IXL Skill Plan | Arkansas Mathematics Standards (adopted in 2023): Critical Algebra I

Arkansas Mathematics Standards (adopted in 2023): Critical Algebra I

Skills available for Arkansas Critical Algebra I standards

Standard

Expressions
Functions
Linear Functions, Equations, & Inequalities
Quadratic Functions & Equations
Exponential Functions & Equations
Statistics & Probability
Critical Algebra I Supporting Standards

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EX	Expressions
Polynomials, Roots, & Exponent Laws: Students simplify algebraic and numerical expressions.
A1.EX.1 Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations. Supporting standards: 6.ALG.5, 7.ALG.1, 8.NCC.3		Understand polynomials 1. Model polynomials with algebra tiles Addition and subtraction 2. Add and subtract polynomials using algebra tiles 3. Add and subtract polynomials 4. Add polynomials to find perimeter Multiplication 5. Multiply a polynomial by a monomial 6. Multiply two binomials using algebra tiles 7. Multiply two binomials 8. Multiply two binomials: special cases 9. Multiply polynomials using area models 10. Multiply polynomials
A1.EX.1 Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations. Supporting standards: 6.ALG.5, 7.ALG.1, 8.NCC.3
Understand polynomials 1. Model polynomials with algebra tiles Addition and subtraction 2. Add and subtract polynomials using algebra tiles 3. Add and subtract polynomials 4. Add polynomials to find perimeter Multiplication 5. Multiply a polynomial by a monomial 6. Multiply two binomials using algebra tiles 7. Multiply two binomials 8. Multiply two binomials: special cases 9. Multiply polynomials using area models 10. Multiply polynomials

A1.EX.2 Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates. Supporting standards: 6.NCC.11, 8.NCC.8		1. Simplify radical expressions 2. Add and subtract radical expressions 3. Simplify radical expressions using the distributive property 4. Simplify radicals with fractions 5. Multiply radicals
A1.EX.2 Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates. Supporting standards: 6.NCC.11, 8.NCC.8
1. Simplify radical expressions 2. Add and subtract radical expressions 3. Simplify radical expressions using the distributive property 4. Simplify radicals with fractions 5. Multiply radicals

A1.EX.3 Simplify algebraic expressions using the laws of exponents. Supporting standards: 6.ALG.3, 7.NCC.7, 7.NCC.8, 8.NCC.3		Integer exponents 1. Multiplication rule for exponents 2. Division rule for exponents 3. Power rule for exponents 4. Evaluate expressions using exponent rules 5. Identify equivalent exponential expressions I 6. Identify equivalent exponential expressions II Rational exponents 7. Evaluate integers raised to positive rational exponents 8. Evaluate integers raised to rational exponents 9. Multiplication with rational exponents 10. Division with rational exponents 11. Power rule with rational exponents 12. Simplify expressions involving rational exponents Polynomial expressions 13. Simplify variable expressions involving like terms and the distributive property 14. Simplify exponential expressions using the multiplication rule 15. Simplify exponential expressions using the division rule 16. Simplify exponential expressions using the multiplication and division rules 17. Simplify exponential expressions using the power rule 18. Factor out a monomial
A1.EX.3 Simplify algebraic expressions using the laws of exponents. Supporting standards: 6.ALG.3, 7.NCC.7, 7.NCC.8, 8.NCC.3
Integer exponents 1. Multiplication rule for exponents 2. Division rule for exponents 3. Power rule for exponents 4. Evaluate expressions using exponent rules 5. Identify equivalent exponential expressions I 6. Identify equivalent exponential expressions II Rational exponents 7. Evaluate integers raised to positive rational exponents 8. Evaluate integers raised to rational exponents 9. Multiplication with rational exponents 10. Division with rational exponents 11. Power rule with rational exponents 12. Simplify expressions involving rational exponents Polynomial expressions 13. Simplify variable expressions involving like terms and the distributive property 14. Simplify exponential expressions using the multiplication rule 15. Simplify exponential expressions using the division rule 16. Simplify exponential expressions using the multiplication and division rules 17. Simplify exponential expressions using the power rule 18. Factor out a monomial

A1.EX.4 Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context. Supporting standards: 5.CAR.13, 6.ALG.1, 6.ALG.2		1. Sort factors of variable expressions 2. Polynomial vocabulary 3. Interpret parts of quadratic expressions: word problems
A1.EX.4 Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context. Supporting standards: 5.CAR.13, 6.ALG.1, 6.ALG.2
1. Sort factors of variable expressions 2. Polynomial vocabulary 3. Interpret parts of quadratic expressions: word problems

Checkpoint opportunity		1. Checkpoint: Exponents and radicals
Checkpoint opportunity
1. Checkpoint: Exponents and radicals

FN	Functions
Domain & Range, Function Notation: Students understand the concept of a function, domain and range, and use function notation; students use function notation to solve problems.
A1.FN.1 Explain that a function assigns each element in the domain to exactly one element in the range. Supporting standards: 7.ALG.5, 8.FN.3		Independent and dependent variables 1. Identify independent and dependent variables Identify functions 2. Identify functions 3. Identify functions: vertical line test Domain and range of relations 4. Domain and range of relations
A1.FN.1 Explain that a function assigns each element in the domain to exactly one element in the range. Supporting standards: 7.ALG.5, 8.FN.3
Independent and dependent variables 1. Identify independent and dependent variables Identify functions 2. Identify functions 3. Identify functions: vertical line test Domain and range of relations 4. Domain and range of relations

A1.FN.2 Use function notation to represent functions, understanding that if f is a function and x is an element of its domain, then f(x) represents the output of f corresponding to the input x. Supporting standards: 7.ALG.5, 8.FN.3		1. Find values using function graphs 2. Complete a function table from a graph 3. Complete a function table from an equation
A1.FN.2 Use function notation to represent functions, understanding that if f is a function and x is an element of its domain, then f(x) represents the output of f corresponding to the input x. Supporting standards: 7.ALG.5, 8.FN.3
1. Find values using function graphs 2. Complete a function table from a graph 3. Complete a function table from an equation

A1.FN.3 Graph functions given in function notation, understanding that the graph contains the points (x, f(x)). Supporting standards: 5.CAR.12, 6.ALG.3, 6.ALG.6, 7.NCC.9		1. Complete a table and graph a linear function
A1.FN.3 Graph functions given in function notation, understanding that the graph contains the points (x, f(x)). Supporting standards: 5.CAR.12, 6.ALG.3, 6.ALG.6, 7.NCC.9
1. Complete a table and graph a linear function

A1.FN.4 Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation. Supporting standards: 7.ALG.5, 8.FN.3		Evaluate a function 1. Evaluate a function 2. Evaluate a function: plug in an expression 3. Evaluate piecewise-defined functions 4. Evaluate an exponential function Interpret function notation 5. Interpret functions using everyday language Tables and graphs 6. Find values using function graphs 7. Complete a function table from a graph 8. Complete a function table from an equation 9. Complete a function table: quadratic functions 10. Complete a function table: absolute value functions
A1.FN.4 Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation. Supporting standards: 7.ALG.5, 8.FN.3
Evaluate a function 1. Evaluate a function 2. Evaluate a function: plug in an expression 3. Evaluate piecewise-defined functions 4. Evaluate an exponential function Interpret function notation 5. Interpret functions using everyday language Tables and graphs 6. Find values using function graphs 7. Complete a function table from a graph 8. Complete a function table from an equation 9. Complete a function table: quadratic functions 10. Complete a function table: absolute value functions

Checkpoint opportunity		1. Checkpoint: Function concepts
Checkpoint opportunity
1. Checkpoint: Function concepts
Construct & Compare: Students construct and compare linear, quadratic, and exponential models and solve problems.
A1.FN.5 Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.5, 7.PR.6, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		1. Exponential growth and decay: word problems 2. Write linear and exponential functions: word problems 3. Linear functions over unit intervals 4. Exponential functions over unit intervals 5. Describe linear and exponential growth and decay
A1.FN.5 Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.5, 7.PR.6, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
1. Exponential growth and decay: word problems 2. Write linear and exponential functions: word problems 3. Linear functions over unit intervals 4. Exponential functions over unit intervals 5. Describe linear and exponential growth and decay

