of a number on a number line
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.2.1.5: [RIT 228 - 242] Understands the additive inverse property
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
![Screenshot of Solving Algebraic Equations I](/Assets/img/blank.gif)
Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
1.2.1.6: [RIT 231 - 231] Names the property of operation shown by a given statement
![Screenshot of Solving Algebraic Equations I](/Assets/img/blank.gif)
Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
1.2.1.7: [RIT 243 - 243] Understands the multiplicative inverse property
![Screenshot of Solving Algebraic Equations I](/Assets/img/blank.gif)
Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
1.2.1.8: [RIT 243 - 243] Understands a negative number is less than its opposite
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
1.2.1.9: [RIT 245 - 245] Understands that the product of two negative numbers is positive
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
1.2.1.10: [RIT 245 - 245] Understands the multiplicative identity property
![Screenshot of Solving Algebraic Equations I](/Assets/img/blank.gif)
Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
1.2.1.11: [RIT 262 - 262] Defines properties of equality
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
2: Computation and Estimation with Real Numbers
2.1: Computation with Real Numbers
2.1.1: Numerical Expressions
2.1.1.1: [RIT 263 - 273] Multiplies binomial radical expressions
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
2.1.2: Exponents
2.1.2.1: [RIT 212 - 221] Evaluates numbers with whole-number bases and whole-number exponents
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
2.1.2.2: [RIT 235 - 235] Evaluates numbers with negative integer bases and whole-number exponents
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
2.1.3: Properties and Relationships of Operations
2.1.3.2: [RIT 242 - 242] Determines the distance between two integers on a number line
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
2.1.4: Rational Numbers: Computation
2.1.4.1: [RIT 207 - 223] Identifies two rational numbers that combine to make 0
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
2.1.4.3: [RIT 225 - 253] Multiplies rational numbers, including combinations of positive or negative fractions, decimals, and integers
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
2.1.4.4: [RIT 228 - 242] Adds and subtracts rational numbers, including combinations of positive or negative fractions, decimals, and integers
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
2.1.5: Rational Numbers: Solve Real-World and Mathematical Problems
2.1.5.1: [RIT 202 - 244] Solves real-world problems involving the addition and subtraction of integers
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
2.1.6: Scientific Notation
2.1.6.1: [RIT 233 - 244] Solves real-world problems with numbers expressed in scientific notation
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
2.1.6.2: [RIT 235 - 278] Multiplies and divides numbers expressed in scientific notation
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
2.1.7: Radicals
2.1.7.1: [RIT 228 - 260] Evaluates the square root of a perfect square
![Screenshot of Ordering and Approximating Square Roots](/Assets/img/blank.gif)
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
![Screenshot of Square Roots](/Assets/img/blank.gif)
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
2.1.7.2: [RIT 263 - 273] Multiplies binomial radical expressions
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
2.1.8: Integers: Computation
2.1.8.1: [RIT 203 - 203] Adds and subtracts integers using a number line
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
2.1.8.2: [RIT 205 - 220] Multiplies and divides integers
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
2.1.8.3: [RIT 211 - 229] Adds and subtracts integers
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
2.1.8.4: [RIT 229 - 236] Represents addition and subtraction of integers on a number line
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
2.1.8.5: [RIT 231 - 231] Understands subtracting an integer is the same as adding its opposite
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
2.2: Ratio, Proportion, Percent, and Rate
2.2.1: Conversion of Units
2.2.1.1: [RIT 219 - 257] Converts unit rates to solve real-world problems
![Screenshot of Unit Conversions](/Assets/img/blank.gif)
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
2.2.1.2: [RIT 224 - 257] Converts units of speed
![Screenshot of Unit Conversions](/Assets/img/blank.gif)
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
2.2.2: Rates/Ratios/Proportions/Percents
2.2.2.1: [RIT 188 - 228] Solves for a missing value in a proportion by basic reasoning with equivalent fractions
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
![Screenshot of Proportions and Common Multipliers](/Assets/img/blank.gif)
Proportions and Common Multipliers
Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview
2.2.2.2: [RIT 190 - 242] Uses a given unit rate to solve a one-step real-world problem
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.3: [RIT 191 - 240] Uses ratios of whole numbers to calculate unit rates
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.5: [RIT 203 - 246] Solves one-step percent problems within a real-world or mathematical context
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.6: [RIT 205 - 228] Uses ratios of whole numbers and fractions to calculate unit rates
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.7: [RIT 206 - 233] Uses ratios of whole numbers and decimals to calculate unit rates
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.8: [RIT 207 - 212] Identifies ratios between two quantities not from the same whole
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.9: [RIT 209 - 209] Recognizes a ratio within a context
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.11: [RIT 209 - 246] Calculates percents of numbers
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.12: [RIT 210 - 241] Identifies the part-to-whole ratio between two quantities
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.13: [RIT 214 - 249] Determines equivalent ratios
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.16: [RIT 216 - 253] Solves for a missing value in a proportion by taking a cross product
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
2.2.2.17: [RIT 216 - 263] Uses a given unit rate to solve a multi-step real-world problem
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.18: [RIT 217 - 247] Compares unit rates within a real-world context
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.19: [RIT 219 - 239] Identifies the part-to-part ratio between two quantities
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.20: [RIT 219 - 236] Uses ratios of decimals to calculate unit rates
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
2.2.2.21: [RIT 219 - 244] Calculates the percent one number is of another number
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
2.2.2.22: [RIT 219 - 257] Converts unit rates to solve real-world problems
![Screenshot of Unit Conversions](/Assets/img/blank.gif)
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
2.2.2.23: [RIT 220 - 231] Converts between percents and ratios expressed verbally or in the form a:b
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.24: [RIT 220 - 237] Calculates the whole when given a part and the percent
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
2.2.2.26: [RIT 225 - 234] Determines the whole in a real-world percent problem given the part and the percent
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
2.2.2.27: [RIT 226 - 252] Writes a proportion to solve a real-world problem
![Screenshot of Estimating Population Size](/Assets/img/blank.gif)
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
2.2.2.28: [RIT 227 - 258] Solves multi-step percent problems within a real-world or mathematical context
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.2.29: [RIT 235 - 256] Calculates the percent one number is of another number for percents greater than 100%
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
2.2.2.30: [RIT 235 - 258] Solves real-world problems involving percent or fractional increase
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
2.2.2.32: [RIT 242 - 256] Calculates simple interest
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
2.2.2.33: [RIT 242 - 244] Writes a corresponding linear equation for a given proportion
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
![Screenshot of Percents and Proportions](/Assets/img/blank.gif)
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
2.2.2.34: [RIT 247 - 255] Compares ratios within a real-world context
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.3: Rational Numbers: Equivalence
2.2.3.1: [RIT 215 - 229] Converts between percents and fractions with denominators other than 10 and 100
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.2.3.2: [RIT 220 - 231] Converts between percents and ratios expressed verbally or in the form a:b
![Screenshot of Part-to-part and Part-to-whole Ratios](/Assets/img/blank.gif)
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.3: Estimation with Real Numbers
2.3.1: Real/Complex Numbers: Concepts/Properties
2.3.1.1: [RIT 227 - 260] Approximates the value of an irrational number
![Screenshot of Square Roots](/Assets/img/blank.gif)
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
3: Measurement
3.1: Perimeter and Circumference
3.1.1: Perimeter/Circumference
3.1.1.1: [RIT 213 - 251] Determines the circumference of circles, formula not provided
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.1.1.2: [RIT 213 - 239] Determines the circumference of circles, given the formula
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.1.1.4: [RIT 231 - 231] Determines the ratio between perimeters of scaled figures
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
3.1.1.5: [RIT 232 - 240] Describes the effect on perimeter when dimensions of a non-rectangular polygon are changed
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
3.1.1.6: [RIT 233 - 244] Identifies the formula for the perimeter of a polygon
![Screenshot of Perimeter and Area of Rectangles](/Assets/img/blank.gif)
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
3.2: Area and Surface Area
3.2.1: Area
3.2.1.1: [RIT 213 - 250] Determines the area of parallelograms, formula not provided
![Screenshot of Area of Parallelograms](/Assets/img/blank.gif)
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
3.2.1.3: [RIT 218 - 235] Determines the area of triangles, given the formula
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
3.2.1.4: [RIT 224 - 224] Determines the base or height given the area of a parallelogram
![Screenshot of Area of Parallelograms](/Assets/img/blank.gif)
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
3.2.1.5: [RIT 224 - 252] Describes the effect on area when dimensions of a triangle are changed
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
3.2.1.7: [RIT 228 - 267] Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
![Screenshot of Area of Parallelograms](/Assets/img/blank.gif)
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
Chocomatic (Multiplication, Arrays, and Area)
Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview
![Screenshot of Fido's Flower Bed (Perimeter and Area)](/Assets/img/blank.gif)
Fido's Flower Bed (Perimeter and Area)
Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview
![Screenshot of Perimeter and Area of Rectangles](/Assets/img/blank.gif)
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
3.2.1.8: [RIT 232 - 232] Identifies the formula for the area of a circle
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.10: [RIT 234 - 239] Determines the area of circles, given the formula
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.11: [RIT 236 - 260] Determines the area of figures composed of polygons
![Screenshot of Area of Parallelograms](/Assets/img/blank.gif)
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
Chocomatic (Multiplication, Arrays, and Area)
Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview
![Screenshot of Fido's Flower Bed (Perimeter and Area)](/Assets/img/blank.gif)
Fido's Flower Bed (Perimeter and Area)
Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview
3.2.1.12: [RIT 236 - 254] Determines the area of triangles, formula not provided
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
3.2.1.13: [RIT 240 - 269] Determines the ratio between areas of scaled figures
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
3.2.1.14: [RIT 242 - 259] Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.15: [RIT 244 - 260] Determines the circumference given the area of a circle
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.18: [RIT 247 - 247] Determines the radius or diameter given the area of a circle
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.19: [RIT 249 - 257] Determines the area of circles, formula not provided
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.20: [RIT 251 - 251] Determines the area of figures composed of polygons and circles
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.23: [RIT 260 - 270] Describes the effect on area when the radius or diameter of a circle is changed
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.24: [RIT 261 - 261] Describes the effect on area when the circumference of a circle is changed
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.1.26: [RIT 265 - 265] Solves problems involving areas of circles within a real-world or mathematical context
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
3.2.3: Surface Area
3.2.3.1: [RIT 236 - 246] Uses the net of a prism to solve surface area problems within a real-world or mathematical context
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.3: [RIT 240 - 248] Determines the surface area of a prism given a net
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.4: [RIT 241 - 241] Determines the surface area of cylinders, given the formula
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.5: [RIT 246 - 246] Determines the surface area of cones, given the formula
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.6: [RIT 251 - 252] Determines the surface area of pyramids, given the formula
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.7: [RIT 252 - 256] Determines the surface area of pyramids, formula not provided
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.8: [RIT 252 - 252] Determines the surface area of triangular prisms, formula not provided
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.9: [RIT 255 - 263] Describes the effect on surface area when dimensions of a rectangular prism are changed
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.11: [RIT 260 - 263] Solves problems involving surface areas of prisms within a real-world or mathematical context
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.2.3.12: [RIT 266 - 269] Determines the surface area of cylinders, formula not provided
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
3.3: Volume
3.3.1: Conversion of Units
3.3.1.1: [RIT 282 - 282] Converts units of volume within the same measurement system
![Screenshot of Unit Conversions](/Assets/img/blank.gif)
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
3.3.2: Volume
3.3.2.1: [RIT 227 - 268] Determines the volume of pyramids, given the formula
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
3.3.2.2: [RIT 237 - 240] Determines the volume of cylinders, given the formula
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
3.3.2.3: [RIT 239 - 273] Describes the effect on volume when dimensions of a rectangular prism are changed
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
3.3.2.5: [RIT 245 - 245] Determines the volume of spheres, given the formula
![Screenshot of Measuring Volume](/Assets/img/blank.gif)
Measuring Volume
Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview
3.3.2.6: [RIT 250 - 275] Determines the volume of cylinders, formula not provided
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
3.3.2.8: [RIT 254 - 274] Determines the volume of pyramids, formula not provided
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
3.3.2.10: [RIT 258 - 258] Determines the radius or diameter of a cylinder given the volume and height
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
3.3.2.12: [RIT 259 - 278] Solves problems involving volumes of cylinders within a real-world or mathematical context
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
3.3.2.15: [RIT 266 - 266] Determines the volume of figures composed of rectangular and triangular prisms
![Screenshot of Balancing Blocks (Volume)](/Assets/img/blank.gif)
Balancing Blocks (Volume)
This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview
![Screenshot of Measuring Volume](/Assets/img/blank.gif)
Measuring Volume
Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
3.3.2.16: [RIT 266 - 266] Solves problems involving volumes of 3-D figures composed of cones, cylinders, and spheres within a real-world or mathematical context
![Screenshot of Measuring Volume](/Assets/img/blank.gif)
Measuring Volume
Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
3.3.2.18: [RIT 269 - 281] Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
3.3.2.19: [RIT 270 - 270] Determines the volume of spheres, formula not provided
![Screenshot of Measuring Volume](/Assets/img/blank.gif)
Measuring Volume
Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview
3.3.2.20: [RIT 273 - 273] Determines the volume of cones, formula not provided
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
3.3.2.21: [RIT 276 - 276] Solves problems involving volumes of cones within a real-world or mathematical context
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
4: Geometry
4.1: Points, Lines, Planes, and Angles
4.1.1: Geometric Constructions
4.1.1.1: [RIT 257 - 257] Identifies the geometric construction of an angle bisector
![Screenshot of Constructing Parallel and Perpendicular Lines](/Assets/img/blank.gif)
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
4.1.1.2: [RIT 263 - 263] Identifies the geometric construction of a line segment bisector or the midpoint of a line segment
![Screenshot of Constructing Parallel and Perpendicular Lines](/Assets/img/blank.gif)
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
4.1.2: Points, Lines, Segments, Rays, and Angles
4.1.2.1: [RIT 248 - 248] Defines midpoints of line segments
![Screenshot of Segment and Angle Bisectors](/Assets/img/blank.gif)
Segment and Angle Bisectors
Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview
4.1.2.2: [RIT 275 - 275] Defines bisectors of line segments
![Screenshot of Segment and Angle Bisectors](/Assets/img/blank.gif)
Segment and Angle Bisectors
Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview
4.1.3: Relationships involving Lines, Angles, and Polygons
4.1.3.1: [RIT 226 - 257] Solves problems involving parallel lines cut by a transversal
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.1.3.2: [RIT 240 - 240] Defines complementary and supplementary angles
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
4.1.3.3: [RIT 245 - 249] Identifies corresponding, alternate interior, and alternate exterior angles
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.1.3.4: [RIT 248 - 258] Identifies complementary and supplementary angles
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
4.1.3.5: [RIT 253 - 267] Determines the conditions necessary to show that two lines are parallel
![Screenshot of Constructing Parallel and Perpendicular Lines](/Assets/img/blank.gif)
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
4.1.3.6: [RIT 269 - 269] Identifies vertical angles
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
4.1.4: Geometric Proof/Logic/Inductive and Deductive Reasoning
4.1.4.1: [RIT 253 - 267] Determines the conditions necessary to show that two lines are parallel
![Screenshot of Constructing Parallel and Perpendicular Lines](/Assets/img/blank.gif)
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
4.2: Polygons and Circles
4.2.1: Circles
4.2.1.1: [RIT 208 - 208] Knows the number of degrees in a circle
![Screenshot of Radians](/Assets/img/blank.gif)
Radians
As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview
4.2.1.2: [RIT 218 - 231] Identifies radii and diameters of circles
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
4.2.1.4: [RIT 236 - 236] Recognizes the relationship between the diameter and the radius of a circle
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
4.2.1.6: [RIT 242 - 292] Uses properties of central and inscribed angles to solve problems involving circles
![Screenshot of Chords and Arcs](/Assets/img/blank.gif)
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
![Screenshot of Inscribed Angles](/Assets/img/blank.gif)
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
4.2.1.7: [RIT 243 - 271] Solves problems involving inscribed angles on a diameter
![Screenshot of Inscribed Angles](/Assets/img/blank.gif)
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
4.2.1.8: [RIT 250 - 263] Understands that the ratio between the circumference and the diameter of a circle is equal to pi
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
4.2.1.9: [RIT 256 - 271] Uses properties of chords to solve problems involving circles
![Screenshot of Chords and Arcs](/Assets/img/blank.gif)
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
4.2.1.12: [RIT 262 - 263] Recognizes a precise definition of circles
![Screenshot of Circles](/Assets/img/blank.gif)
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
4.2.1.13: [RIT 263 - 274] Calculates arc lengths
![Screenshot of Chords and Arcs](/Assets/img/blank.gif)
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
![Screenshot of Inscribed Angles](/Assets/img/blank.gif)
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
4.2.1.15: [RIT 266 - 266] Solves problems involving arc measures of a circle
![Screenshot of Chords and Arcs](/Assets/img/blank.gif)
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
4.2.1.16: [RIT 285 - 285] Justifies relationships between the arc length, radius, and central angle measured in radians
![Screenshot of Radians](/Assets/img/blank.gif)
Radians
As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview
4.2.1.17: [RIT 286 - 286] Describes properties of quadrilaterals inscribed in a circle
![Screenshot of Inscribed Angles](/Assets/img/blank.gif)
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
4.2.2: Identification and Classification of 2-D Shapes
4.2.2.1: [RIT 210 - 260] Knows properties of parallelograms, including special parallelograms such as squares, rhombuses, etc.
