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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

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

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

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

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

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

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

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

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

Integers, Opposites, and Absolute Values

1.1.6.5: [RIT 207 - 214] Justifies a comparison of two rational numbers using a number line

Rational Numbers, Opposites, and Absolute Values

1.1.6.6: [RIT 207 - 211] Compares two rational numbers shown on a number line

Rational Numbers, Opposites, and Absolute Values

1.1.6.7: [RIT 209 - 239] Compares integers given the meaning of zero within a real-world situation

Integers, Opposites, and Absolute Values

1.1.6.8: [RIT 211 - 211] Compares integers

Integers, Opposites, and Absolute Values

1.1.6.9: [RIT 213 - 230] Compares two rational numbers using a number line

Rational Numbers, Opposites, and Absolute Values

1.1.6.10: [RIT 218 - 255] Orders positive and negative rational numbers

Rational Numbers, Opposites, and Absolute Values

1.1.6.11: [RIT 224 - 230] Compares positive rational numbers represented in multiple forms

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

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

Integers, Opposites, and Absolute Values

1.1.7.2: [RIT 200 - 218] Locates integers on a number line

Integers, Opposites, and Absolute Values

1.1.7.3: [RIT 204 - 204] Locates positive and negative rational numbers on a number line

Rational Numbers, Opposites, and Absolute Values

1.1.7.4: [RIT 214 - 232] Locates negative rational numbers on a number line

Rational Numbers, Opposites, and Absolute Values

1.1.7.5: [RIT 233 - 233] Locates the opposite of a negative rational number on a number line

Rational Numbers, Opposites, and Absolute Values

1.1.7.6: [RIT 237 - 237] Identifies values that are a given distance from a point on a number line

Integers, Opposites, and Absolute Values

1.1.8: Scientific Notation

1.1.8.1: [RIT 224 - 230] Converts a number from scientific notation to standard form

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

Number Systems

Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview

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

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

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

Integers, Opposites, and Absolute Values

1.2.1.5: [RIT 228 - 242] Understands the additive inverse property

Integers, Opposites, and Absolute Values

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 â€“ a foundational skill for solving algebraic equations. 5 Minute Preview

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

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 â€“ a foundational skill for solving algebraic equations. 5 Minute Preview

1.2.1.7: [RIT 243 - 243] Understands the multiplicative inverse property

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 â€“ a foundational skill for solving algebraic equations. 5 Minute Preview

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

Integers, Opposites, and Absolute Values

1.2.1.9: [RIT 245 - 245] Understands that the product of two negative numbers is positive

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

Solving Algebraic Equations I

1.2.1.11: [RIT 262 - 262] Defines properties of equality

Solving Algebraic Equations II

### 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

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

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

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

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

Rational Numbers, Opposites, and Absolute Values

2.1.4.3: [RIT 225 - 253] Multiplies rational numbers, including combinations of positive or negative fractions, decimals, and integers

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

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

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

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

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

Unit Conversions 2 - Scientific Notation and Significant Digits

2.1.7: Radicals

2.1.7.1: [RIT 228 - 260] Evaluates the square root of a perfect square

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

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

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

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

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

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

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

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

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

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

Unit Conversions 2 - Scientific Notation and Significant Digits

2.2.1.2: [RIT 224 - 257] Converts units of speed

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

Unit Conversions 2 - Scientific Notation and Significant Digits

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

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

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

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

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

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

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

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

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

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

Road Trip (Problem Solving)

2.2.2.8: [RIT 207 - 212] Identifies ratios between two quantities not from the same whole

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

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

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

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

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

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

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

Part-to-part and Part-to-whole Ratios

2.2.2.13: [RIT 214 - 249] Determines equivalent ratios

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

2.2.2.16: [RIT 216 - 253] Solves for a missing value in a proportion by taking a cross product

Percents and Proportions

2.2.2.17: [RIT 216 - 263] Uses a given unit rate to solve a multi-step real-world problem

Road Trip (Problem Solving)

2.2.2.18: [RIT 217 - 247] Compares unit rates within a real-world context

Road Trip (Problem Solving)

2.2.2.19: [RIT 219 - 239] Identifies the part-to-part ratio between two quantities