A1.FN.6 Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.5, 7.PR.6, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		Linear and exponential functions 1. Identify linear and exponential functions from graphs 2. Identify linear and exponential functions from tables 3. Write linear and exponential functions from tables 4. Compare linear and exponential growth Linear, quadratic, and exponential functions 5. Identify linear, quadratic, and exponential functions from graphs 6. Identify linear, quadratic, and exponential functions from tables 7. Write linear, quadratic, and exponential functions from tables 8. Compare linear, exponential, and quadratic growth
A1.FN.6 Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.5, 7.PR.6, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
Linear and exponential functions 1. Identify linear and exponential functions from graphs 2. Identify linear and exponential functions from tables 3. Write linear and exponential functions from tables 4. Compare linear and exponential growth Linear, quadratic, and exponential functions 5. Identify linear, quadratic, and exponential functions from graphs 6. Identify linear, quadratic, and exponential functions from tables 7. Write linear, quadratic, and exponential functions from tables 8. Compare linear, exponential, and quadratic growth

LFE	Linear Functions, Equations, & Inequalities
Create & Solve: Students create and solve equations that model linear relationships.
A1.LFE.1 Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		1. Solve one-step and two-step linear equations: word problems 2. Consecutive integer problems 3. Solve linear equations with variables on both sides: word problems 4. Weighted averages: word problems
A1.LFE.1 Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
1. Solve one-step and two-step linear equations: word problems 2. Consecutive integer problems 3. Solve linear equations with variables on both sides: word problems 4. Weighted averages: word problems

A1.LFE.2 Construct linear functions from arithmetic sequences with and without context. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.6, 8.FN.6, 8.FN.7		1. Arithmetic sequences 2. Write variable expressions for arithmetic sequences 3. Write formulas for arithmetic sequences: function notation
A1.LFE.2 Construct linear functions from arithmetic sequences with and without context. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.6, 8.FN.6, 8.FN.7
1. Arithmetic sequences 2. Write variable expressions for arithmetic sequences 3. Write formulas for arithmetic sequences: function notation

A1.LFE.3 Solve linear formulas for a specified variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		1. Rearrange multi-variable equations
A1.LFE.3 Solve linear formulas for a specified variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
1. Rearrange multi-variable equations

A1.LFE.4 Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used. Supporting standards: 6.NCC.4, 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		Properties of equality 1. Properties of equality 2. Identify equivalent equations Equations with models 3. Write and solve linear equations that represent diagrams 4. Model and solve linear equations using algebra tiles Linear equations 5. Solve one-step linear equations 6. Solve two-step linear equations 7. Solve one-step and two-step linear equations: word problems 8. Solve linear equations with variables on one side 9. Solve linear equations with variables on both sides 10. Solve linear equations: mixed review 11. Solve linear equations: complete the solution 12. Solve linear equations with variables on both sides: word problems Absolute value equations 13. Solve absolute value equations Linear inequalities 14. Identify solutions to inequalities 15. Solve one-step linear inequalities: addition and subtraction 16. Solve one-step linear inequalities: multiplication and division 17. Solve one-step linear inequalities 18. Solve two-step linear inequalities 19. Solve multi-step linear inequalities Compound inequalities 20. Solve compound inequalities
A1.LFE.4 Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used. Supporting standards: 6.NCC.4, 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
Properties of equality 1. Properties of equality 2. Identify equivalent equations Equations with models 3. Write and solve linear equations that represent diagrams 4. Model and solve linear equations using algebra tiles Linear equations 5. Solve one-step linear equations 6. Solve two-step linear equations 7. Solve one-step and two-step linear equations: word problems 8. Solve linear equations with variables on one side 9. Solve linear equations with variables on both sides 10. Solve linear equations: mixed review 11. Solve linear equations: complete the solution 12. Solve linear equations with variables on both sides: word problems Absolute value equations 13. Solve absolute value equations Linear inequalities 14. Identify solutions to inequalities 15. Solve one-step linear inequalities: addition and subtraction 16. Solve one-step linear inequalities: multiplication and division 17. Solve one-step linear inequalities 18. Solve two-step linear inequalities 19. Solve multi-step linear inequalities Compound inequalities 20. Solve compound inequalities

Checkpoint opportunity		1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Problem solving with linear equations and inequalities
Checkpoint opportunity
1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Problem solving with linear equations and inequalities
Interpret Key Features: Students interpret key features of equations that model linear relationships.
A1.LFE.5 Determine the domain and range of linear functions in mathematical problems. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8		1. Domain and range of linear functions: graphs
A1.LFE.5 Determine the domain and range of linear functions in mathematical problems. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8
1. Domain and range of linear functions: graphs

A1.LFE.6 Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8		1. Domain and range of linear functions: word problems
A1.LFE.6 Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8
1. Domain and range of linear functions: word problems

A1.LFE.7 Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		Linear functions 1. Find the slope of a graph 2. Find the slope from a table 3. Slope-intercept form: find the slope and y-intercept 4. Standard form: find x- and y-intercepts 5. Find the slope and intercepts from an equation 6. Identify linear functions from graphs and equations 7. Identify linear functions from tables 8. Evaluate a linear function from its graph: word problems Absolute value functions 9. Complete a function table: absolute value functions
A1.LFE.7 Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
Linear functions 1. Find the slope of a graph 2. Find the slope from a table 3. Slope-intercept form: find the slope and y-intercept 4. Standard form: find x- and y-intercepts 5. Find the slope and intercepts from an equation 6. Identify linear functions from graphs and equations 7. Identify linear functions from tables 8. Evaluate a linear function from its graph: word problems Absolute value functions 9. Complete a function table: absolute value functions

A1.LFE.8 Flexibly use different representations of a linear function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		Equations, tables, and graphs 1. Relate the graph of a linear equation to its solutions 2. Complete a table and graph a linear function Slope-intercept form 3. Slope-intercept form: graph an equation 4. Slope-intercept form: write an equation from a graph 5. Slope-intercept form: write an equation 6. Slope-intercept form: write an equation from a table 7. Write a linear function: word problems Standard form 8. Write linear equations in standard form 9. Standard form: graph a line from an equation Point-slope form 10. Point-slope form: graph an equation 11. Point-slope form: write an equation 12. Point-slope form: write an equation from a graph Horizontal and vertical lines 13. Equations of horizontal and vertical lines 14. Graph a horizontal or vertical line
A1.LFE.8 Flexibly use different representations of a linear function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
Equations, tables, and graphs 1. Relate the graph of a linear equation to its solutions 2. Complete a table and graph a linear function Slope-intercept form 3. Slope-intercept form: graph an equation 4. Slope-intercept form: write an equation from a graph 5. Slope-intercept form: write an equation 6. Slope-intercept form: write an equation from a table 7. Write a linear function: word problems Standard form 8. Write linear equations in standard form 9. Standard form: graph a line from an equation Point-slope form 10. Point-slope form: graph an equation 11. Point-slope form: write an equation 12. Point-slope form: write an equation from a graph Horizontal and vertical lines 13. Equations of horizontal and vertical lines 14. Graph a horizontal or vertical line

A1.LFE.9 Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		1. Find the slope of a graph 2. Find the slope from two points 3. Find the slope from a table 4. Slope-intercept form: find the slope and y-intercept 5. Interpret the slope and y-intercept of a linear function
A1.LFE.9 Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
1. Find the slope of a graph 2. Find the slope from two points 3. Find the slope from a table 4. Slope-intercept form: find the slope and y-intercept 5. Interpret the slope and y-intercept of a linear function

A1.LFE.10 Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context. Supporting standards: 6.ALG.4, 7.NCC.9, 7.ALG.1		1. Linear equations: solve for y 2. Write linear equations in standard form
A1.LFE.10 Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context. Supporting standards: 6.ALG.4, 7.NCC.9, 7.ALG.1
1. Linear equations: solve for y 2. Write linear equations in standard form
Systems of Equations & Inequalities: Students solve systems of equations and inequalities.
A1.LFE.11 Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3		Understand solutions 1. Is (x, y) a solution to the system of equations? 2. Find the number of solutions to a system of equations by graphing 3. Find the number of solutions to a system of equations 4. Classify a system of equations by graphing Graphing 5. Solve a system of equations by graphing 6. Solve a system of equations by graphing: word problems Substitution 7. Solve a system of equations using substitution 8. Solve a system of equations using substitution: word problems Elimination 9. Solve a system of equations using elimination 10. Solve a system of equations using elimination: word problems Any method 11. Solve a system of equations using any method 12. Solve a system of equations using any method: word problems
A1.LFE.11 Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3
Understand solutions 1. Is (x, y) a solution to the system of equations? 2. Find the number of solutions to a system of equations by graphing 3. Find the number of solutions to a system of equations 4. Classify a system of equations by graphing Graphing 5. Solve a system of equations by graphing 6. Solve a system of equations by graphing: word problems Substitution 7. Solve a system of equations using substitution 8. Solve a system of equations using substitution: word problems Elimination 9. Solve a system of equations using elimination 10. Solve a system of equations using elimination: word problems Any method 11. Solve a system of equations using any method 12. Solve a system of equations using any method: word problems