![Screenshot of Special Parallelograms](/Assets/img/blank.gif)
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
4.2.2.2: [RIT 213 - 245] Knows properties of special triangles, such as acute, right, scalene, etc.
![Screenshot of Classifying Triangles](/Assets/img/blank.gif)
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
4.2.3: Relationships involving Lines, Angles, and Polygons
4.2.3.1: [RIT 194 - 194] Identifies diagonals of polygons
![Screenshot of Polygon Angle Sum](/Assets/img/blank.gif)
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
4.2.3.2: [RIT 220 - 250] Applies the formula for the sum of the interior angles of a polygon
![Screenshot of Polygon Angle Sum](/Assets/img/blank.gif)
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
4.2.3.3: [RIT 221 - 233] Applies the Triangle Angle-Sum Theorem to determine the measure of an unknown angle
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.2.3.4: [RIT 223 - 241] Recognizes that the sum of the interior angles of a triangle is 180 degrees
![Screenshot of Polygon Angle Sum](/Assets/img/blank.gif)
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.2.3.5: [RIT 228 - 250] Applies properties of isosceles triangles to determine the measure of an unknown angle
![Screenshot of Isosceles and Equilateral Triangles](/Assets/img/blank.gif)
Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview
4.2.3.7: [RIT 232 - 268] Solves problems by applying multiple properties of angles, including interior and exterior angles of triangles; complementary, supplementary, and vertical angles; and angles created by perpendicular lines or parallel lines cut by a transversal
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.2.3.9: [RIT 238 - 246] Solves multi-step problems by applying the Triangle Angle-Sum Theorem
![Screenshot of Isosceles and Equilateral Triangles](/Assets/img/blank.gif)
Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.2.3.10: [RIT 240 - 240] Determines the number of diagonals that can be drawn from one vertex in a polygon
![Screenshot of Polygon Angle Sum](/Assets/img/blank.gif)
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
4.2.3.11: [RIT 241 - 276] Applies the Triangle Inequality Theorem
![Screenshot of Triangle Inequalities](/Assets/img/blank.gif)
Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
4.2.3.12: [RIT 242 - 249] Applies the Triangle Exterior Angle Theorem to determine the measure of an unknown angle
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4.2.3.13: [RIT 256 - 258] Applies the formula for the measure of each exterior angle of a regular polygon
![Screenshot of Polygon Angle Sum](/Assets/img/blank.gif)
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
4.2.3.15: [RIT 269 - 269] Applies the formula for the measure of each interior angle of a regular polygon
![Screenshot of Polygon Angle Sum](/Assets/img/blank.gif)
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
4.2.4: Geometric Proof/Logic/Inductive and Deductive Reasoning
4.2.4.1: [RIT 252 - 275] Proves theorems involving the properties of parallelograms
![Screenshot of Parallelogram Conditions](/Assets/img/blank.gif)
Parallelogram Conditions
Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram. 5 Minute Preview
![Screenshot of Special Parallelograms](/Assets/img/blank.gif)
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
4.2.4.3: [RIT 285 - 285] Justifies relationships between the arc length, radius, and central angle measured in radians
![Screenshot of Radians](/Assets/img/blank.gif)
Radians
As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview
4.3: Three-Dimensional Figures
4.3.1: Identification and Classification of 3-D Shapes
4.3.1.2: [RIT 241 - 241] Identifies and names polyhedrons
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
4.3.2: Spatial Concepts and Symmetry
4.3.2.1: [RIT 184 - 229] Identifies and creates nets for prisms
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
4.3.2.2: [RIT 186 - 202] Identifies and creates nets for pyramids
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
4.3.2.3: [RIT 211 - 269] Identifies the cross-sections of 3-D shapes
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
4.4: Congruence and Similarity
4.4.1: Congruence
4.4.1.1: [RIT 153 - 184] Identifies congruent shapes, given informal language
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
4.4.1.2: [RIT 186 - 230] Identifies congruent shapes, given formal language
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.1.4: [RIT 194 - 206] Identifies corresponding sides and angles in congruent figures
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
4.4.1.7: [RIT 229 - 229] Uses formal notation to denote corresponding sides and angles in congruent triangles
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.1.9: [RIT 251 - 255] Identifies congruent triangles using AAS, ASA, SAS, or SSS
![Screenshot of Congruence in Right Triangles](/Assets/img/blank.gif)
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.1.10: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent
![Screenshot of Congruence in Right Triangles](/Assets/img/blank.gif)
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.1.12: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent
![Screenshot of Congruence in Right Triangles](/Assets/img/blank.gif)
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.2: Similarity
4.4.2.1: [RIT 180 - 181] Identifies similar figures
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.2: [RIT 204 - 253] Applies scale factors to solve problems involving scale drawings, maps, and models
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
4.4.2.3: [RIT 212 - 260] Determines lengths of corresponding sides in similar figures
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.4: [RIT 212 - 212] Determines scale factors in problems involving scale drawings, maps, and models
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
4.4.2.5: [RIT 213 - 226] Identifies corresponding sides and angles in similar figures
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.6: [RIT 215 - 249] Applies properties of similar triangles to solve real-world problems involving indirect measurements
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
4.4.2.7: [RIT 220 - 220] Knows the definition of similarity
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.8: [RIT 223 - 239] Determines scale factors in problems involving scale drawings of geometric figures
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
4.4.2.10: [RIT 224 - 224] Determines the ratio between perimeters of similar figures
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
4.4.2.11: [RIT 225 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
4.4.2.12: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.2.13: [RIT 232 - 257] Applies properties of similar figures to determine a perimeter
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
4.4.2.15: [RIT 235 - 235] Applies properties of similar figures to determine an area
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
4.4.2.16: [RIT 239 - 239] Identifies the proportion of corresponding sides of similar figures
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.17: [RIT 244 - 263] Applies similarity postulates to solve for missing lengths and angles
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.18: [RIT 245 - 256] Identifies similar triangles using AA
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.19: [RIT 247 - 247] Applies similarity postulates to identify corresponding sides and angles
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.22: [RIT 260 - 279] Applies the geometric mean to solve for missing lengths and angles in triangles
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.2.23: [RIT 261 - 271] Identifies the similarity postulate that proves two triangles are similar
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.2.26: [RIT 285 - 286] Determines the ratio between areas of similar figures
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
4.4.2.27: [RIT 288 - 288] Solves problems involving multiple theorems of similar triangles, including the Triangle Proportionality Theorem, segment proportionality property for parallel lines, and similarity postulates
![Screenshot of Similarity in Right Triangles](/Assets/img/blank.gif)
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
4.4.3: Geometric Proof/Logic/Inductive and Deductive Reasoning
4.4.3.1: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.3.2: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent
![Screenshot of Congruence in Right Triangles](/Assets/img/blank.gif)
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.3.3: [RIT 261 - 271] Identifies the similarity postulate that proves two triangles are similar
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.4.3.4: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent
![Screenshot of Congruence in Right Triangles](/Assets/img/blank.gif)
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4.5: Pythagorean Theorem, Right Triangle Trig
4.5.1: Pythagorean Theorem
4.5.1.1: [RIT 241 - 275] Uses the Pythagorean Theorem to solve real-world or mathematical problems
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
4.5.1.2: [RIT 242 - 266] Uses the Pythagorean Theorem to calculate the length of a missing side of a right triangle
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
4.5.1.3: [RIT 250 - 268] Applies the converse of the Pythagorean Theorem to identify right triangles
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
4.5.1.5: [RIT 280 - 280] Uses similarity to prove the Pythagorean Theorem
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
4.5.2: Trigonometry
4.5.2.1: [RIT 241 - 263] Represents the sine of an angle as a ratio of sides in a right triangle
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
4.5.2.2: [RIT 246 - 266] Represents the tangent of an angle as a ratio of sides in a right triangle
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
![Screenshot of Tangent Function](/Assets/img/blank.gif)
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
4.5.2.3: [RIT 247 - 263] Represents the cosine of an angle as a ratio of sides in a right triangle
![Screenshot of Cosine Function](/Assets/img/blank.gif)
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
4.5.2.4: [RIT 250 - 272] Uses sine, cosine, or tangent to determine the length of a side in a right triangle
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
4.5.2.6: [RIT 263 - 273] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
4.5.3: Relationships involving Lines, Angles, and Polygons
4.5.3.1: [RIT 255 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to solve real-world and mathematical problems
![Screenshot of Cosine Function](/Assets/img/blank.gif)
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Tangent Function](/Assets/img/blank.gif)
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
4.5.3.2: [RIT 258 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to calculate the length of a missing side of a right triangle
![Screenshot of Cosine Function](/Assets/img/blank.gif)
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Tangent Function](/Assets/img/blank.gif)
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
4.5.4: Geometric Proof/Logic/Inductive and Deductive Reasoning
4.5.4.1: [RIT 280 - 280] Uses similarity to prove the Pythagorean Theorem
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
4.6: Transformations and Symmetry
4.6.1: Spatial Concepts and Symmetry
4.6.1.1: [RIT 165 - 228] Determines the number of lines of symmetry in 2-D figures
![Screenshot of Holiday Snowflake Designer](/Assets/img/blank.gif)
Holiday Snowflake Designer
Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper. 5 Minute Preview
![Screenshot of Quilting Bee (Symmetry)](/Assets/img/blank.gif)
Quilting Bee (Symmetry)
Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview
4.6.1.2: [RIT 206 - 217] Identifies 2-D figures which have rotational symmetry
![Screenshot of Quilting Bee (Symmetry)](/Assets/img/blank.gif)
Quilting Bee (Symmetry)
Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview
4.6.1.4: [RIT 275 - 284] Identifies the rotational or reflectional symmetry of a shape
