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- Growth: Grades 6+ Math - Algebraic Concepts (2017)

# Growth: Grades 6+ Math - Algebraic Concepts (2017)

### 6: Algebraic Concepts

6.1: Patterns, Function Tables, and the Coordinate Plane

6.1.1: Coordinate Geometry

6.1.1.1: [RIT 187 - 208] Interprets points with whole number coordinates in the first quadrant within the given context

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

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

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

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

6.1.1.2: [RIT 198 - 212] Determines the coordinates of points in the first quadrant of a coordinate plane

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

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

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

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

6.1.1.3: [RIT 202 - 210] Plots the coordinates of points in the first quadrant of a coordinate plane

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

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

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

6.1.1.4: [RIT 206 - 236] Plots points in all four quadrants of a coordinate plane

Points in the Coordinate Plane

6.1.1.5: [RIT 216 - 216] Determines the quadrant for a given ordered pair

Points in the Coordinate Plane

6.1.1.6: [RIT 228 - 228] Plots points to represent solutions to real-world and mathematical problems

Points in the Coordinate Plane

6.1.2: Patterns/Sequences/Series

6.1.2.1: [RIT 165 - 196] Determines the single-step rule, and extends or finds a missing term for number patterns involving additionÂ

Finding Patterns

Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview

6.1.2.2: [RIT 167 - 197] Determines the single-step rule for number patterns involving addition or subtractionÂ

Finding Patterns

Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview

6.1.2.3: [RIT 168 - 210] Determines the rule, and extends or finds a missing term for repeating shape patterns

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

6.1.2.4: [RIT 175 - 201] Determines missing values in a table representing a proportional relationship, given the function rule

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

Function Machines 2 (Functions, Tables, and Graphs)

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

Points, Lines, and Equations

6.1.2.5: [RIT 176 - 188] Determines the single-step rule, and extends or finds a missing term for number patterns involving models Â

Finding Patterns

Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview

6.1.2.6: [RIT 179 - 179] Creates or extends repeating shape patterns, given the rule

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

6.1.2.7: [RIT 183 - 230] Analyzes and describes patterns without stating the ruleÂ

Finding Patterns

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

6.1.2.8: [RIT 183 - 220] Determines missing values in a table representing a proportional relationship, function rule not given

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

6.1.2.9: [RIT 185 - 206] Determines the single-step rule, and extends or finds a missing term for number patterns involving subtraction Â

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

6.1.2.10: [RIT 187 - 233] Determines missing values in a function table representing a nonproportional relationship, given the rule

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Points, Lines, and Equations

6.1.2.11: [RIT 191 - 195] Determines the two-step rule for number patterns involving multiple operationsÂ

Function Machines 3 (Functions and Problem Solving)

6.1.2.12: [RIT 191 - 207] Creates or extends number patterns, given the rule

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

6.1.2.14: [RIT 193 - 217] Determines the rule, and extends or finds a missing term for growing/shrinking shape patterns

Finding Patterns

6.1.2.17: [RIT 195 - 233] Determines the two-step rule, and extends or finds a missing term for number patterns involving multiple operations

Function Machines 3 (Functions and Problem Solving)

6.1.2.18: [RIT 197 - 227] Determines the rule for growing/shrinking shape patterns

Finding Patterns

6.1.2.20: [RIT 201 - 201] Determines the single-step rule for number patterns involving multiplication or divisionÂ

Function Machines 1 (Functions and Tables)

6.1.2.21: [RIT 202 - 218] Determines the rule for a given function table representing a proportional relationship

Function Machines 1 (Functions and Tables)

6.1.2.23: [RIT 205 - 219] Determines the single-step rule, and extends or finds a missing term for number patterns involving multiplication or divisionÂ

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

6.1.2.24: [RIT 205 - 226] Determines the rule for a given function table representing a nonproportional relationship

Function Machines 1 (Functions and Tables)

6.1.2.26: [RIT 210 - 228] Identifies a function table that matches a given rule

Points, Lines, and Equations

6.1.2.28: [RIT 215 - 218] Determines the rule, and extends or finds a missing term given descriptions of number patterns within a real-world context