A1.LFE.12 Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3		1. Solve a system of linear and quadratic equations by graphing
A1.LFE.12 Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3
1. Solve a system of linear and quadratic equations by graphing

A1.LFE.13 Explain why a solution to the equation f(x) = g(x) is the x-coordinate where the y-coordinate of f(x) and g(x) are the same using graphs, tables, or approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3		Tables 1. Find solutions using a table 2. Approximate solutions using a table Graphs 3. Solve a system of equations by graphing 4. Solve a system of equations by graphing: word problems 5. Find the number of solutions to a system of equations by graphing
A1.LFE.13 Explain why a solution to the equation f(x) = g(x) is the x-coordinate where the y-coordinate of f(x) and g(x) are the same using graphs, tables, or approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3
Tables 1. Find solutions using a table 2. Approximate solutions using a table Graphs 3. Solve a system of equations by graphing 4. Solve a system of equations by graphing: word problems 5. Find the number of solutions to a system of equations by graphing

A1.LFE.14 Solve linear inequalities and systems of linear inequalities in two variables by graphing. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 8.ALG.1, 8.ALG.2, 8.ALG.3		One-variable inequalities 1. Graph solutions to one-step linear inequalities 2. Graph solutions to two-step linear inequalities 3. Graph solutions to multi-step linear inequalities 4. Graph compound inequalities 5. Graph solutions to compound inequalities Two-variable inequalities 6. Does (x, y) satisfy the inequality? 7. Graph a two-variable linear inequality 8. Is (x, y) a solution to the system of linear inequalities? 9. Solve systems of linear inequalities by graphing
A1.LFE.14 Solve linear inequalities and systems of linear inequalities in two variables by graphing. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 8.ALG.1, 8.ALG.2, 8.ALG.3
One-variable inequalities 1. Graph solutions to one-step linear inequalities 2. Graph solutions to two-step linear inequalities 3. Graph solutions to multi-step linear inequalities 4. Graph compound inequalities 5. Graph solutions to compound inequalities Two-variable inequalities 6. Does (x, y) satisfy the inequality? 7. Graph a two-variable linear inequality 8. Is (x, y) a solution to the system of linear inequalities? 9. Solve systems of linear inequalities by graphing

Checkpoint opportunity		1. Checkpoint: Solve equations using graphs and tables 2. Checkpoint: Systems of equations and inequalities
Checkpoint opportunity
1. Checkpoint: Solve equations using graphs and tables 2. Checkpoint: Systems of equations and inequalities
Graphing & Transformations: Students graph linear functions, equations, and inequalities.
A1.LFE.15 Write linear equations that model the relationship between two quantities and produce a graph of the equation. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.ALG.1, 6.ALG.2, 6.ALG.3, 7.ALG.2, 7.ALG.4, 7.PR.6, 8.ALG.1, 8.ALG.2, 8.FN.9		Slope-intercept form 1. Slope-intercept form: write an equation from a graph 2. Slope-intercept form: write an equation 3. Slope-intercept form: write an equation from a table 4. Write a linear function: word problems Standard form 5. Write linear equations in standard form 6. Standard form: graph a line from an equation Point-slope form 7. Point-slope form: graph an equation 8. Point-slope form: write an equation
A1.LFE.15 Write linear equations that model the relationship between two quantities and produce a graph of the equation. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.ALG.1, 6.ALG.2, 6.ALG.3, 7.ALG.2, 7.ALG.4, 7.PR.6, 8.ALG.1, 8.ALG.2, 8.FN.9
Slope-intercept form 1. Slope-intercept form: write an equation from a graph 2. Slope-intercept form: write an equation 3. Slope-intercept form: write an equation from a table 4. Write a linear function: word problems Standard form 5. Write linear equations in standard form 6. Standard form: graph a line from an equation Point-slope form 7. Point-slope form: graph an equation 8. Point-slope form: write an equation

A1.LFE.16 Graph linear functions expressed as an equation and show intercepts of the graph without technology.Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7		1. Slope-intercept form: graph an equation 2. Standard form: graph a line from an equation 3. Graph a horizontal or vertical line 4. Point-slope form: graph an equation
A1.LFE.16 Graph linear functions expressed as an equation and show intercepts of the graph without technology.Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
1. Slope-intercept form: graph an equation 2. Standard form: graph a line from an equation 3. Graph a horizontal or vertical line 4. Point-slope form: graph an equation

A1.LFE.17 Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.NCC.4, 7.NCC.3, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7		1. Graph an absolute value function
A1.LFE.17 Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.NCC.4, 7.NCC.3, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
1. Graph an absolute value function

A1.LFE.18 Graph and generalize the effect of transformations on linear and absolute value functions. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.NCC.4, 7.NCC.3, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7		1. Transformations of linear functions 2. Transformations of absolute value functions: translations and reflections 3. Transformations of absolute value functions: translations, reflections, and dilations
A1.LFE.18 Graph and generalize the effect of transformations on linear and absolute value functions. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.NCC.4, 7.NCC.3, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
1. Transformations of linear functions 2. Transformations of absolute value functions: translations and reflections 3. Transformations of absolute value functions: translations, reflections, and dilations

A1.LFE.19 Given the graph of a linear function, explain the effects of the transformation from the parent function, y = x. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
A1.LFE.19 Given the graph of a linear function, explain the effects of the transformation from the parent function, y = x. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7


Checkpoint opportunity		1. Checkpoint: Write linear functions 2. Checkpoint: Graph linear functions
Checkpoint opportunity
1. Checkpoint: Write linear functions 2. Checkpoint: Graph linear functions
Statistical Relationships: Students explore linear statistical relationships.
A1.LFE.20 Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context. Supporting standards: 8.SP.1, 8.SP.2		1. Write equations for lines of best fit 2. Find the equation of a regression line 3. Interpret regression lines 4. Analyze a regression line of a data set
A1.LFE.20 Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context. Supporting standards: 8.SP.1, 8.SP.2
1. Write equations for lines of best fit 2. Find the equation of a regression line 3. Interpret regression lines 4. Analyze a regression line of a data set

A1.LFE.21 Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association. Supporting standards: 8.SP.1, 8.SP.2		1. Match correlation coefficients to scatter plots 2. Calculate correlation coefficients
A1.LFE.21 Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association. Supporting standards: 8.SP.1, 8.SP.2
1. Match correlation coefficients to scatter plots 2. Calculate correlation coefficients

A1.LFE.22 Compare and contrast correlation and causation in real-world problems. Supporting standards: 8.SP.1, 8.SP.2		1. Correlation and causation
A1.LFE.22 Compare and contrast correlation and causation in real-world problems. Supporting standards: 8.SP.1, 8.SP.2
1. Correlation and causation

Checkpoint opportunity		1. Checkpoint: Linear modeling
Checkpoint opportunity
1. Checkpoint: Linear modeling

QFE	Quadratic Functions & Equations
Create & Solve: Students create and solve equations that model quadratic relationships.
A1.QFE.1 Represent and solve real-world problems using quadratic expressions and equations in one variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.NCC.7, 8.NCC.8, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		1. Interpret parts of quadratic expressions: word problems 2. Solve quadratic equations: word problems
A1.QFE.1 Represent and solve real-world problems using quadratic expressions and equations in one variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.NCC.7, 8.NCC.8, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
1. Interpret parts of quadratic expressions: word problems 2. Solve quadratic equations: word problems

A1.QFE.2 Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.ALG.1, 6.ALG.2, 6.ALG.3, 7.ALG.2, 7.ALG.4, 7.PR.6, 8.ALG.1, 8.ALG.2, 8.FN.9		Write quadratic functions 1. Write a quadratic function in vertex form 2. Write a quadratic function in vertex form from its vertex and another point Graph quadratic functions 3. Graph quadratic functions in vertex form 4. Graph quadratic functions in standard form 5. Match quadratic functions and graphs
A1.QFE.2 Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.ALG.1, 6.ALG.2, 6.ALG.3, 7.ALG.2, 7.ALG.4, 7.PR.6, 8.ALG.1, 8.ALG.2, 8.FN.9
Write quadratic functions 1. Write a quadratic function in vertex form 2. Write a quadratic function in vertex form from its vertex and another point Graph quadratic functions 3. Graph quadratic functions in vertex form 4. Graph quadratic functions in standard form 5. Match quadratic functions and graphs