![Screenshot of Quilting Bee (Symmetry)](/Assets/img/blank.gif)
Quilting Bee (Symmetry)
Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview
4.6.2: Transformations
4.6.2.1: [RIT 196 - 251] Describes a single transformation that shows two shapes are congruent, without the coordinate plane
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
4.6.2.2: [RIT 198 - 227] Describes a single transformation that will map one figure onto another, without the coordinate plane
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.4: [RIT 207 - 232] Understands that rigid transformations preserve congruency
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.5: [RIT 214 - 214] Identifies the degree of rotation that shows that two given figures are congruent, without a coordinate plane
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
4.6.2.7: [RIT 221 - 254] Determines the image of a polygon on a coordinate plane after a reflection or a series of reflections
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.8: [RIT 223 - 254] Determines the coordinates of the vertices of a polygon after a dilation or a series of dilations, with center at the origin
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
4.6.2.9: [RIT 225 - 241] Determines the coordinates of the vertices of a polygon after a translation or a series of translations
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.10: [RIT 226 - 226] Determines the image of a polygon on a coordinate plane after a rotation or a series of rotations
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.13: [RIT 231 - 242] Describes the effects of dilation on lengths and angle measures
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
4.6.2.14: [RIT 231 - 259] Determines the coordinates of the vertices of a polygon after a reflection or a series of reflections
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.15: [RIT 232 - 268] Describes a single transformation that will map one figure onto itself, without the coordinate plane
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
4.6.2.16: [RIT 235 - 271] Determines the coordinates of the vertices of a polygon after a rotation or a series of rotations
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.17: [RIT 237 - 246] Describes a series of transformations that show two shapes are congruent on the coordinate plane
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.18: [RIT 239 - 239] Represents translations in the plane using matrices
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.19: [RIT 240 - 240] Determines the image of a translation represented in coordinate notation
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.22: [RIT 243 - 261] Describes a single transformation that shows two shapes are congruent on the coordinate plane
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.23: [RIT 249 - 263] Describes a translation using coordinate notation
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
4.6.2.24: [RIT 250 - 250] Determines the image of a polygon on a coordinate plane after a series of translations, reflections, or rotations
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.25: [RIT 251 - 251] Determines the image of a dilation represented in coordinate notation
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
4.6.2.26: [RIT 252 - 252] Identifies the center and scale factor used in a dilation represented in the coordinate plane
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
4.6.2.27: [RIT 253 - 253] Applies the scale factor in a dilation to solve for unknown lengths
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
4.6.2.30: [RIT 264 - 264] Determines the image of a reflection represented in coordinate notation
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
4.6.2.31: [RIT 275 - 278] Describes a series of transformations that will map one figure onto another, without the coordinate plane
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
4.6.3: Geometric Proof/Logic/Inductive and Deductive Reasoning
4.6.3.1: [RIT 263 - 268] Describes a series of transformations that show two given circles are similar on the coordinate plane
![Screenshot of Circles](/Assets/img/blank.gif)
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
4.7: Coordinate Graphing and Distance
4.7.1: Coordinate Geometry
4.7.1.1: [RIT 181 - 229] Determines the coordinates of points in all four quadrants of a coordinate graph
![Screenshot of Points in the Coordinate Plane](/Assets/img/blank.gif)
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
4.7.1.2: [RIT 183 - 236] Plots points in all four quadrants of a coordinate plane
![Screenshot of Points in the Coordinate Plane](/Assets/img/blank.gif)
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
4.7.1.3: [RIT 202 - 242] Determines the quadrant for a given ordered pair
![Screenshot of Points in the Coordinate Plane](/Assets/img/blank.gif)
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
4.7.1.4: [RIT 205 - 232] Determines the distance between two points with the same first or second coordinate
![Screenshot of Distance Formula](/Assets/img/blank.gif)
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
![Screenshot of Points in the Coordinate Plane](/Assets/img/blank.gif)
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
4.7.1.8: [RIT 235 - 235] Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate
![Screenshot of Points in the Coordinate Plane](/Assets/img/blank.gif)
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
4.7.1.9: [RIT 242 - 268] Determines the distance between two points on the coordinate plane
![Screenshot of Distance Formula](/Assets/img/blank.gif)
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
4.7.1.12: [RIT 251 - 280] Identifies collinear points
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
5: Statistics and Probability
5.1: Collect, Organize, Analyze Data
5.1.2: Bivariate Data
5.1.2.1: [RIT 189 - 234] Constructs scatter plots of bivariate data
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.2: [RIT 198 - 198] Reads and interprets data from a scatter plot
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.3: [RIT 199 - 236] Describes and interprets data in a scatter plot
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.4: [RIT 206 - 249] Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.7: [RIT 213 - 264] Analyzes linear trends in scatter plots to make predictions
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.8: [RIT 219 - 268] Describes and interprets outliers and clusters in a scatter plot
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.9: [RIT 220 - 220] Determines whether two quantitative variables have a positive linear, negative linear, or zero association
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.10: [RIT 221 - 221] Distinguishes between linear and nonlinear relationships in scatter plots
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
5.1.2.11: [RIT 222 - 270] Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
5.1.2.12: [RIT 222 - 237] Uses a given equation of a line of best fit to make predictions
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.13: [RIT 230 - 267] Interprets the meaning of the slope or y-intercept of a line of best fit or regression line
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.14: [RIT 231 - 271] Determines a pair of quantitative variables that has either a positive, negative, or zero correlation
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.15: [RIT 233 - 233] Approximates the line of best fit on a scatter plot
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.16: [RIT 242 - 271] Compares two sets of bivariate data to draw conclusions
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
5.1.2.18: [RIT 246 - 260] Estimates the slope of a line of best fit
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.2.19: [RIT 261 - 261] Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a real-world context
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
5.1.2.20: [RIT 261 - 276] Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a scatter plot
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
5.1.2.21: [RIT 262 - 262] Approximates the equation of the line of best fit
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.3: Data Analysis
5.1.3.1: [RIT 163 - 210] Reads and interprets data from a circle graph
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Mascot Election (Pictographs and Bar Graphs)](/Assets/img/blank.gif)
Mascot Election (Pictographs and Bar Graphs)
A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview
5.1.3.3: [RIT 193 - 235] Identifies the median, quartiles, extreme values, and outliers from a box plot
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
5.1.3.4: [RIT 198 - 198] Reads and interprets data from a scatter plot
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.3.13: [RIT 243 - 243] Compares the means and medians of related data sets from random samples represented in histograms
![Screenshot of Populations and Samples](/Assets/img/blank.gif)
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
5.1.4: Data Representation
5.1.4.1: [RIT 189 - 234] Constructs scatter plots of bivariate data
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
5.1.4.2: [RIT 196 - 224] Represents data in circle graphs
![Screenshot of Graphing Skills](/Assets/img/blank.gif)
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
![Screenshot of Mascot Election (Pictographs and Bar Graphs)](/Assets/img/blank.gif)
Mascot Election (Pictographs and Bar Graphs)
A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview
5.1.4.6: [RIT 247 - 261] Represents data in box plots
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
5.1.5: Measures of Center and Spread (Variability)
5.1.5.1: [RIT 193 - 235] Identifies the median, quartiles, extreme values, and outliers from a box plot
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
5.1.5.5: [RIT 238 - 243] Explains why the mean and median differ in a single data set
![Screenshot of Mean, Median, and Mode](/Assets/img/blank.gif)
Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
5.1.5.7: [RIT 243 - 243] Compares the means and medians of related data sets from random samples represented in histograms
![Screenshot of Populations and Samples](/Assets/img/blank.gif)
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
5.1.5.9: [RIT 255 - 272] Compares the measures of center of two data sets after the addition or deletion of data values, including outliers
![Screenshot of Describing Data Using Statistics](/Assets/img/blank.gif)
Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
![Screenshot of Movie Reviewer (Mean and Median)](/Assets/img/blank.gif)
Movie Reviewer (Mean and Median)
Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview
5.1.6: Populations/Random Processes
5.1.6.1: [RIT 187 - 217] Identifies a data collection method that best answers a question
![Screenshot of Polling: City](/Assets/img/blank.gif)
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.2: [RIT 202 - 202] Identifies random samples
![Screenshot of Polling: City](/Assets/img/blank.gif)
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.4: [RIT 214 - 250] Writes and solves proportions to make inferences about populations
![Screenshot of Estimating Population Size](/Assets/img/blank.gif)
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.6: [RIT 226 - 241] Identifies valid inferences given a population sample
![Screenshot of Polling: City](/Assets/img/blank.gif)
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.7: [RIT 230 - 247] Identifies a sampling method that produces the most representative sample
![Screenshot of Polling: City](/Assets/img/blank.gif)
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.8: [RIT 230 - 231] Identifies an appropriate research design, including surveys, experiments and observational studies, to answer a question
![Screenshot of Polling: City](/Assets/img/blank.gif)
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.9: [RIT 243 - 243] Writes proportions to make inferences about populations
![Screenshot of Estimating Population Size](/Assets/img/blank.gif)