Function Machines 1 (Functions and Tables)

Function Machines 3 (Functions and Problem Solving)

6.1.2.30: [RIT 223 - 258] Determines the value of a term in an arithmetic sequence given a contextual situation

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

6.1.2.31: [RIT 227 - 232] Determines the single-step rule, and extends or finds a missing term for number patterns involving fractionsÂ

Function Machines 1 (Functions and Tables)

6.1.2.32: [RIT 229 - 266] Determines the value of a term in a geometric sequence given a contextual situation

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

6.1.2.34: [RIT 232 - 238] Recognizes arithmetic sequences

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

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

6.1.2.35: [RIT 235 - 256] Determines the rule, and extends or finds a missing term in a Fibonacci sequence

Arithmetic Sequences

6.1.2.38: [RIT 243 - 275] Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence

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

6.1.2.39: [RIT 252 - 252] Determines the rule, and extends or finds a missing term for number patterns which increase or decrease by a nonconstant amount, within a real-world context

Arithmetic Sequences

6.1.2.40: [RIT 253 - 285] Determines the value of a term in a geometric sequence defined by a list

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

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

6.1.2.41: [RIT 256 - 256] Determines the common ratio in a geometric sequence

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

6.1.2.43: [RIT 260 - 271] Writes an expression or formula for the nth term of a geometric sequence given a number sequence

Arithmetic and Geometric Sequences

Geometric Sequences

6.2: Expressions

6.2.1: Algebraic Expressions

6.2.1.1: [RIT 212 - 240] Writes linear expressions in one variable to represent real-world or mathematical contexts

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

6.2.1.3: [RIT 213 - 246] Evaluates linear expressions at given values with variables involving positive rational numbers

Equivalent Algebraic Expressions I

Grumpyâ€™s Restaurant is now hiring! As a new chef at this underwater bistro, youâ€™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

6.2.1.4: [RIT 216 - 247] Translates between verbal and algebraic expressions

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

6.2.1.5: [RIT 220 - 248] Generates equivalent linear expressions by using the associative, commutative, or distributive property

Equivalent Algebraic Expressions I

Grumpyâ€™s Restaurant is now hiring! As a new chef at this underwater bistro, youâ€™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

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

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 intoâ€¦ 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

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 â€“ 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

6.2.1.8: [RIT 226 - 249] Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms

Equivalent Algebraic Expressions I

Grumpyâ€™s Restaurant is now hiring! As a new chef at this underwater bistro, youâ€™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

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

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 intoâ€¦ 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

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 â€“ 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

6.2.1.9: [RIT 227 - 242] Generates equivalent linear expressions by combining like terms

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 â€“ 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

6.2.1.10: [RIT 232 - 268] Adds and subtracts polynomials

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

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

6.2.1.11: [RIT 232 - 261] Multiplies a polynomial by a monomial

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

6.2.1.12: [RIT 233 - 233] Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient

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 intoâ€¦ 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

Simplifying Algebraic Expressions II

6.2.1.13: [RIT 236 - 263] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

Dividing Exponential Expressions

Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

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

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

6.2.1.14: [RIT 237 - 260] Multiplies two binomial expressions

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

Modeling the Factorization of *x*^{2}+*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

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

6.2.1.15: [RIT 237 - 262] Evaluates nonlinear expressions at given values with variables involving negative rational numbers

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

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

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

6.2.1.16: [RIT 238 - 252] Factors polynomials using a difference of squares

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

Modeling the Factorization of *ax*^{2}+*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

Modeling the Factorization of *x*^{2}+*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

6.2.1.17: [RIT 239 - 261] Factors quadratic trinomials

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

Modeling the Factorization of *ax*^{2}+*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

Modeling the Factorization of *x*^{2}+*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

6.2.1.18: [RIT 239 - 239] Generates equivalent nonlinear expressions by combining like terms

Simplifying Algebraic Expressions II

6.2.1.19: [RIT 239 - 257] Multiplies monomials

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

6.2.1.20: [RIT 240 - 240] Writes algebraic expressions from a mathematical description of its component parts, including sum, product, quotient, term, and coefficient