A1.QFE.3 Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by: graphing, factoring (including perfect square trinomials and difference of squares binomials), using the quadratic formula, completing the square, or taking the square root. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 7.NCC.9, 8.ALG.1, 8.ALG.2, 8.NCC.7, 8.NCC.8		Square roots 1. Solve a quadratic equation using square roots Factor 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring Complete the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant
A1.QFE.3 Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by: graphing, factoring (including perfect square trinomials and difference of squares binomials), using the quadratic formula, completing the square, or taking the square root. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 7.NCC.9, 8.ALG.1, 8.ALG.2, 8.NCC.7, 8.NCC.8
Square roots 1. Solve a quadratic equation using square roots Factor 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring Complete the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant

Checkpoint opportunity		1. Checkpoint: Solve quadratic equations
Checkpoint opportunity
1. Checkpoint: Solve quadratic equations
Interpret Key Features: Students interpret key features of equations that model quadratic relationships.
A1.QFE.4 Determine the domain and range of quadratic functions in mathematical problems. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8		1. Domain and range of quadratic functions: graphs 2. Domain and range of quadratic functions: equations
A1.QFE.4 Determine the domain and range of quadratic functions in mathematical problems. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8
1. Domain and range of quadratic functions: graphs 2. Domain and range of quadratic functions: equations

A1.QFE.5 Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8
A1.QFE.5 Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8


A1.QFE.6 Interpret the key features of a quadratic function that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		1. Characteristics of quadratic functions: graphs 2. Characteristics of quadratic functions: equations
A1.QFE.6 Interpret the key features of a quadratic function that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
1. Characteristics of quadratic functions: graphs 2. Characteristics of quadratic functions: equations

A1.QFE.7 Flexibly use different representations of a quadratic function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		Tables 1. Complete a function table: quadratic functions Graphs 2. Graph quadratic functions in vertex form 3. Graph quadratic functions in standard form 4. Match quadratic functions and graphs Equations 5. Write a quadratic function in vertex form 6. Write a quadratic function in vertex form from its vertex and another point
A1.QFE.7 Flexibly use different representations of a quadratic function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
Tables 1. Complete a function table: quadratic functions Graphs 2. Graph quadratic functions in vertex form 3. Graph quadratic functions in standard form 4. Match quadratic functions and graphs Equations 5. Write a quadratic function in vertex form 6. Write a quadratic function in vertex form from its vertex and another point

A1.QFE.8 Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context. Supporting standards: 6.ALG.4, 7.NCC.9, 7.ALG.1, 8.NCC.3, 8.NCC.7, 8.NCC.8, 8.FN.5		1. Interpret parts of quadratic expressions: word problems
A1.QFE.8 Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context. Supporting standards: 6.ALG.4, 7.NCC.9, 7.ALG.1, 8.NCC.3, 8.NCC.7, 8.NCC.8, 8.FN.5
1. Interpret parts of quadratic expressions: word problems

A1.QFE.9 Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 7.NCC.9, 8.ALG.1, 8.ALG.2, 8.NCC.3, 8.NCC.7, 8.NCC.8, 8.FN.5		Factor quadratics 1. Factor quadratics with leading coefficient 1 2. Factor quadratics with other leading coefficients 3. Factor quadratics: special cases 4. Factor by grouping 5. Factor using a quadratic pattern Complete the square 6. Complete the square
A1.QFE.9 Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 7.NCC.9, 8.ALG.1, 8.ALG.2, 8.NCC.3, 8.NCC.7, 8.NCC.8, 8.FN.5
Factor quadratics 1. Factor quadratics with leading coefficient 1 2. Factor quadratics with other leading coefficients 3. Factor quadratics: special cases 4. Factor by grouping 5. Factor using a quadratic pattern Complete the square 6. Complete the square
Graphing & Transformations: Students graph quadratic functions and explore different transformations of f(x) = x².
A1.QFE.10 Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7		1. Graph quadratic functions in vertex form 2. Graph quadratic functions in standard form 3. Match quadratic functions and graphs
A1.QFE.10 Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
1. Graph quadratic functions in vertex form 2. Graph quadratic functions in standard form 3. Match quadratic functions and graphs

A1.QFE.11 Graph and describe the effect of transformations on quadratic functions. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7		1. Transformations of quadratic functions
A1.QFE.11 Graph and describe the effect of transformations on quadratic functions. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
1. Transformations of quadratic functions

A1.QFE.12 Given the graph of a quadratic function, explain the effects of the transformation from the parent function, y = x². Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
A1.QFE.12 Given the graph of a quadratic function, explain the effects of the transformation from the parent function, y = x². Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7


Checkpoint opportunity		1. Checkpoint: Write and interpret equivalent expressions
Checkpoint opportunity
1. Checkpoint: Write and interpret equivalent expressions
Statistical Relationships: Students explore quadratic statistical relationships.
A1.QFE.13 Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology. Supporting standards: 8.SP.1, 8.SP.2
A1.QFE.13 Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology. Supporting standards: 8.SP.1, 8.SP.2

EFE	Exponential Functions & Equations
Create & Solve: Students create and solve problems that model exponential relationships.
A1.EFE.1 Represent and solve real-world problems, using exponential equations in one variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		1. Write exponential functions: word problems
A1.EFE.1 Represent and solve real-world problems, using exponential equations in one variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
1. Write exponential functions: word problems

A1.EFE.2 Represent real-world problems (growth, decay, and compound interest), using exponential equations. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		1. Exponential growth and decay: word problems 2. Compound interest: word problems 3. Exponential growth and decay
A1.EFE.2 Represent real-world problems (growth, decay, and compound interest), using exponential equations. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
1. Exponential growth and decay: word problems 2. Compound interest: word problems 3. Exponential growth and decay

A1.EFE.3 Construct exponential equations from geometric sequences with and without context. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2		1. Geometric sequences 2. Write variable expressions for geometric sequences 3. Write formulas for geometric sequences: function notation
A1.EFE.3 Construct exponential equations from geometric sequences with and without context. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2
1. Geometric sequences 2. Write variable expressions for geometric sequences 3. Write formulas for geometric sequences: function notation
Interpret Key Features: Students interpret key features of equations that model exponential relationships.
A1.EFE.4 Determine the domain and range of exponential functions in mathematical problems. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8		1. Domain and range of exponential functions: graphs 2. Domain and range of exponential functions: equations
A1.EFE.4 Determine the domain and range of exponential functions in mathematical problems. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8
1. Domain and range of exponential functions: graphs 2. Domain and range of exponential functions: equations

A1.EFE.5 Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8
A1.EFE.5 Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8


A1.EFE.6 Interpret the key features of an exponential function that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		1. Match exponential functions and graphs I 2. Match exponential functions and graphs II
A1.EFE.6 Interpret the key features of an exponential function that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
1. Match exponential functions and graphs I 2. Match exponential functions and graphs II

A1.EFE.7 Flexibly use different representations of an exponential function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		1. Graph exponential functions 2. Match exponential functions and graphs I 3. Match exponential functions and graphs II
A1.EFE.7 Flexibly use different representations of an exponential function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
1. Graph exponential functions 2. Match exponential functions and graphs I 3. Match exponential functions and graphs II

A1.EFE.8 Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9		1. Write exponential functions: word problems 2. Exponential growth and decay: word problems 3. Compound interest: word problems 4. Exponential growth and decay
A1.EFE.8 Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9
1. Write exponential functions: word problems 2. Exponential growth and decay: word problems 3. Compound interest: word problems 4. Exponential growth and decay

Checkpoint opportunity		1. Checkpoint: Compare linear and exponential functions 2. Checkpoint: Write linear, exponential, and quadratic functions
Checkpoint opportunity
1. Checkpoint: Compare linear and exponential functions 2. Checkpoint: Write linear, exponential, and quadratic functions
Graphing: Students graph exponential functions.
A1.EFE.9 Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7		1. Graph exponential functions 2. Match exponential functions and graphs I 3. Match exponential functions and graphs II
A1.EFE.9 Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7
1. Graph exponential functions 2. Match exponential functions and graphs I 3. Match exponential functions and graphs II

Checkpoint opportunity		1. Checkpoint: Exponential functions
Checkpoint opportunity
1. Checkpoint: Exponential functions
Statistical Relationships: Students explore exponential statistical relationships.
A1.EFE.10 Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology. Supporting standards: 8.SP.1, 8.SP.2
A1.EFE.10 Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology. Supporting standards: 8.SP.1, 8.SP.2