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.1.6.10: [RIT 246 - 254] Explains the difference between values describing a population and values describing a sample within a real-world context
![Screenshot of Polling: City](/Assets/img/blank.gif)
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.2: Probability
5.2.1: Probability
5.2.1.1: [RIT 168 - 218] Identifies a simple event given the likelihood of the event as more likely, less likely, neither likely nor unlikely, impossible, or certain
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
5.2.1.3: [RIT 185 - 213] Describes the likelihood of simple events occurring
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
5.2.1.4: [RIT 190 - 249] Determines theoretical probabilities of simple events
![Screenshot of Geometric Probability](/Assets/img/blank.gif)
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
5.2.1.5: [RIT 193 - 241] Makes predictions based on theoretical probabilities of simple events
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
5.2.1.6: [RIT 207 - 244] Makes predictions based on experimental probabilities of simple events
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
5.2.1.7: [RIT 208 - 220] Identifies the likelihood of a simple event as more likely, less likely, neither likely nor unlikely, impossible, or certain, given the probability of the event
![Screenshot of Geometric Probability](/Assets/img/blank.gif)
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
![Screenshot of Theoretical and Experimental Probability](/Assets/img/blank.gif)
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
5.2.1.8: [RIT 213 - 242] Determines experimental probabilities of simple events
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
![Screenshot of Theoretical and Experimental Probability](/Assets/img/blank.gif)
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
5.2.1.10: [RIT 215 - 230] Determines the probability of the complement of an event
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
![Screenshot of Theoretical and Experimental Probability](/Assets/img/blank.gif)
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
5.2.1.11: [RIT 219 - 232] Describes the likelihood of compound events occurring
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
![Screenshot of Spin the Big Wheel! (Probability)](/Assets/img/blank.gif)
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
5.2.1.12: [RIT 221 - 268] Determines probabilities of compound independent events
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.13: [RIT 221 - 271] Distinguishes between independent and dependent events in situations
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.14: [RIT 222 - 239] Understands independence as it relates to previous outcomes
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.15: [RIT 224 - 224] Determines the odds of simple events
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
5.2.1.16: [RIT 224 - 224] Writes proportions to make predictions based on experimental probabilities
![Screenshot of Estimating Population Size](/Assets/img/blank.gif)
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
5.2.1.19: [RIT 238 - 286] Determines probabilities of two compound events given organized lists, tree diagrams, or charts
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.20: [RIT 239 - 242] Determines conditional probabilities of events without replacement
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.21: [RIT 240 - 240] Modifies sample space to change the probability of an event
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
5.2.1.22: [RIT 244 - 288] Interprets conditional probability with and without a context
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.23: [RIT 245 - 266] Determines probabilities using geometric models
![Screenshot of Geometric Probability](/Assets/img/blank.gif)
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
5.2.1.24: [RIT 246 - 246] Makes predictions based on probability distributions
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
5.2.1.25: [RIT 257 - 257] Makes predictions based on theoretical probabilities of compound events
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.26: [RIT 257 - 276] Determines probabilities using the general Multiplication Rule of probability
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.27: [RIT 257 - 278] Determines conditional probabilities of compound events using relative frequencies
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.28: [RIT 258 - 266] Determines probabilities of compound dependent events
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.1.31: [RIT 276 - 284] Justifies the independence of two events using the product of their probabilities
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
5.2.2: Sample Spaces
5.2.2.1: [RIT 187 - 219] Determines the sample space for a simple event using lists, tree diagrams, or charts
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
![Screenshot of Theoretical and Experimental Probability](/Assets/img/blank.gif)
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
5.2.2.2: [RIT 201 - 242] Determines the sample space for two compound events using organized lists, tree diagrams, or charts
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
5.2.2.3: [RIT 212 - 232] Determines the sample space for more than two compound events using organized lists, tree diagrams, or charts
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
5.2.2.5: [RIT 220 - 272] Uses permutations and combinations to determine the number of possible outcomes
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
6: Algebraic Concepts
6.1: Patterns, Sequences: Arithmetic and Geometric
6.1.1: Patterns/Sequences/Series
6.1.1.1: [RIT 218 - 258] Determines the value of a term in an arithmetic sequence given a contextual situation
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
6.1.1.4: [RIT 229 - 285] Determines the value of a term in a geometric sequence defined by a list
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
6.1.1.5: [RIT 229 - 266] Determines the value of a term in a geometric sequence given a contextual situation
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
6.1.1.6: [RIT 232 - 238] Recognizes arithmetic sequences
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
6.1.1.7: [RIT 243 - 272] Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
6.1.1.8: [RIT 256 - 256] Determines the common ratio in a geometric sequence
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
6.1.1.9: [RIT 260 - 271] Writes an expression or formula for the nth term of a geometric sequence given a number sequence
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
6.1.1.10: [RIT 277 - 277] Determines the value of a term in an arithmetic sequence defined recursively
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
6.2: Functions
6.2.1: Algebraic Expressions
6.2.1.1: [RIT 279 - 279] Identifies equivalent exponential expressions
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
6.2.2: Properties and Operations of Functions
6.2.2.1: [RIT 206 - 206] Expresses a relation defined by a mapping diagram as a set of ordered pairs
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
6.2.2.2: [RIT 235 - 239] Determines the input of a function given an output
![Screenshot of Function Machines 1 (Functions and Tables)](/Assets/img/blank.gif)
Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
6.2.2.3: [RIT 238 - 276] Performs operations with functions
![Screenshot of Addition and Subtraction of Functions](/Assets/img/blank.gif)
Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
6.2.2.4: [RIT 238 - 263] Identifies the type of function by its equation
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
![Screenshot of Radical Functions](/Assets/img/blank.gif)
Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
6.2.2.6: [RIT 244 - 270] Distinguishes between linear and nonlinear functions given an equation, a graph, or a table of values
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
6.2.2.7: [RIT 245 - 246] Writes a function in the form f(x) = g(x) - h(x) to represent real-world scenarios
![Screenshot of Addition and Subtraction of Functions](/Assets/img/blank.gif)
Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
6.2.2.14: [RIT 261 - 270] Determines if a relation defined by a set of ordered pairs, a table of values, or a graph is a function
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
6.2.2.16: [RIT 264 - 280] Determines the domain of a rational function
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
6.2.2.23: [RIT 283 - 283] Writes the inverse of an exponential function
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
6.2.2.24: [RIT 283 - 289] Graphs the inverse of a function
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
6.2.3: Number Sentences/Equations/Equivalence
6.2.3.1: [RIT 238 - 266] Identifies an ordered pair that is a solution to a two-variable equation
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.4: Polynomial Functions
6.2.4.1: [RIT 227 - 254] Identifies the zeros of a polynomial function from a graph
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
6.2.4.2: [RIT 256 - 275] Applies the polynomial Remainder Theorem
![Screenshot of Dividing Polynomials Using Synthetic Division](/Assets/img/blank.gif)
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
6.2.4.3: [RIT 262 - 275] Factors polynomial functions to determine zeros
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
6.2.4.5: [RIT 267 - 267] Evaluates a polynomial function using synthetic division
![Screenshot of Dividing Polynomials Using Synthetic Division](/Assets/img/blank.gif)
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
6.2.4.6: [RIT 270 - 270] Identifies key features of a polynomial function given a graph
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
6.2.4.7: [RIT 270 - 270] Describes the effects of transformations on the graphs of polynomial functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
6.2.4.8: [RIT 284 - 286] Identifies the factors of a polynomial function from a graph
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
6.2.5: Rate of Change/Slope
6.2.5.1: [RIT 202 - 249] Compares the rate of change between two proportional relationships represented in different ways
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.5.2: [RIT 212 - 255] Interprets the meaning of the slope of a graph in a real-world linear relationship
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Elevator Operator (Line Graphs)](/Assets/img/blank.gif)
Elevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview
6.2.5.3: [RIT 212 - 225] Identifies the unit rate from the graph of a proportional relationship
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.5.4: [RIT 213 - 260] Calculates the rate of change from a graph representing a real-world linear relationship
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Elevator Operator (Line Graphs)](/Assets/img/blank.gif)
Elevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview
6.2.5.5: [RIT 215 - 245] Calculates the rate of change from a table or description of a real-world linear relationship
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.6: [RIT 227 - 257] Calculates the rate of change of a piecewise function over a given interval
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Elevator Operator (Line Graphs)](/Assets/img/blank.gif)
Elevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview
6.2.5.8: [RIT 233 - 233] Interprets the meaning of the slope and y-intercept of a graph within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.9: [RIT 236 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.10: [RIT 237 - 250] Identifies the y-intercept and the slope of a line given an equation of the line in the form y = mx + b
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.11: [RIT 238 - 258] Understands that the slope is the same between any two points on a line
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.12: [RIT 239 - 259] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx + b
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.13: [RIT 243 - 243] Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.5.14: [RIT 247 - 250] Calculates the slope of a line on a graph