Part-to-part and Part-to-whole Ratios

2.2.2.20: [RIT 219 - 236] Uses ratios of decimals to calculate unit rates

Road Trip (Problem Solving)

2.2.2.21: [RIT 219 - 244] Calculates the percent one number is of another number

Percents and Proportions

2.2.2.22: [RIT 219 - 257] Converts unit rates to solve real-world problems

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

Unit Conversions 2 - Scientific Notation and Significant Digits

2.2.2.23: [RIT 220 - 231] Converts between percents and ratios expressed verbally or in the form a:b

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

2.2.2.24: [RIT 220 - 237] Calculates the whole when given a part and the percent

Percents and Proportions

2.2.2.26: [RIT 225 - 234] Determines the whole in a real-world percent problem given the part and the percent

Percents and Proportions

2.2.2.27: [RIT 226 - 252] Writes a proportion to solve a real-world problem

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

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

Part-to-part and Part-to-whole Ratios

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

Percents, Fractions, and Decimals

2.2.2.29: [RIT 235 - 256] Calculates the percent one number is of another number for percents greater than 100%

Percent of Change

2.2.2.30: [RIT 235 - 258] Solves real-world problems involving percent or fractional increase

Percent of Change

2.2.2.32: [RIT 242 - 256] Calculates simple interest

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

Percent of Change

Percents and Proportions

2.2.2.34: [RIT 247 - 255] Compares ratios within a real-world context

Part-to-part and Part-to-whole Ratios

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

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

Percents, Fractions, and Decimals

2.2.3.2: [RIT 220 - 231] Converts between percents and ratios expressed verbally or in the form a:b

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

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

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

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

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

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

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

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

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,Â given the formula

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

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

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

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

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

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

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

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

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,Â given the formula

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

Area of Parallelograms

Area of Triangles

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

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

Area of Triangles

3.2.1.13: [RIT 240 - 269] Determines the ratio between areas of scaled figures

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Surface and Lateral Areas of Prisms and Cylinders

3.2.3.9: [RIT 255 - 263] Describes the effect on surface area when dimensions of a rectangular prism are changed

Surface and Lateral Areas of Prisms and Cylinders

3.2.3.11: [RIT 260 - 263] Solves problems involving surface areas of prisms within a real-world or mathematical context

Surface and Lateral Areas of Prisms and Cylinders

3.2.3.12: [RIT 266 - 269] Determines the surface area of cylinders, formula not provided

Surface and Lateral Areas of Prisms and Cylinders

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

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

3.3.2: Volume

3.3.2.1: [RIT 227 - 268] Determines the volume of pyramids, given the formula

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

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

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

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

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

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

Prisms and Cylinders

3.3.2.12: [RIT 259 - 278] Solves problems involving volumes of cylinders within a real-world or mathematical context

Prisms and Cylinders

3.3.2.15: [RIT 266 - 266] Determines the volume of figures composed of rectangular and triangular prisms

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

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

Prisms and Cylinders

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

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

Prisms and Cylinders

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

Pyramids and Cones

3.3.2.19: [RIT 270 - 270] Determines the volume of spheres, formula not provided

Measuring Volume

3.3.2.20: [RIT 273 - 273] Determines the volume of cones, formula not provided

Pyramids and Cones

3.3.2.21: [RIT 276 - 276] Solves problems involving volumes of cones within a real-world or mathematical context

Pyramids and Cones

### 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

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

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

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

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

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

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

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

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

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

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

Constructing Parallel and Perpendicular Lines

4.2: Polygons and Circles

4.2.1: Circles

4.2.1.1: [RIT 208 - 208] Knows the number of degrees in a circle

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 beltâ€™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

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

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

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

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

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

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

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

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

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

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

Chords and Arcs

4.2.1.16: [RIT 285 - 285] Justifies relationships between the arc length, radius, and central angle measured in radians

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 beltâ€™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

Inscribed Angles

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.

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.