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

6.2.1.21: [RIT 242 - 242] Interprets the variable in a linear expression within the context of a real-world relationship

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

6.2.1.23: [RIT 244 - 244] Determines the number of terms in a polynomial

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

6.2.1.24: [RIT 244 - 273] Simplifies rational expressions

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

6.2.1.25: [RIT 245 - 248] Uses algebra tiles to model polynomials

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

Modeling the Factorization of *ax*^{2}+*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

Modeling the Factorization of *x*^{2}+*bx*+*c*

6.2.1.28: [RIT 251 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero

Dividing Exponential Expressions

Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

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

6.2.1.31: [RIT 254 - 269] Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

6.2.1.33: [RIT 256 - 263] Multiplies polynomials

Factoring Special Products

6.2.1.34: [RIT 256 - 256] Interprets the constant in a quadratic expression within the context of a real-world relationship

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

6.2.1.35: [RIT 260 - 260] Writes a rational expression as a sum of a polynomial and a proper rational expression

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

6.2.1.37: [RIT 263 - 263] Writes linear expressions in two variables to represent real-world or mathematical contexts

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

6.2.1.39: [RIT 265 - 274] Writes quadratic expressions in one variable to represent real-world or mathematical contexts

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

Quadratics in Polynomial Form

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

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

6.2.1.40: [RIT 265 - 270] Squares binomial expressions

Factoring Special Products

6.2.1.43: [RIT 271 - 271] Writes rational expressions in one variable to represent real-world or mathematical contexts

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

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

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: Numerical Expressions

6.2.2.1: [RIT 173 - 199] Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses

Equivalent Algebraic Expressions I

6.2.2.2: [RIT 196 - 235] Evaluates numerical expressions involving multiple operations with whole numbers and parentheses

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview

6.2.2.4: [RIT 211 - 230] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview

6.2.2.5: [RIT 215 - 215] Represents real-world problems involving the addition and subtraction of integers with numerical expressions

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

6.2.2.6: [RIT 217 - 240] Evaluates numerical expressions involving multiple operations with whole numbers, no parenthesis

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview

6.2.2.8: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only

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

Multiplying Exponential Expressions

6.2.2.9: [RIT 218 - 218] Evaluates numerical expressions involving addition and subtraction with whole numbers, no parentheses

Adding and Subtracting Integers

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

6.2.2.10: [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

Order of Operations

6.2.2.11: [RIT 223 - 243] Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers

Order of Operations

6.2.2.12: [RIT 224 - 245] Applies the order of operations, without grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers

Order of Operations

6.2.2.14: [RIT 229 - 255] Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers

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

6.2.2.17: [RIT 237 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero

Exponents and Power Rules

6.2.2.18: [RIT 238 - 243] Applies the order of operations, without grouping symbols or whole-number exponents, to simplify numerical expressions involving positive rational numbers

Order of Operations

6.2.2.20: [RIT 257 - 257] Represents descriptions of exponential growth with numerical expressions

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

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

6.2.3: Exponents

6.2.3.1: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only

Exponents and Power Rules

Multiplying Exponential Expressions

6.2.3.2: [RIT 236 - 263] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

Dividing Exponential Expressions

Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

Exponents and Power Rules

Multiplying Exponential Expressions

6.2.3.3: [RIT 237 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero

Exponents and Power Rules

6.2.3.4: [RIT 251 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero

Dividing Exponential Expressions

Exponents and Power Rules

6.3: Equations and Inequalities

6.3.1: Inequalities

6.3.1.1: [RIT 216 - 234] Determines whether a linear equation or inequality is true for a given value of the variable

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

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.2: [RIT 221 - 243] Identifies an ordered pair that is a solution to a two-variable linear inequality

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

6.3.1.3: [RIT 227 - 249] Writes a one-step linear inequality in one variable to represent a real-world or mathematical context

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

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.4: [RIT 228 - 243] Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context