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Slope](/Assets/img/blank.gif)
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
6.2.5.15: [RIT 248 - 259] Calculates the slope of a line given ordered pairs
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Slope](/Assets/img/blank.gif)
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.6: Quadratic Functions
6.2.6.1: [RIT 214 - 214] Interprets zeros, extreme values, and symmetry of a graph within the context of a real-world quadratic relationship
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.2: [RIT 220 - 249] Describes the effects that changes in the constant terms have on the graphs of quadratic functions
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
6.2.6.4: [RIT 232 - 251] Evaluates a quadratic function for a given value in its domain
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.5: [RIT 237 - 259] Evaluates a quadratic function for a given value in its domain to solve a real-world problem
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.6: [RIT 239 - 255] Identifies the vertex, intercepts, or axis of symmetry of a quadratic function given a graph
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.7: [RIT 242 - 261] Determines the zeros of a quadratic function from a table of values
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.9: [RIT 247 - 280] Graphs quadratic functions
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.10: [RIT 249 - 276] Graphs transformations of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.11: [RIT 250 - 280] Determines the maximum, minimum, y-intercept, or zeros of a quadratic function to solve real-world problems
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.12: [RIT 253 - 253] Recognizes the graph of a quadratic relationship
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.13: [RIT 254 - 268] Writes a quadratic function given the zeros
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.6.14: [RIT 258 - 275] Determines the vertex, intercepts, or axis of symmetry of a quadratic function given an equation
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.15: [RIT 259 - 259] Writes a quadratic function to represent real-world or mathematical contexts
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.18: [RIT 261 - 275] Determines an x-intercept of a quadratic function given the other x-intercept and the vertex or the axis of symmetry
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.19: [RIT 262 - 273] Determines the zeros of a quadratic function by factoring
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.20: [RIT 262 - 289] Describes the effects that changes in the coefficients have on the graphs of quadratic functions
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
6.2.6.21: [RIT 265 - 265] Understands the relationship between the zeros of a function and the x-intercepts of the graph of the function
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.22: [RIT 266 - 274] Describes the effects of transformations on the graphs of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
6.2.6.23: [RIT 269 - 288] Recognizes the advantages of standard, factored, and vertex form of quadratic functions
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.2.6.24: [RIT 270 - 272] Writes a quadratic function given a graph
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
6.2.6.25: [RIT 272 - 277] Rewrites a quadratic equation into vertex form
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
6.2.7: Linear Functions
6.2.7.1: [RIT 192 - 223] Graphs a linear function of the form y = mx given a simple scenario
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.2: [RIT 195 - 256] Interprets the meaning of the y-intercept of a graph within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.3: [RIT 198 - 206] Expresses the linear relationship between variables in words
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.4: [RIT 200 - 232] Translates between the graph of a piecewise linear function and a verbal description of the real-world relationship
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
6.2.7.5: [RIT 202 - 249] Compares the rate of change between two proportional relationships represented in different ways
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.8: [RIT 212 - 255] Interprets the meaning of the slope of a graph in a real-world linear relationship
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Elevator Operator (Line Graphs)](/Assets/img/blank.gif)
Elevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview
6.2.7.9: [RIT 213 - 260] Calculates the rate of change from a graph representing a real-world linear relationship
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Elevator Operator (Line Graphs)](/Assets/img/blank.gif)
Elevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview
6.2.7.10: [RIT 215 - 245] Calculates the rate of change from a table or description of a real-world linear relationship
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.11: [RIT 219 - 232] Identifies the table of values given a graph of a linear relationship in the form y = mx + b
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.12: [RIT 219 - 259] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given the slope and y-intercept
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.13: [RIT 224 - 252] Understands independent and dependent variables within a linear context
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
6.2.7.15: [RIT 226 - 240] Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.16: [RIT 228 - 259] Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.18: [RIT 229 - 237] Translates between the graph of a linear function and a verbal description of the real-world relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.22: [RIT 231 - 233] Describes a situation that can be represented by a given linear equation
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.24: [RIT 233 - 233] Interprets the meaning of the slope and y-intercept of a graph within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.25: [RIT 234 - 234] Interprets the meaning of the y-intercept for the equation y = mx + b within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.27: [RIT 235 - 273] Determines whether a real-world situation can be modeled by a linear or an exponential function
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.7.28: [RIT 235 - 235] Identifies an intercept of a graph of a linear function
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.30: [RIT 235 - 243] Interprets the meaning of the constant term in the equation y = mx + b within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.31: [RIT 236 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.32: [RIT 237 - 250] Identifies the y-intercept and the slope of a line given an equation of the line in the form y = mx + b
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.33: [RIT 237 - 273] Writes an equation in the form y = mx to represent a real-world proportional relationship for a given ratio
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.34: [RIT 237 - 274] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a complex scenario
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.35: [RIT 238 - 258] Understands that the slope is the same between any two points on a line
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.36: [RIT 238 - 253] Solves direct variation problems
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.38: [RIT 239 - 259] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx+b
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.40: [RIT 239 - 239] Describes the effects of changes in parameters on linear functions that represent real-world relationships
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.41: [RIT 240 - 261] Describes the effects that changes in the constant terms have on the graphs of linear functions
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.44: [RIT 240 - 240] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a simple scenario
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.46: [RIT 243 - 243] Recognizes direct variation situations
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.47: [RIT 243 - 243] Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.50: [RIT 245 - 250] Graphs the equation of a line in the form y = mx + b
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.52: [RIT 247 - 250] Calculates the slope of a line on a graph
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Slope](/Assets/img/blank.gif)
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
6.2.7.53: [RIT 248 - 259] Calculates the slope of a line given ordered pairs
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Slope](/Assets/img/blank.gif)
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.54: [RIT 250 - 250] Determines the y-intercept of a line given two points on the line
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
6.2.7.55: [RIT 250 - 262] Illustrates the result of changes in the slope and y-intercept within a real-world linear relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.56: [RIT 253 - 253] Graphs the equation of a line in standard form
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.57: [RIT 253 - 253] Rewrites a linear equation in the form y = mx + b
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.58: [RIT 255 - 269] Rewrites a linear equation into the form Ax + By = C
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.60: [RIT 255 - 255] Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.7.61: [RIT 255 - 255] Justifies that linear models increase and decrease by equal differences over equal intervals
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.62: [RIT 257 - 257] Writes the equation of a line in the form y = mx + b given the slope and a point on the line
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.63: [RIT 259 - 270] Writes the equation of a line in standard form given a table of values or two ordered pairs
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.65: [RIT 268 - 268] Writes the equation of a line in standard form given the slope and a point on the line
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.7.67: [RIT 268 - 268] Writes the equation of a line in standard form given the slope and y-intercept
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.8: Exponential and Logarithmic Functions
6.2.8.1: [RIT 225 - 225] Interprets the meaning of the y-intercept of a graph within the context of a real-world exponential relationship
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.2: [RIT 234 - 255] Identifies the appropriate linear or exponential model that represents a real-world situation
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.2.8.3: [RIT 235 - 273] Determines whether a real-world situation can be modeled by a linear or an exponential function
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.4: [RIT 235 - 264] Evaluates an exponential function for a given value in its domain to solve a real-world problem
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.5: [RIT 237 - 271] Understands that exponential models grow and decay by equal factors over equal intervals
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.6: [RIT 238 - 238] Describes the effects that changes in parameters have on the tables of values of exponential functions
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.7: [RIT 241 - 277] Writes exponential functions to represent real-world or mathematical problems
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.8: [RIT 244 - 244] Identifies a table of values that represents an exponential relationship
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.9: [RIT 246 - 261] Classifies exponential functions as representations of growth or decay
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.10: [RIT 248 - 272] Describes the effects of changes in parameters on exponential functions that represent real-world relationships