SP	Statistics & Probability
Numerical Data: Students summarize and describe distributions.
A1.SP.1 Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets. Supporting standards: 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.6, 6.SP.7, 6.SP.8, 7.SP.1, 7.SP.3, 7.SP.4		Histograms 1. Create histograms 2. Interpret histograms Bar graphs, line graphs, and histograms 3. Create bar graphs, line graphs, and histograms Box plots 4. Box plots Center and spread 5. Mean, median, mode, and range 6. Calculate quartiles and interquartile range 7. Variance and standard deviation 8. Choose appropriate measures of center and variation
A1.SP.1 Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets. Supporting standards: 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.6, 6.SP.7, 6.SP.8, 7.SP.1, 7.SP.3, 7.SP.4
Histograms 1. Create histograms 2. Interpret histograms Bar graphs, line graphs, and histograms 3. Create bar graphs, line graphs, and histograms Box plots 4. Box plots Center and spread 5. Mean, median, mode, and range 6. Calculate quartiles and interquartile range 7. Variance and standard deviation 8. Choose appropriate measures of center and variation

A1.SP.2 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points. Supporting standards: 6.SP.4, 6.SP.5, 6.SP.7		1. Box plots 2. Identify an outlier and describe the effect of removing it
A1.SP.2 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points. Supporting standards: 6.SP.4, 6.SP.5, 6.SP.7
1. Box plots 2. Identify an outlier and describe the effect of removing it

Checkpoint opportunity		1. Checkpoint: Compare data sets 2. Checkpoint: Histograms and box plots
Checkpoint opportunity
1. Checkpoint: Compare data sets 2. Checkpoint: Histograms and box plots
Bivariate Data: Students will investigate patterns of association in bivariate data.
A1.SP.3 Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations. Supporting standards: 6.SP.8, 7.SP.1, 8.SP.3		1. Find probabilities using two-way frequency tables 2. Find conditional probabilities using two-way frequency tables
A1.SP.3 Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations. Supporting standards: 6.SP.8, 7.SP.1, 8.SP.3
1. Find probabilities using two-way frequency tables 2. Find conditional probabilities using two-way frequency tables

Checkpoint opportunity		1. Checkpoint: Two-way frequency tables
Checkpoint opportunity
1. Checkpoint: Two-way frequency tables

CAR	Critical Algebra I Supporting Standards
Fifth Grade
5.CAR.12 Evaluate numerical expressions with parentheses or brackets and exponents with the base of ten, using the Order of Operations.		1. Evaluate numerical expressions 2. Evaluate numerical expressions with parentheses and brackets 3. Identify mistakes involving the order of operations 4. Evaluate numerical expressions with parentheses in different places
5.CAR.12 Evaluate numerical expressions with parentheses or brackets and exponents with the base of ten, using the Order of Operations.
1. Evaluate numerical expressions 2. Evaluate numerical expressions with parentheses and brackets 3. Identify mistakes involving the order of operations 4. Evaluate numerical expressions with parentheses in different places

5.CAR.13 Write simple expressions that record calculations with numbers, interpreting numerical expressions without evaluating them.		1. Write numerical expressions: one operation 2. Write numerical expressions: two operations 3. Comparison statements with numerical expressions 4. Write numerical expressions for word problems 5. Use numerical expressions to solve multi-step word problems
5.CAR.13 Write simple expressions that record calculations with numbers, interpreting numerical expressions without evaluating them.
1. Write numerical expressions: one operation 2. Write numerical expressions: two operations 3. Comparison statements with numerical expressions 4. Write numerical expressions for word problems 5. Use numerical expressions to solve multi-step word problems

5.GM.7 Graph points with whole number coordinates on a coordinate plane in the first quadrant, explaining how the coordinates relate to the horizontal and vertical axes to describe the location of points in the plane.		1. Describe the coordinate plane 2. Objects on a coordinate plane
5.GM.7 Graph points with whole number coordinates on a coordinate plane in the first quadrant, explaining how the coordinates relate to the horizontal and vertical axes to describe the location of points in the plane.
1. Describe the coordinate plane 2. Objects on a coordinate plane

5.GM.8 Represent real-world and mathematical problems by graphing points in the first quadrant on a coordinate plane, interpreting coordinate values of points in the context of the situation.		1. Graph points on a coordinate plane 2. Graph triangles and quadrilaterals 3. Graph points from a table 4. Analyze graphed relationships 5. Coordinate planes as maps 6. Follow directions on a coordinate plane
5.GM.8 Represent real-world and mathematical problems by graphing points in the first quadrant on a coordinate plane, interpreting coordinate values of points in the context of the situation.
1. Graph points on a coordinate plane 2. Graph triangles and quadrilaterals 3. Graph points from a table 4. Analyze graphed relationships 5. Coordinate planes as maps 6. Follow directions on a coordinate plane
Sixth Grade
6.NCC.4 Interpret the absolute value of numbers for positive or negative quantities in a real-world context.		1. Understanding absolute value 2. Absolute value 3. Absolute value and integers: word problems 4. Absolute value of rational numbers
6.NCC.4 Interpret the absolute value of numbers for positive or negative quantities in a real-world context.
1. Understanding absolute value 2. Absolute value 3. Absolute value and integers: word problems 4. Absolute value of rational numbers

6.NCC.11 Solve real-world and mathematical problems with the greatest common factor of two whole numbers less than or equal to 100.		1. Identify factors 2. Find all the factor pairs of a number 3. Greatest common factor
6.NCC.11 Solve real-world and mathematical problems with the greatest common factor of two whole numbers less than or equal to 100.
1. Identify factors 2. Find all the factor pairs of a number 3. Greatest common factor

6.PR.2 Calculate unit rates to include unit pricing and constant speed.		Unit rates 1. Unit rates 2. Compare rates: word problems 3. Ratios and rates: word problems Unit prices 4. Unit prices Constant speed 5. Calculate speed, distance, or time: word problems
6.PR.2 Calculate unit rates to include unit pricing and constant speed.
Unit rates 1. Unit rates 2. Compare rates: word problems 3. Ratios and rates: word problems Unit prices 4. Unit prices Constant speed 5. Calculate speed, distance, or time: word problems

6.ALG.1 Read and write expressions in real-world or mathematical problems in which letters stand for numbers.		1. Write variable expressions: one operation 2. Write variable expressions: two operations 3. Write variable expressions: word problems
6.ALG.1 Read and write expressions in real-world or mathematical problems in which letters stand for numbers.
1. Write variable expressions: one operation 2. Write variable expressions: two operations 3. Write variable expressions: word problems

6.ALG.2 Use mathematical terms to identify parts of an expression, including the names of operations, terms, factors, coefficients, variables, and constants.		1. Identify terms and coefficients 2. Sort factors of variable expressions
6.ALG.2 Use mathematical terms to identify parts of an expression, including the names of operations, terms, factors, coefficients, variables, and constants.
1. Identify terms and coefficients 2. Sort factors of variable expressions

6.ALG.3 Write and evaluate expressions for given values of variables, using order of operations, including expressions with whole number exponents.		Order of operations 1. Evaluate numerical expressions one step at a time 2. Evaluate numerical expressions involving whole numbers 3. Identify mistakes involving the order of operations 4. Evaluate numerical expressions involving decimals 5. Evaluate numerical expressions involving fractions Evaluate variable expressions 6. Evaluate variable expressions with whole numbers 7. Evaluate multi-variable expressions 8. Evaluate variable expressions with decimals, fractions, and mixed numbers 9. Evaluate variable expressions: word problems Real-world formulas 10. Convert between Celsius and Fahrenheit
6.ALG.3 Write and evaluate expressions for given values of variables, using order of operations, including expressions with whole number exponents.
Order of operations 1. Evaluate numerical expressions one step at a time 2. Evaluate numerical expressions involving whole numbers 3. Identify mistakes involving the order of operations 4. Evaluate numerical expressions involving decimals 5. Evaluate numerical expressions involving fractions Evaluate variable expressions 6. Evaluate variable expressions with whole numbers 7. Evaluate multi-variable expressions 8. Evaluate variable expressions with decimals, fractions, and mixed numbers 9. Evaluate variable expressions: word problems Real-world formulas 10. Convert between Celsius and Fahrenheit