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

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.5: [RIT 229 - 229] Solves one-step linear inequalities with positive rational numbers

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.7: [RIT 231 - 260] Writes a compound inequality to represent a real-world or mathematical context

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

6.3.1.8: [RIT 232 - 232] Writes a quadratic inequality in one variable to represent a real-world or mathematical context

Quadratic Inequalities

Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview

6.3.1.9: [RIT 233 - 234] Writes a linear inequality in two variables to represent a real-world or mathematical context

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

6.3.1.10: [RIT 233 - 257] Solves two-step linear inequalities

Exploring Linear Inequalities in One Variable

6.3.1.11: [RIT 236 - 246] Writes and solves a one-step linear inequality in one variable involving a real-world or mathematical context

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.12: [RIT 236 - 253] Solves one-step linear inequalities with negative rational numbers

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.13: [RIT 238 - 243] Writes an inequality in the form x > c or x

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.14: [RIT 239 - 239] Writes a linear inequality to represent a region on the coordinate plane

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

6.3.1.16: [RIT 241 - 250] Represents the solutions of a compound linear inequality on a number line

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

6.3.1.17: [RIT 241 - 246] Represents the solutions of a one-step linear inequality on a number line

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.18: [RIT 243 - 243] Represents an inequality in the form x > c or x

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.19: [RIT 243 - 262] Solves multi-step linear inequalities

Exploring Linear Inequalities in One Variable

6.3.1.20: [RIT 244 - 251] Writes an inequality in the form x > c or x

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.1.21: [RIT 244 - 254] Represents the solutions of a two-step linear inequality on a number line

Exploring Linear Inequalities in One Variable

6.3.1.22: [RIT 244 - 271] Represents the solutions of an absolute value inequality on a number line

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

6.3.1.25: [RIT 248 - 253] Determines whether an absolute value equation or inequality is true for a given value of the variable

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

6.3.1.26: [RIT 255 - 255] Represents a compound inequality on a number line given a real-world or mathematical context

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

6.3.1.27: [RIT 257 - 266] Solves compound linear inequalities

Compound Inequalities

6.3.1.28: [RIT 259 - 264] Represents the solutions of a two-variable linear inequality on the coordinate plane

Linear Inequalities in Two Variables

6.3.1.29: [RIT 260 - 275] Solves absolute value inequalities

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

6.3.1.30: [RIT 260 - 264] Represents the solutions of a multistep linear inequality on a number line

Exploring Linear Inequalities in One Variable

6.3.1.31: [RIT 263 - 263] Solves quadratic inequalities

Quadratic Inequalities

Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview

6.3.1.33: [RIT 268 - 268] Represents the solutions of a two-variable quadratic inequality on the coordinate plane

Quadratic Inequalities

Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview

6.3.1.34: [RIT 270 - 275] Writes an absolute value inequality to represent a real-world or mathematical context

Absolute Value Equations and Inequalities

6.3.2: Number Sentences/Equations/Equivalence

6.3.2.1: [RIT 158 - 185] Determines unknown parts in addition equations with whole numbers, sums within 20

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 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

6.3.2.2: [RIT 167 - 199] Determines unknown parts in addition equations with whole numbers, sums within 100

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 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

6.3.2.3: [RIT 167 - 181] Determines start or change unknown in subtraction equations with whole numbers within 20

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview

6.3.2.4: [RIT 169 - 185] Determines start or change unknown in subtraction equations with whole numbers within 100

Number Line Frog Hop (Addition and Subtraction)

6.3.2.5: [RIT 173 - 245] Solves one-step linear equations with positive rational numbers

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

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

6.3.2.6: [RIT 174 - 210] Determines unknown factors in multiplication equations with whole numbers and products within 100

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

6.3.2.7: [RIT 176 - 200] Identifies equivalent whole-number addition or subtraction expressions

Equivalent Algebraic Expressions I

Number Line Frog Hop (Addition and Subtraction)

6.3.2.8: [RIT 182 - 199] Determines unknown parts in addition equations with whole numbers, sums greater than 100

Target Sum Card Game (Multi-digit Addition)