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.12: [RIT 252 - 264] Graphs an exponential function given a table of values
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.13: [RIT 254 - 261] Describes the effects that changes in parameters have on the graphs of exponential functions
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.14: [RIT 259 - 270] Graphs exponential functions
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.15: [RIT 260 - 260] Determines real-world situations that can be modeled by an exponential function
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.16: [RIT 261 - 261] Justifies that exponential models grow and decay by equal factors over equal intervals
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.17: [RIT 267 - 267] Writes an exponential function given a graph
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.18: [RIT 267 - 274] Writes the equation representing transformations of exponential functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
6.2.8.19: [RIT 270 - 270] Identifies the table of values given an exponential equation
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.20: [RIT 275 - 275] Understands the exponential impact of the growth factor on values of an exponential function
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
6.2.8.21: [RIT 283 - 283] Writes the inverse of an exponential function
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
6.2.9: Piecewise/Absolute Value Functions
6.2.9.1: [RIT 200 - 232] Translates between the graph of a piecewise linear function and a verbal description of the real-world relationship
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
6.2.9.3: [RIT 227 - 257] Calculates the rate of change of a piecewise function over a given interval
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Elevator Operator (Line Graphs)](/Assets/img/blank.gif)
Elevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview
6.2.9.4: [RIT 249 - 276] Graphs absolute value functions
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
6.2.9.5: [RIT 250 - 250] Describes the effects of transformations on the graphs of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
6.2.9.6: [RIT 253 - 253] Determines the y-intercept of the transformation of an absolute value function, given the equation
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
6.2.9.7: [RIT 264 - 266] Writes the equation representing transformations of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
6.2.9.8: [RIT 269 - 269] Graphs transformations of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
6.2.9.9: [RIT 270 - 280] Graphs piecewise functions
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
6.2.9.10: [RIT 276 - 276] Writes a piecewise function given a graph
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
6.2.10: Rational Functions
6.2.10.1: [RIT 251 - 291] Determines end behavior of rational functions
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
6.2.10.2: [RIT 253 - 253] Writes rational functions to represent real-world or mathematical problems
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
6.2.10.3: [RIT 260 - 265] Identifies the table of values that represents an inverse-variation relationship
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.10.4: [RIT 260 - 281] Graphs rational functions
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
6.2.10.5: [RIT 261 - 282] Determines x-intercepts for rational functions
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
6.2.10.6: [RIT 268 - 268] Determines points of discontinuity for rational functions
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
6.2.10.7: [RIT 269 - 269] Solves inverse variation problems
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.2.11: Radical Functions
6.2.11.1: [RIT 278 - 278] Describes the effects of transformations on the graphs of radical functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a
![Screenshot of Radical Functions](/Assets/img/blank.gif)
Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
6.3: Evaluate and Simplify Expressions
6.3.1: Algebraic Expressions
6.3.1.1: [RIT 213 - 235] Evaluates linear expressions at given values with variables involving positive rational numbers
![Screenshot of Equivalent Algebraic Expressions I](/Assets/img/blank.gif)
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
6.3.1.2: [RIT 217 - 259] Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms
![Screenshot of Equivalent Algebraic Expressions I](/Assets/img/blank.gif)
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
![Screenshot of Equivalent Algebraic Expressions II](/Assets/img/blank.gif)
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions I](/Assets/img/blank.gif)
Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
6.3.1.5: [RIT 221 - 248] Generates equivalent linear expressions by using the associative, commutative, or distributive property
![Screenshot of Equivalent Algebraic Expressions I](/Assets/img/blank.gif)
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
![Screenshot of Equivalent Algebraic Expressions II](/Assets/img/blank.gif)
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions I](/Assets/img/blank.gif)
Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
6.3.1.7: [RIT 227 - 242] Generates equivalent linear expressions by combining like terms
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
6.3.1.8: [RIT 233 - 282] Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
![Screenshot of Simplifying Algebraic Expressions I](/Assets/img/blank.gif)
Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
6.3.1.9: [RIT 236 - 267] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.3.1.10: [RIT 237 - 267] Evaluates nonlinear expressions at given values with variables involving negative rational numbers
![Screenshot of Exponential Growth and Decay](/Assets/img/blank.gif)
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.3.1.11: [RIT 239 - 253] Generates equivalent nonlinear expressions by combining like terms
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
6.3.1.12: [RIT 240 - 240] Writes algebraic expressions from a mathematical description of its component parts, including sum, product, quotient, term, and coefficient
![Screenshot of Using Algebraic Expressions](/Assets/img/blank.gif)
Using Algebraic Expressions
Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview
6.3.1.13: [RIT 242 - 242] Interprets the variable in a linear expression within the context of a real-world relationship
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.3.1.15: [RIT 244 - 244] Determines the number of terms in a polynomial
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
6.3.1.16: [RIT 244 - 273] Simplifies rational expressions
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
6.3.1.17: [RIT 245 - 248] Uses algebra tiles to model polynomials
![Screenshot of Addition of Polynomials](/Assets/img/blank.gif)
Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
6.3.1.19: [RIT 254 - 269] Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.3.1.20: [RIT 256 - 256] Interprets the constant in a quadratic expression within the context of a real-world relationship
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.3.1.21: [RIT 263 - 263] Writes linear expressions in two variables to represent real-world or mathematical contexts
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.3.1.22: [RIT 265 - 274] Writes quadratic expressions in one variable to represent real-world or mathematical contexts
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.3.1.23: [RIT 271 - 271] Writes rational expressions in one variable to represent real-world or mathematical contexts
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
6.3.2: Numerical Expressions
6.3.2.1: [RIT 211 - 247] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers
![Screenshot of Order of Operations](/Assets/img/blank.gif)
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
6.3.2.2: [RIT 215 - 234] Represents real-world problems involving the addition and subtraction of integers with numerical expressions
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
6.3.2.4: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.3.2.5: [RIT 218 - 255] Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers
![Screenshot of Equivalent Algebraic Expressions II](/Assets/img/blank.gif)
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
6.3.2.6: [RIT 220 - 240] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving both positive and negative rational numbers
![Screenshot of Order of Operations](/Assets/img/blank.gif)
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
6.3.2.7: [RIT 221 - 243] Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
![Screenshot of Order of Operations](/Assets/img/blank.gif)
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
6.3.2.8: [RIT 223 - 232] Applies the order of operations, without grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
![Screenshot of Order of Operations](/Assets/img/blank.gif)
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
6.3.2.11: [RIT 238 - 238] Applies the order of operations, without grouping symbols or whole-number exponents, to simplify numerical expressions involving positive rational numbers
![Screenshot of Order of Operations](/Assets/img/blank.gif)
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
6.3.2.13: [RIT 243 - 270] Uses properties of radicals to simplify radical expressions
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
6.3.2.15: [RIT 246 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
6.3.2.16: [RIT 256 - 271] Simplifies numerical expressions involving sums and differences of radicals
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
6.3.2.18: [RIT 279 - 279] Simplifies numerical expressions containing radicals and rational exponents
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
6.3.3: Exponents
6.3.3.2: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.3.3.3: [RIT 225 - 232] Represents the value of digits in whole numbers using powers of 10 in exponential form
![Screenshot of Number Systems](/Assets/img/blank.gif)
Number Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview
6.3.3.4: [RIT 236 - 267] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.3.3.6: [RIT 246 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
6.3.3.9: [RIT 279 - 279] Simplifies numerical expressions containing radicals and rational exponents
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
6.3.5: Radicals
6.3.5.1: [RIT 243 - 270] Uses properties of radicals to simplify radical expressions
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
6.3.5.2: [RIT 256 - 271] Simplifies numerical expressions involving sums and differences of radicals
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
6.3.5.3: [RIT 279 - 279] Simplifies numerical expressions containing radicals and rational exponents
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
6.4: Operations with Algebraic Expressions
6.4.1: Algebraic Expressions
6.4.1.1: [RIT 233 - 257] Adds and subtracts polynomials
![Screenshot of Addition and Subtraction of Functions](/Assets/img/blank.gif)
Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Addition of Polynomials](/Assets/img/blank.gif)
Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
6.4.1.2: [RIT 237 - 260] Multiplies two binomial expressions
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
6.4.1.3: [RIT 238 - 260] Multiplies a polynomial by a monomial
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
6.4.1.5: [RIT 246 - 257] Factors polynomials using a difference of squares
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
6.4.1.6: [RIT 247 - 261] Factors quadratic trinomials
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
6.4.1.7: [RIT 248 - 257] Multiplies monomials
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.4.1.11: [RIT 254 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
6.4.1.13: [RIT 256 - 267] Multiplies polynomials
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.4.1.14: [RIT 260 - 260] Writes a rational expression as a sum of a polynomial and a proper rational expression
![Screenshot of Dividing Polynomials Using Synthetic Division](/Assets/img/blank.gif)