6.ALG.4 Generate equivalent expressions by applying the associative, commutative, distributive, and identity properties.		1. Multiply using the distributive property: area models 2. Multiply using the distributive property 3. Factor variable expressions: area models 4. Factor variable expressions using the distributive property 5. Write equivalent expressions using properties 6. Add and subtract like terms
6.ALG.4 Generate equivalent expressions by applying the associative, commutative, distributive, and identity properties.
1. Multiply using the distributive property: area models 2. Multiply using the distributive property 3. Factor variable expressions: area models 4. Factor variable expressions using the distributive property 5. Write equivalent expressions using properties 6. Add and subtract like terms

6.ALG.5 Identify when two expressions are equivalent by using properties of operations including like terms.		1. Identify equivalent expressions using strip models 2. Identify equivalent expressions I 3. Identify equivalent expressions II
6.ALG.5 Identify when two expressions are equivalent by using properties of operations including like terms.
1. Identify equivalent expressions using strip models 2. Identify equivalent expressions I 3. Identify equivalent expressions II

6.ALG.6 Use substitution to determine if a given value in a specified set makes an equation or inequality true.		1. Does x satisfy an equation? 2. Which x satisfies an equation? 3. Solutions to inequalities
6.ALG.6 Use substitution to determine if a given value in a specified set makes an equation or inequality true.
1. Does x satisfy an equation? 2. Which x satisfies an equation? 3. Solutions to inequalities

6.ALG.7 Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero.		Solve equations 1. Write an equation from words 2. Model and solve equations using algebra tiles 3. Model and solve equations using diagrams 4. Write and solve equations that represent diagrams 5. Solve one-step addition and subtraction equations with whole numbers 6. Solve one-step multiplication and division equations with whole numbers 7. Solve one-step equations with whole numbers 8. Solve one-step addition and subtraction equations with decimals and fractions 9. Solve one-step multiplication and division equations with decimals and fractions 10. Solve one-step equations with decimals and fractions Real-world problems 11. Solve one-step addition and subtraction equations: word problems 12. Solve one-step multiplication and division equations: word problems 13. Write a one-step equation: word problems 14. Solve one-step equations: word problems 15. Which word problem matches the one-step equation?
6.ALG.7 Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero.
Solve equations 1. Write an equation from words 2. Model and solve equations using algebra tiles 3. Model and solve equations using diagrams 4. Write and solve equations that represent diagrams 5. Solve one-step addition and subtraction equations with whole numbers 6. Solve one-step multiplication and division equations with whole numbers 7. Solve one-step equations with whole numbers 8. Solve one-step addition and subtraction equations with decimals and fractions 9. Solve one-step multiplication and division equations with decimals and fractions 10. Solve one-step equations with decimals and fractions Real-world problems 11. Solve one-step addition and subtraction equations: word problems 12. Solve one-step multiplication and division equations: word problems 13. Write a one-step equation: word problems 14. Solve one-step equations: word problems 15. Which word problem matches the one-step equation?

6.ALG.8 Write, solve, and graph one-step inequalities in real-world and mathematical problems.		1. Solve one-step inequalities 2. Graph solutions to one-step inequalities 3. One-step inequalities: word problems
6.ALG.8 Write, solve, and graph one-step inequalities in real-world and mathematical problems.
1. Solve one-step inequalities 2. Graph solutions to one-step inequalities 3. One-step inequalities: word problems

6.GM.4 Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in real-world and mathematical problems.		1. Describe the coordinate plane 2. Objects on a coordinate plane 3. Graph points on a coordinate plane 4. Quadrants
6.GM.4 Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in real-world and mathematical problems.
1. Describe the coordinate plane 2. Objects on a coordinate plane 3. Graph points on a coordinate plane 4. Quadrants

6.SP.2 Calculate and interpret any measure of center (mean, median, and mode) of a numerical data set.		1. Calculate mean, median, and mode 2. Mean, median, and mode: find the missing number
6.SP.2 Calculate and interpret any measure of center (mean, median, and mode) of a numerical data set.
1. Calculate mean, median, and mode 2. Mean, median, and mode: find the missing number

6.SP.3 Determine which measure of center (mean or median) is more appropriate to describe the center of data and justify the choice.
6.SP.3 Determine which measure of center (mean or median) is more appropriate to describe the center of data and justify the choice.


6.SP.4 Describe how the mean or median is affected by outliers of a numerical data set.		1. Identify an outlier 2. Identify an outlier and describe the effect of removing it
6.SP.4 Describe how the mean or median is affected by outliers of a numerical data set.
1. Identify an outlier 2. Identify an outlier and describe the effect of removing it

6.SP.5 Calculate and interpret the measure of variation [range and interquartile range (IQR)] of a numerical data set.		1. Calculate range and interquartile range
6.SP.5 Calculate and interpret the measure of variation [range and interquartile range (IQR)] of a numerical data set.
1. Calculate range and interquartile range

6.SP.6 Determine which measure of variation (range or interquartile range) is more appropriate to describe the shape; justify the choice.
6.SP.6 Determine which measure of variation (range or interquartile range) is more appropriate to describe the shape; justify the choice.


6.SP.7 Represent numerical data on a number line, histogram, and box plot.		1. Create line plots 2. Create histograms 3. Box plots
6.SP.7 Represent numerical data on a number line, histogram, and box plot.
1. Create line plots 2. Create histograms 3. Box plots

6.SP.8 Calculate the relative frequency of an interval of data values when given a histogram.		1. Create relative frequency tables 2. Interpret histograms
6.SP.8 Calculate the relative frequency of an interval of data values when given a histogram.
1. Create relative frequency tables 2. Interpret histograms
Seventh Grade
7.NCC.3 Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.		1. Understanding absolute value
7.NCC.3 Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.
1. Understanding absolute value

7.NCC.7 Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.		One-step problems 1. Complete addition and subtraction equations with integers 2. Add and subtract integers: word problems 3. Add and subtract decimals: word problems 4. Add and subtract fractions: word problems 5. Add and subtract mixed numbers: word problems Multi-step problems 6. Price lists 7. Add and subtract fractions and mixed numbers: word problems
7.NCC.7 Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.
One-step problems 1. Complete addition and subtraction equations with integers 2. Add and subtract integers: word problems 3. Add and subtract decimals: word problems 4. Add and subtract fractions: word problems 5. Add and subtract mixed numbers: word problems Multi-step problems 6. Price lists 7. Add and subtract fractions and mixed numbers: word problems

7.NCC.8 Use multiplication and division with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.		One-step problems 1. Complete multiplication and division equations with integers 2. Multiply decimals and whole numbers: word problems 3. Divide decimals by whole numbers: word problems 4. Multiply fractions and mixed numbers: word problems 5. Divide fractions and mixed numbers: word problems
7.NCC.8 Use multiplication and division with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.
One-step problems 1. Complete multiplication and division equations with integers 2. Multiply decimals and whole numbers: word problems 3. Divide decimals by whole numbers: word problems 4. Multiply fractions and mixed numbers: word problems 5. Divide fractions and mixed numbers: word problems

7.NCC.9 Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.		1. Evaluate numerical expressions involving integers 2. Evaluate numerical expressions involving decimals 3. Evaluate numerical expressions involving fractions 4. Evaluate numerical expressions involving exponents
7.NCC.9 Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.
1. Evaluate numerical expressions involving integers 2. Evaluate numerical expressions involving decimals 3. Evaluate numerical expressions involving fractions 4. Evaluate numerical expressions involving exponents

7.PR.1 Determine the unit rate (constant of proportionality) from tables, graphs, equations, diagrams, or verbal descriptions of proportional relationships.		1. Find the constant of proportionality from a table 2. Find the constant of proportionality from a graph
7.PR.1 Determine the unit rate (constant of proportionality) from tables, graphs, equations, diagrams, or verbal descriptions of proportional relationships.
1. Find the constant of proportionality from a table 2. Find the constant of proportionality from a graph

7.PR.4 Determine whether two quantities represent proportional relationships by using equivalent ratios in a table and by graphing on a coordinate plane.		Equivalent ratios 1. Identify equivalent ratios 2. Equivalent ratios: word problems Proportions 3. Do the ratios form a proportion? 4. Do the ratios form a proportion: word problems Proportional relationships 5. Identify proportional relationships by graphing 6. Identify proportional relationships from graphs and equations 7. Identify proportional relationships from tables
7.PR.4 Determine whether two quantities represent proportional relationships by using equivalent ratios in a table and by graphing on a coordinate plane.
Equivalent ratios 1. Identify equivalent ratios 2. Equivalent ratios: word problems Proportions 3. Do the ratios form a proportion? 4. Do the ratios form a proportion: word problems Proportional relationships 5. Identify proportional relationships by graphing 6. Identify proportional relationships from graphs and equations 7. Identify proportional relationships from tables

7.PR.5 Compare two different proportional relationships represented in different forms.
7.PR.5 Compare two different proportional relationships represented in different forms.