Play an addition card game! The goal is to create a sum that is as close as possible to the target sum. Students will deepen their understanding of place value as they get better at playing the game. Many game options allow students to vary the game for more practice. The game can be played with one or two players. 5 Minute Preview

6.3.2.9: [RIT 183 - 183] Identifies true one-step addition and subtraction equations involving whole numbers

Number Line Frog Hop (Addition and Subtraction)

6.3.2.10: [RIT 186 - 186] Determines start or change unknown in addition equations with decimals

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

6.3.2.13: [RIT 194 - 228] Determines unknown parts in multi-step equations with whole numbers

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

Solving Algebraic Equations II

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview

6.3.2.18: [RIT 202 - 229] Solves problems involving equations represented on a balanced scale

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview

6.3.2.19: [RIT 203 - 214] Identifies trueÂ multi-step addition and subtraction equations with whole numbers

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

6.3.2.20: [RIT 204 - 204] Translates between verbal and algebraic equations

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

6.3.2.22: [RIT 206 - 239] Solves one-step linear equations with negative rational numbers

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

6.3.2.23: [RIT 211 - 217] Determines unknown parts in multi-step equations with whole numbers and parentheses

Solving Algebraic Equations II

6.3.2.25: [RIT 213 - 242] Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context

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

Solving Algebraic Equations II

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview

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

6.3.2.27: [RIT 216 - 248] Solves two-step linear equations with positive rational numbers

Solving Algebraic Equations II

6.3.2.28: [RIT 216 - 229] Writes a one-step linear equation in one variable to represent a real-world or mathematical context

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

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

6.3.2.29: [RIT 216 - 234] Determines whether a linear equation or inequality is true for a given value of the variable

Exploring Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

6.3.2.31: [RIT 219 - 219] Determines unknown parts in addition equations with fractions, like denominators

Solving Algebraic Equations II

6.3.2.32: [RIT 221 - 275] Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method

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

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

6.3.2.33: [RIT 224 - 248] Determines unknown factors in multiplication equations with fractions

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview

Solving Algebraic Equations II

6.3.2.34: [RIT 226 - 259] Solves multi-step linear equations with positive and negative rational numbers

Solving Algebraic Equations II

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

6.3.2.35: [RIT 226 - 247] Solves two-step linear equations with negative rational numbers

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

6.3.2.36: [RIT 226 - 265] Solves absolute value equations

Absolute Value Equations and Inequalities

6.3.2.38: [RIT 232 - 253] Determines unknown dividends or divisors in division equations with fractions

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview

6.3.2.39: [RIT 232 - 242] Evaluates formulas or linear equations at given values for the variables

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

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

Equivalent Algebraic Expressions I

6.3.2.40: [RIT 235 - 262] Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context

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

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

6.3.2.41: [RIT 236 - 253] Writes a multi-step linear equation in one variable to represent a real-world or mathematical context

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

6.3.2.42: [RIT 239 - 239] Applies the multiplicative property of equality when solving an equation

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

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

Solving Two-Step Equations

6.3.2.43: [RIT 239 - 240] Writes a two-step linear equation in one variable to represent a real-world or mathematical context

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

Solving Two-Step Equations

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

6.3.2.44: [RIT 240 - 267] Solves radical equations that lead to linear equations

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

6.3.2.45: [RIT 240 - 240] Writes the equation of a vertical line given a graph

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

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

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

6.3.2.47: [RIT 241 - 247] Applies the simple interest formula to solve for the interest rate, principal, or time invested

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

6.3.2.48: [RIT 242 - 274] Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

Solving Two-Step Equations

6.3.2.49: [RIT 243 - 264] Solves literal equations for linear variables

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

6.3.2.51: [RIT 245 - 245] Determines unknown parts in addition equations with fractions, unlike denominators

Fractions with Unlike Denominators

Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview

6.3.2.52: [RIT 246 - 266] Identifies an ordered pair that is a solution to a two-variable equation

Points, Lines, and Equations

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

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

6.3.2.53: [RIT 248 - 253] Determines whether an absolute value equation or inequality is true for a given value of the variable