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
6.4.1.16: [RIT 263 - 267] Squares binomial expressions
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.4.2: Exponents
6.4.2.1: [RIT 254 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
6.5: Linear Equations
6.5.1: Number Sentences/Equations/Equivalence
6.5.1.1: [RIT 173 - 245] Solves one-step linear equations with positive rational numbers
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
6.5.1.2: [RIT 198 - 217] Determines unknown parts in multi-step equations with whole numbers and parentheses
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
6.5.1.3: [RIT 201 - 239] Solves one-step linear equations with negative rational numbers
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
6.5.1.4: [RIT 210 - 242] Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Using Algebraic Equations](/Assets/img/blank.gif)
Using Algebraic Equations
Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview
6.5.1.5: [RIT 218 - 240] Determines the number of solutions of a linear equation in one variable given the corresponding equation in the form x=a, x=x, or a=b
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
6.5.1.6: [RIT 220 - 248] Solves two-step linear equations with positive rational numbers
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
6.5.1.7: [RIT 222 - 242] Evaluates formulas or linear equations at given values for the variables
![Screenshot of Area of Parallelograms](/Assets/img/blank.gif)
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
![Screenshot of Distance Formula](/Assets/img/blank.gif)
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
![Screenshot of Equivalent Algebraic Expressions I](/Assets/img/blank.gif)
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
6.5.1.8: [RIT 226 - 262] Solves multi-step linear equations with positive and negative rational numbers
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
6.5.1.9: [RIT 226 - 247] Solves two-step linear equations with negative rational numbers
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
6.5.1.10: [RIT 231 - 287] Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
6.5.1.11: [RIT 239 - 239] Applies the multiplicative property of equality when solving an equation
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.5.1.12: [RIT 239 - 240] Writes a two-step linear equation in one variable to represent a real-world or mathematical context
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Using Algebraic Equations](/Assets/img/blank.gif)
Using Algebraic Equations
Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview
6.5.1.13: [RIT 240 - 240] Writes the equation of a vertical line given a graph
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.5.1.14: [RIT 241 - 247] Applies the simple interest formula to solve for the interest rate, principal, or time invested
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
6.5.1.15: [RIT 242 - 258] Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
6.5.1.16: [RIT 243 - 274] Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.5.1.17: [RIT 247 - 265] Solves literal equations for linear variables
![Screenshot of Solving Formulas for any Variable](/Assets/img/blank.gif)
Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.5.1.18: [RIT 250 - 250] Understands the slope of a vertical line is undefined
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
6.5.1.19: [RIT 265 - 290] Justifies the steps in solving a linear equation
![Screenshot of Modeling One-Step Equations](/Assets/img/blank.gif)
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.6: Linear Inequalities
6.6.1: Inequalities
6.6.1.1: [RIT 190 - 262] Determines whether a linear equation or inequality is true for a given value of the variable
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.2: [RIT 215 - 243] Identifies an ordered pair that is a solution to a two-variable linear inequality
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
6.6.1.3: [RIT 223 - 228] Writes a linear inequality in two variables to represent a real-world or mathematical context
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
6.6.1.4: [RIT 227 - 249] Writes a one-step linear inequality in one variable to represent a real-world or mathematical context
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.5: [RIT 228 - 243] Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.6: [RIT 229 - 261] Solves two-step linear inequalities
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
6.6.1.7: [RIT 229 - 229] Solves one-step linear inequalities with positive rational numbers
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.9: [RIT 231 - 260] Writes a compound inequality to represent a real-world or mathematical context
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
6.6.1.10: [RIT 234 - 245] Writes an inequality in the form x > c or x
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.11: [RIT 236 - 253] Solves one-step linear inequalities with negative rational numbers
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.12: [RIT 236 - 246] Writes and solves a one-step linear inequality in one variable involving a real-world or mathematical context
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.13: [RIT 238 - 244] Writes an inequality in the form x > c or x
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.14: [RIT 241 - 246] Represents the solutions of a one-step linear inequality on a number line
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.15: [RIT 241 - 250] Represents the solutions of a compound linear inequality on a number line
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
6.6.1.16: [RIT 243 - 243] Represents an inequality in the form x > c or x
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
6.6.1.17: [RIT 243 - 262] Solves multi-step linear inequalities
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
6.6.1.18: [RIT 243 - 243] Writes and solves a two-step linear inequality in one variable involving a real-world or mathematical context
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
6.6.1.19: [RIT 244 - 271] Represents the solutions of an absolute value inequality on a number line
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
6.6.1.20: [RIT 244 - 254] Represents the solutions of a two-step linear inequality on a number line
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
6.6.1.22: [RIT 248 - 253] Determines whether an absolute value equation or inequality is true for a given value of the variable
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
6.6.1.23: [RIT 252 - 252] Writes a linear inequality to represent a region on the coordinate plane
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
6.6.1.24: [RIT 255 - 255] Represents a compound inequality on a number line given a real-world or mathematical context
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
6.6.1.25: [RIT 257 - 266] Solves compound linear inequalities
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
6.6.1.26: [RIT 259 - 264] Represents the solutions of a two-variable linear inequality on the coordinate plane
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
6.6.1.27: [RIT 260 - 275] Solves absolute value inequalities
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
6.6.1.28: [RIT 260 - 264] Represents the solutions of a multistep linear inequality on a number line
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
6.6.1.29: [RIT 270 - 275] Writes an absolute value inequality to represent a real-world or mathematical context
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
6.7: Systems of Linear Equations and Inequalities
6.7.1: System of Equations/Inequalities
6.7.1.1: [RIT 195 - 204] Solves a system of linear equations involving a real-world context, given a table
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.2: [RIT 215 - 259] Writes and solves a system of linear equations involving a real-world or mathematical context
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.3: [RIT 217 - 238] Solves a system of linear equations graphically
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.4: [RIT 222 - 254] Writes a system of linear equations to represent a real-world or mathematical context
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.5: [RIT 236 - 261] Solves a system of linear equations algebraically
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.6: [RIT 238 - 257] Identifies an ordered pair that is a solution to a system of linear inequalities
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
6.7.1.7: [RIT 240 - 253] Writes a system of linear inequalities to represent a real-world or mathematical context
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
6.7.1.8: [RIT 240 - 240] Solves a system of linear inequalities
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
6.7.1.9: [RIT 250 - 257] Shows the steps to solve a system of linear equations using linear combinations
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.10: [RIT 252 - 274] Solves a system of linear equations given a table
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.11: [RIT 253 - 261] Shows the steps to solve a system of linear equations using the substitution method
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.12: [RIT 259 - 259] Graphs a system of linear equations
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.13: [RIT 259 - 261] Writes a system of linear equations given a graph
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.14: [RIT 260 - 262] Graphs a system of linear inequalities
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
6.7.1.15: [RIT 262 - 262] Writes a system of linear inequalities given a graph
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
6.7.1.16: [RIT 263 - 277] Determines the number of solutions to a system of linear equations
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
6.7.1.19: [RIT 283 - 283] Solves real-world problems involving rates and distances that lead to a system of linear equations
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
6.7.1.20: [RIT 286 - 286] Solves a system of linear equations using matrices
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
6.8: Non-Linear Equations
6.8.1: Number Sentences/Equations/Equivalence
6.8.1.2: [RIT 221 - 275] Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.8.1.3: [RIT 226 - 265] Solves absolute value equations
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
6.8.1.5: [RIT 230 - 262] Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.8.1.7: [RIT 240 - 267] Solves radical equations that lead to linear equations
![Screenshot of Radical Functions](/Assets/img/blank.gif)
Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
6.8.1.9: [RIT 248 - 279] Writes a quadratic equation in one variable to represent a real-world or mathematical context
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.8.1.11: [RIT 254 - 264] Determines the nature of the solutions of a quadratic equation
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
6.8.1.12: [RIT 257 - 257] Solves polynomial equations
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
6.8.1.14: [RIT 264 - 264] Writes an absolute value equation in one variable to represent a real-world or mathematical context
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
6.8.1.17: [RIT 271 - 297] Solves literal equations for nonlinear variables
![Screenshot of Distance Formula](/Assets/img/blank.gif)
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
6.8.1.18: [RIT 278 - 278] Understands the relationship between the discriminant and the nature of solutions
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
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Start teaching with 20-40 Free Gizmos. See the full list.
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Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
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Free Gizmos change each semester. The new collection will be available January 1 and July 1.
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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