7.PR.6 Create equations in the form of y = mx from tables, verbal descriptions, or graphs.		Represent relationships 1. Write equations for proportional relationships from tables 2. Write equations for proportional relationships from graphs 3. Write and solve equations for proportional relationships Solve proportional problems 4. Solve proportions: word problems 5. Estimate population size using proportions 6. Percents of numbers and money amounts 7. Percents of numbers: word problems 8. Solve percent equations 9. Solve percent equations: word problems
7.PR.6 Create equations in the form of y = mx from tables, verbal descriptions, or graphs.
Represent relationships 1. Write equations for proportional relationships from tables 2. Write equations for proportional relationships from graphs 3. Write and solve equations for proportional relationships Solve proportional problems 4. Solve proportions: word problems 5. Estimate population size using proportions 6. Percents of numbers and money amounts 7. Percents of numbers: word problems 8. Solve percent equations 9. Solve percent equations: word problems

7.PR.7 Given a graph with a proportional relationship, explain the meaning of a point (x, y) on the graph, including the origin (0, 0) and the unit rate (1, r).		1. Interpret graphs of proportional relationships
7.PR.7 Given a graph with a proportional relationship, explain the meaning of a point (x, y) on the graph, including the origin (0, 0) and the unit rate (1, r).
1. Interpret graphs of proportional relationships

7.ALG.1 Generate and justify equivalent expressions, using properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients within mathematical and real-world problems.		Properties of operations 1. Multiply using the distributive property: area models 2. Multiply using the distributive property 3. Write equivalent expressions using properties Add and subtract 4. Simplify expressions by combining like terms 5. Add and subtract linear expressions Factor 6. Factor linear expressions: area models 7. Factors of linear expressions Identify linear expressions 8. Identify equivalent linear expressions using algebra tiles 9. Identify equivalent linear expressions I 10. Identify equivalent linear expressions II Word problems 11. Identify equivalent linear expressions: word problems
7.ALG.1 Generate and justify equivalent expressions, using properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients within mathematical and real-world problems.
Properties of operations 1. Multiply using the distributive property: area models 2. Multiply using the distributive property 3. Write equivalent expressions using properties Add and subtract 4. Simplify expressions by combining like terms 5. Add and subtract linear expressions Factor 6. Factor linear expressions: area models 7. Factors of linear expressions Identify linear expressions 8. Identify equivalent linear expressions using algebra tiles 9. Identify equivalent linear expressions I 10. Identify equivalent linear expressions II Word problems 11. Identify equivalent linear expressions: word problems

7.ALG.2 Model and solve fluently two-step equations in real-world or mathematical problems.		Solve equations 1. Model and solve equations using algebra tiles 2. Solve two-step equations without parentheses 3. Solve two-step equations with parentheses 4. Solve two-step equations 5. Solve two-step equations with fractions 6. Solve equations: complete the solution Word problems 7. Choose two-step equations: word problems 8. Solve two-step equations: word problems
7.ALG.2 Model and solve fluently two-step equations in real-world or mathematical problems.
Solve equations 1. Model and solve equations using algebra tiles 2. Solve two-step equations without parentheses 3. Solve two-step equations with parentheses 4. Solve two-step equations 5. Solve two-step equations with fractions 6. Solve equations: complete the solution Word problems 7. Choose two-step equations: word problems 8. Solve two-step equations: word problems

7.ALG.3 Create, solve, and graph two-step inequalities in real-world and mathematical problems in the forms px ± q > r, px ± q < r, px ± q ≥ r, and px ± q ≤ r.		One-step inequalities 1. Solve one-step inequalities 2. Graph solutions to one-step inequalities 3. One-step inequalities: word problems Two-step inequalities 4. Solve two-step inequalities 5. Graph solutions to two-step inequalities
7.ALG.3 Create, solve, and graph two-step inequalities in real-world and mathematical problems in the forms px ± q > r, px ± q < r, px ± q ≥ r, and px ± q ≤ r.
One-step inequalities 1. Solve one-step inequalities 2. Graph solutions to one-step inequalities 3. One-step inequalities: word problems Two-step inequalities 4. Solve two-step inequalities 5. Graph solutions to two-step inequalities

7.ALG.4 Write an equation to express two quantities in terms of the dependent and independent variables.		1. Identify independent and dependent variables 2. Write a two-variable equation
7.ALG.4 Write an equation to express two quantities in terms of the dependent and independent variables.
1. Identify independent and dependent variables 2. Write a two-variable equation

7.ALG.5 Describe the relationship between the dependent and independent variables in an equation using tables and graphs, relating these to the equation.		1. Complete a table for a two-variable relationship 2. Identify the graph of an equation 3. Graph a two-variable equation 4. Interpret a graph: word problems 5. Write an equation from a graph using a table
7.ALG.5 Describe the relationship between the dependent and independent variables in an equation using tables and graphs, relating these to the equation.
1. Complete a table for a two-variable relationship 2. Identify the graph of an equation 3. Graph a two-variable equation 4. Interpret a graph: word problems 5. Write an equation from a graph using a table

7.SP.1 Interpret data displayed in a histogram and box plot to answer questions about the data.		1. Interpret histograms 2. Box plots
7.SP.1 Interpret data displayed in a histogram and box plot to answer questions about the data.
1. Interpret histograms 2. Box plots

7.SP.3 Graph two numerical data sets and compare their variability.		Graph numerical data 1. Create line plots 2. Create stem-and-leaf plots 3. Create bar graphs 4. Create histograms 5. Interpret charts and graphs to find mean, median, mode, and range Measures of variability 6. Calculate mean absolute deviation 7. Calculate range, quartiles, and interquartile range 8. Identify an outlier
7.SP.3 Graph two numerical data sets and compare their variability.
Graph numerical data 1. Create line plots 2. Create stem-and-leaf plots 3. Create bar graphs 4. Create histograms 5. Interpret charts and graphs to find mean, median, mode, and range Measures of variability 6. Calculate mean absolute deviation 7. Calculate range, quartiles, and interquartile range 8. Identify an outlier

7.SP.4 Select an appropriate measure(s) of center or variability and draw valid comparative inferences for two data sets.		1. Compare populations using measures of center and spread
7.SP.4 Select an appropriate measure(s) of center or variability and draw valid comparative inferences for two data sets.
1. Compare populations using measures of center and spread
Eighth Grade
8.NCC.3 Know and apply the properties of integer exponents to generate equivalent numerical expressions.		Positive exponents 1. Powers with negative bases Negative exponents 2. Understanding negative exponents 3. Evaluate powers with negative exponents 4. Evaluate powers with negative or zero exponents Properties of exponents 5. Multiply powers: integer bases 6. Divide powers: integer bases 7. Multiply and divide powers: integer bases 8. Power of a power: integer bases 9. Evaluate expressions using properties of exponents 10. Identify equivalent expressions involving exponents I 11. Identify equivalent expressions involving exponents II
8.NCC.3 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Positive exponents 1. Powers with negative bases Negative exponents 2. Understanding negative exponents 3. Evaluate powers with negative exponents 4. Evaluate powers with negative or zero exponents Properties of exponents 5. Multiply powers: integer bases 6. Divide powers: integer bases 7. Multiply and divide powers: integer bases 8. Power of a power: integer bases 9. Evaluate expressions using properties of exponents 10. Identify equivalent expressions involving exponents I 11. Identify equivalent expressions involving exponents II

Checkpoint opportunity		1. Checkpoint: Properties of exponents
Checkpoint opportunity
1. Checkpoint: Properties of exponents

8.NCC.7 Solve equations in the form of x² = p or x³ = p where p is a positive rational number.		1. Solve equations using square roots 2. Solve equations using cube roots
8.NCC.7 Solve equations in the form of x² = p or x³ = p where p is a positive rational number.
1. Solve equations using square roots 2. Solve equations using cube roots

8.NCC.8 Evaluate square roots of perfect squares and cube roots of perfect cubes.		1. Square roots of perfect squares 2. Relationship between squares and square roots 3. Cube roots of positive perfect cubes
8.NCC.8 Evaluate square roots of perfect squares and cube roots of perfect cubes.
1. Square roots of perfect squares 2. Relationship between squares and square roots 3. Cube roots of positive perfect cubes