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

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

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

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

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

Triangle Angle Sum

4.2.3.5: [RIT 228 - 250] Applies properties of isosceles triangles to determine the measure of an unknown angle

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

Investigating Angle Theorems

Triangle Angle Sum

4.2.3.9: [RIT 238 - 246] Solves multi-step problems by applying the Triangle Angle-Sum Theorem

Isosceles and Equilateral Triangles

Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Triangle Angle Sum

4.2.3.10: [RIT 240 - 240] Determines the number of diagonals that can be drawn from one vertex in a polygon

Polygon Angle Sum

4.2.3.11: [RIT 241 - 276] Applies the Triangle Inequality Theorem

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

Triangle Angle Sum

4.2.3.13: [RIT 256 - 258] Applies the formula for the measure of each exterior angle of a regular polygon

Polygon Angle Sum

4.2.3.15: [RIT 269 - 269] Applies the formula for the measure of each interior angle of a regular polygon

Polygon Angle Sum

4.2.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

4.2.4.1: [RIT 252 - 275] Proves theorems involving the properties of parallelograms

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

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

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 beltâ€™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

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

4.3.2: Spatial Concepts and Symmetry

4.3.2.1: [RIT 184 - 229] Identifies and creates nets for prisms

Surface and Lateral Areas of Prisms and Cylinders

4.3.2.2: [RIT 186 - 202] Identifies and creates nets for pyramids

Surface and Lateral Areas of Pyramids and Cones

4.3.2.3: [RIT 211 - 269] Identifies the cross-sections of 3-D shapes

Pyramids and Cones

4.4: Congruence and Similarity

4.4.1: Congruence

4.4.1.1: [RIT 153 - 184] Identifies congruent shapes, given informal language

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

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

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

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

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

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

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

Proving Triangles Congruent

4.4.1.12: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

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

Proving Triangles Congruent

4.4.2: Similarity

4.4.2.1: [RIT 180 - 181] Identifies similar figures

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

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

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Perimeters and Areas of Similar Figures

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

Similar Figures

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

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Perimeters and Areas of Similar Figures

Similar Figures

4.4.2.5: [RIT 213 - 226] Identifies corresponding sides and angles in similar figures

Similar Figures

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

Similar Figures

4.4.2.7: [RIT 220 - 220] Knows the definition of similarity

Similar Figures

Similarity in Right Triangles

4.4.2.8: [RIT 223 - 239] Determines scale factors in problems involving scale drawings of geometric figures

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Perimeters and Areas of Similar Figures

Similar Figures

4.4.2.10: [RIT 224 - 224] Determines the ratio between perimeters of similar figures

Perimeters and Areas of Similar Figures

4.4.2.11: [RIT 225 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

4.4.2.12: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

Proving Triangles Congruent

4.4.2.13: [RIT 232 - 257] Applies properties of similar figures to determine a perimeter

Perimeters and Areas of Similar Figures

4.4.2.15: [RIT 235 - 235] Applies properties of similar figures to determine an area

Perimeters and Areas of Similar Figures

4.4.2.16: [RIT 239 - 239] Identifies the proportion of corresponding sides of similar figures

Similarity in Right Triangles

4.4.2.17: [RIT 244 - 263] Applies similarity postulates to solve for missing lengths and angles

Similarity in Right Triangles

4.4.2.18: [RIT 245 - 256] Identifies similar triangles using AA

Proving Triangles Congruent

Similarity in Right Triangles

4.4.2.19: [RIT 247 - 247] Applies similarity postulates to identify corresponding sides and angles

Similarity in Right Triangles

4.4.2.22: [RIT 260 - 279] Applies the geometric mean to solve for missing lengths and angles in triangles

Similarity in Right Triangles

4.4.2.23: [RIT 261 - 271] Identifies the similarity postulate that proves two triangles are similar

Proving Triangles Congruent

4.4.2.26: [RIT 285 - 286] Determines the ratio between areas of similar figures

Perimeters and Areas of Similar Figures

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

Similarity in Right Triangles

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

Proving Triangles Congruent

4.4.3.2: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent

Congruence in Right Triangles

Proving Triangles Congruent

4.4.3.3: [RIT 261 - 271] Identifies the similarity postulate that proves two triangles are similar

Proving Triangles Congruent

4.4.3.4: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

Congruence in Right Triangles

Proving Triangles Congruent

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

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

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

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

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

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

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

Pythagorean Theorem

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

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

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

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

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

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

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

Sine, Cosine, and Tangent Ratios

4.5.2.6: [RIT 263 - 273] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems

Sine, Cosine, and Tangent Ratios

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

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

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

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

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

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

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

Pythagorean Theorem

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

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

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

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

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