Absolute Value Equations and Inequalities

6.3.2.54: [RIT 248 - 279] Writes a quadratic equation in one variable to represent a real-world or mathematical context

Quadratics in Factored Form

Quadratics in Polynomial Form

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

Roots of a Quadratic

6.3.2.55: [RIT 249 - 251] Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision

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

6.3.2.57: [RIT 250 - 250] Understands the slope of a vertical line is undefined

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

Slope-Intercept Form of a Line

Standard Form of a Line

6.3.2.59: [RIT 254 - 270] Solves quadratic equations with complex solutions

Roots of a Quadratic

6.3.2.60: [RIT 254 - 264] Determines the nature of the solutions of a quadratic equation

Roots of a Quadratic

6.3.2.61: [RIT 257 - 257] Solves polynomial equations

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

6.3.2.62: [RIT 257 - 297] Solves literal equations for nonlinear variables

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

6.3.2.63: [RIT 258 - 258] Writes an absolute value equation in one variable to represent a real-world or mathematical context

Absolute Value Equations and Inequalities

6.3.2.66: [RIT 268 - 268] Writes and solves an exponential equation in one variable involving a real-world or mathematical context

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

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

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

6.3.2.68: [RIT 276 - 276] Writes an exponential equation in one variable to represent a real-world or mathematical context

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

Exponential Growth and Decay

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

6.3.2.69: [RIT 278 - 278] Understands the relationship between the discriminant and the nature of solutions

Roots of a Quadratic

6.3.3: Decimals: Represent and Solve Word Problems

6.3.3.1: [RIT 200 - 200] Represents one-step word problems with expressions or equations and involving decimals with the same number of digits after the decimal point, including contexts involving money

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

Multiplying with Decimals

Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview

6.4: System of Equations and Inequalities

6.4.1: System of Equations/Inequalities

6.4.1.1: [RIT 195 - 204] Solves a system of linear equations involving a real-world context, given a table

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

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

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 *x*, *y*)

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

6.4.1.2: [RIT 215 - 256] Writes and solves a system of linear equations involving a real-world or mathematical context

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

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

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 *x*, *y*)

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

6.4.1.3: [RIT 217 - 238] Solves a system of linear equations graphically

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

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

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 *x*, *y*)

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

6.4.1.4: [RIT 230 - 254] Writes a system of linear equations to represent a real-world or mathematical context

Solving Linear Systems (Matrices and Special Solutions)

*x*, *y*) point to be a solution of an equation, or of a system of equations.
5 Minute Preview

Solving Linear Systems (Slope-Intercept Form)

*x*, *y*)

Solving Linear Systems (Standard Form)

*x*, *y*) values are solutions of an equation, or of a system of equations.
5 Minute Preview

6.4.1.5: [RIT 236 - 261] Solves a system of linear equations algebraically

Solving Linear Systems (Matrices and Special Solutions)

*x*, *y*) point to be a solution of an equation, or of a system of equations.
5 Minute Preview

Solving Linear Systems (Slope-Intercept Form)

*x*, *y*)

Solving Linear Systems (Standard Form)

*x*, *y*) values are solutions of an equation, or of a system of equations.
5 Minute Preview

6.4.1.6: [RIT 238 - 257] Identifies an ordered pair that is a solution to a system of linear inequalities

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

6.4.1.7: [RIT 240 - 240] Solves a system of linear inequalities

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

6.4.1.8: [RIT 240 - 253] Writes a system of linear inequalities to represent a real-world or mathematical context

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

6.4.1.10: [RIT 250 - 257] Shows the steps to solve a system of linear equations using linear combinations

Solving Linear Systems (Standard Form)

*x*, *y*) values are solutions of an equation, or of a system of equations.
5 Minute Preview

6.4.1.13: [RIT 251 - 262] Graphs a system of linear inequalities

Systems of Linear Inequalities (Slope-intercept form)

6.4.1.14: [RIT 252 - 274] Solves a system of linear equations given a table

Cat and Mouse (Modeling with Linear Systems)