8.FN.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph.		1. Find the constant of proportionality from a graph 2. Graph proportional relationships and find the slope 3. Graph proportional relationships from equations
8.FN.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph.
1. Find the constant of proportionality from a graph 2. Graph proportional relationships and find the slope 3. Graph proportional relationships from equations

8.FN.3 Determine whether a relation is a function or not when given a function map, table, graph, equation, or set of ordered pairs.		1. Identify functions 2. Identify functions: graphs 3. Identify functions: tables 4. Identify functions: graphs and mapping diagrams
8.FN.3 Determine whether a relation is a function or not when given a function map, table, graph, equation, or set of ordered pairs.
1. Identify functions 2. Identify functions: graphs 3. Identify functions: tables 4. Identify functions: graphs and mapping diagrams

8.FN.4 Compare the rate of change (slope) and y-intercept (initial value) of two linear functions each represented in different forms.		1. Compare linear functions: graphs and equations 2. Compare linear functions: tables, graphs, and equations
8.FN.4 Compare the rate of change (slope) and y-intercept (initial value) of two linear functions each represented in different forms.
1. Compare linear functions: graphs and equations 2. Compare linear functions: tables, graphs, and equations

8.FN.5 Distinguish between linear and nonlinear functions by comparing graphs and equations.		1. Identify linear and nonlinear functions: graphs and equations
8.FN.5 Distinguish between linear and nonlinear functions by comparing graphs and equations.
1. Identify linear and nonlinear functions: graphs and equations

8.FN.6 Determine the rate of change (slope) and y-intercept (initial value) from tables, graphs, equations, and verbal descriptions of linear relationships.		Rate of change 1. Rate of change of a linear function: graphs Slope 2. Find the slope from a graph 3. Find the slope from two points 4. Find the slope from a table 5. Slope-intercept form: find the slope and y-intercept
8.FN.6 Determine the rate of change (slope) and y-intercept (initial value) from tables, graphs, equations, and verbal descriptions of linear relationships.
Rate of change 1. Rate of change of a linear function: graphs Slope 2. Find the slope from a graph 3. Find the slope from two points 4. Find the slope from a table 5. Slope-intercept form: find the slope and y-intercept

8.FN.7 Interpret and explain the meaning of the rate of change (slope) and y-intercept (initial value) of a linear relationship in a real-world context.		1. Interpret graphs of proportional relationships 2. Interpret the slope and y-intercept of a linear function
8.FN.7 Interpret and explain the meaning of the rate of change (slope) and y-intercept (initial value) of a linear relationship in a real-world context.
1. Interpret graphs of proportional relationships 2. Interpret the slope and y-intercept of a linear function

8.FN.8 Analyze a graph by describing the functional relationships between two quantities.		Proportional relationships 1. Write equations for proportional relationships from tables 2. Write equations for proportional relationships from graphs Linear relationships 3. Write a linear equation from a slope and y-intercept 4. Write a linear equation from a graph 5. Write a linear equation from a slope and a point 6. Write a linear equation from two points 7. Interpret the slope and y-intercept of a linear function 8. Write a linear function from a table 9. Write linear functions: word problems
8.FN.8 Analyze a graph by describing the functional relationships between two quantities.
Proportional relationships 1. Write equations for proportional relationships from tables 2. Write equations for proportional relationships from graphs Linear relationships 3. Write a linear equation from a slope and y-intercept 4. Write a linear equation from a graph 5. Write a linear equation from a slope and a point 6. Write a linear equation from two points 7. Interpret the slope and y-intercept of a linear function 8. Write a linear function from a table 9. Write linear functions: word problems

8.FN.9 Sketch a graph that exhibits qualitative features of a function described verbally.		1. Identify graphs: word problems
8.FN.9 Sketch a graph that exhibits qualitative features of a function described verbally.
1. Identify graphs: word problems

Checkpoint opportunity		1. Checkpoint: Compare linear functions 2. Checkpoint: Sketch and describe graphs 3. Checkpoint: Understand functions 4. Checkpoint: Interpret slopes and y-intercepts
Checkpoint opportunity
1. Checkpoint: Compare linear functions 2. Checkpoint: Sketch and describe graphs 3. Checkpoint: Understand functions 4. Checkpoint: Interpret slopes and y-intercepts

8.ALG.1 Analyze and solve one-variable linear equations with rational coefficients containing solutions with one, zero, or infinitely many solutions.		Analyze linear equations 1. Find the number of solutions 2. Create equations with no solutions or infinitely many solutions Variables on both sides 3. Solve equations with variables on both sides 4. Solve equations with variables on both sides: fractional coefficients 5. Solve equations with variables on both sides: word problems Multi-step equations 6. Which x satisfies an equation? 7. Solve equations involving like terms 8. Solve equations using the distributive property 9. Solve multi-step equations 10. Solve multi-step equations with fractional coefficients 11. Solve equations: mixed review 12. Solve multi-step equations: complete the solution
8.ALG.1 Analyze and solve one-variable linear equations with rational coefficients containing solutions with one, zero, or infinitely many solutions.
Analyze linear equations 1. Find the number of solutions 2. Create equations with no solutions or infinitely many solutions Variables on both sides 3. Solve equations with variables on both sides 4. Solve equations with variables on both sides: fractional coefficients 5. Solve equations with variables on both sides: word problems Multi-step equations 6. Which x satisfies an equation? 7. Solve equations involving like terms 8. Solve equations using the distributive property 9. Solve multi-step equations 10. Solve multi-step equations with fractional coefficients 11. Solve equations: mixed review 12. Solve multi-step equations: complete the solution

8.ALG.2 Analyze and solve one-variable linear inequalities with rational coefficients.		Multi-step inequalities 1. Solve multi-step inequalities 2. Graph solutions to multi-step inequalities 3. Solve inequalities with integers: variables on both sides Solve inequalities with rational numbers 4. Solve inequalities with decimals: variables on both sides 5. Solve two-step inequalities: rational coefficients
8.ALG.2 Analyze and solve one-variable linear inequalities with rational coefficients.
Multi-step inequalities 1. Solve multi-step inequalities 2. Graph solutions to multi-step inequalities 3. Solve inequalities with integers: variables on both sides Solve inequalities with rational numbers 4. Solve inequalities with decimals: variables on both sides 5. Solve two-step inequalities: rational coefficients

Checkpoint opportunity		1. Checkpoint: Solve linear equations
Checkpoint opportunity
1. Checkpoint: Solve linear equations

8.ALG.3 Analyze and solve systems of linear equations in the form y = mx + b in real-world or mathematical contexts, graphically and algebraically.		1. Is (x, y) a solution to the system of equations? 2. Solve a system of equations by graphing: word problems 3. Solve a system of equations using substitution: word problems 4. Find the number of solutions to a system of equations by graphing 5. Solve a system of equations by graphing 6. Solve a system of equations in slope-intercept form
8.ALG.3 Analyze and solve systems of linear equations in the form y = mx + b in real-world or mathematical contexts, graphically and algebraically.
1. Is (x, y) a solution to the system of equations? 2. Solve a system of equations by graphing: word problems 3. Solve a system of equations using substitution: word problems 4. Find the number of solutions to a system of equations by graphing 5. Solve a system of equations by graphing 6. Solve a system of equations in slope-intercept form

Checkpoint opportunity		1. Checkpoint: Systems of equations
Checkpoint opportunity
1. Checkpoint: Systems of equations

8.SP.1 Construct scatter plots using bivariate data; determine if the data displays a linear or nonlinear pattern and positive, negative, or no association.		1. Create scatter plots 2. Identify trends with scatter plots
8.SP.1 Construct scatter plots using bivariate data; determine if the data displays a linear or nonlinear pattern and positive, negative, or no association.
1. Create scatter plots 2. Identify trends with scatter plots

8.SP.2 Construct straight lines to approximately fit data displaying a linear association when presented in scatter plots.		1. Identify lines of best fit 2. Write equations for lines of best fit
8.SP.2 Construct straight lines to approximately fit data displaying a linear association when presented in scatter plots.
1. Identify lines of best fit 2. Write equations for lines of best fit

8.SP.3 Construct and interpret a relative frequency table, using data from two categorical variables collected from the same subject.
8.SP.3 Construct and interpret a relative frequency table, using data from two categorical variables collected from the same subject.


Checkpoint opportunity		1. Checkpoint: Lines of best fit 2. Checkpoint: Two-way frequency tables
Checkpoint opportunity
1. Checkpoint: Lines of best fit 2. Checkpoint: Two-way frequency tables