IXL Skill Plan | Iowa Academic Standards for Mathematics (adopted in 2024): Algebra I

Iowa Academic Standards for Mathematics (adopted in 2024): Algebra I

Skills available for Iowa Algebra I standards

Conceptual Category

Number and Quantity
Algebra
Functions
Statistics and Probability

Print skill plan

A1.N	Number and Quantity
A1.N-RN The Real Number System
A1.N-RN.B Use properties of rational and irrational numbers.
A1.N-RN.B Use properties of rational and irrational numbers.

A1.N-RN.B.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.		1. Sort rational and irrational numbers 2. Classify rational and irrational numbers 3. Properties of operations on rational and irrational numbers
A1.N-RN.B.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
1. Sort rational and irrational numbers 2. Classify rational and irrational numbers 3. Properties of operations on rational and irrational numbers
A1.N-Q Quantities
A1.N-Q.A Reason quantitatively and use units to solve problems.
A1.N-Q.A Reason quantitatively and use units to solve problems.

A1.N-Q.A.1: Use units to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.		1. Scale drawings: word problems 2. Unit prices with unit conversions 3. Multi-step problems with unit conversions 4. Rate of travel: word problems 5. Weighted averages: word problems
A1.N-Q.A.1: Use units to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
1. Scale drawings: word problems 2. Unit prices with unit conversions 3. Multi-step problems with unit conversions 4. Rate of travel: word problems 5. Weighted averages: word problems
A1.N-Q.A.2: Define appropriate quantities for the purpose of descriptive modeling.		Linear models 1. Solve one-step and two-step linear equations: word problems 2. Solve linear equations with variables on both sides: word problems 3. Solve a system of equations using any method: word problems Exponential models 4. Write exponential functions: word problems 5. Exponential growth and decay: word problems Quadratic models 6. Solve quadratic equations: word problems
A1.N-Q.A.2: Define appropriate quantities for the purpose of descriptive modeling.
Linear models 1. Solve one-step and two-step linear equations: word problems 2. Solve linear equations with variables on both sides: word problems 3. Solve a system of equations using any method: word problems Exponential models 4. Write exponential functions: word problems 5. Exponential growth and decay: word problems Quadratic models 6. Solve quadratic equations: word problems
A1.N-Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.		Precision 1. Precision Greatest possible error 2. Greatest possible error 3. Minimum and maximum area and volume Percent error 4. Percent error 5. Percent error: area and volume
A1.N-Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Precision 1. Precision Greatest possible error 2. Greatest possible error 3. Minimum and maximum area and volume Percent error 4. Percent error 5. Percent error: area and volume

Checkpoint opportunity		1. Checkpoint: Units and quantities
Checkpoint opportunity
1. Checkpoint: Units and quantities

A1.A	Algebra
A1.A-SSE Seeing Structure in Expressions and Equations
A-SSE.A Interpret the structure of expressions.
A-SSE.A Interpret the structure of expressions.

A1.A-SSE.A.1.a: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients.		1. Sort factors of variable expressions 2. Polynomial vocabulary 3. Interpret parts of quadratic expressions: word problems
A1.A-SSE.A.1.a: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients.
1. Sort factors of variable expressions 2. Polynomial vocabulary 3. Interpret parts of quadratic expressions: word problems
A1.A-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.		Linear expressions 1. Simplify linear expressions using properties Numeric expressions with exponents 2. Evaluate expressions using exponent rules 3. Identify equivalent exponential expressions I 4. Identify equivalent exponential expressions II Exponential expressions 5. Simplify exponential expressions using the multiplication rule 6. Simplify exponential expressions using the division rule 7. Simplify exponential expressions using the multiplication and division rules 8. Simplify exponential expressions using the power rule Polynomial expressions 9. Simplify variable expressions involving like terms and the distributive property 10. Factor out a monomial Quadratic expressions 11. Factor quadratics with leading coefficient 1 12. Factor quadratics with other leading coefficients 13. Factor quadratics: special cases 14. Factor by grouping 15. Factor using a quadratic pattern Radical expressions 16. Simplify radical expressions 17. Simplify radical expressions with variables 18. Simplify radical expressions involving fractions 19. Simplify radical expressions: mixed review
A1.A-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Linear expressions 1. Simplify linear expressions using properties Numeric expressions with exponents 2. Evaluate expressions using exponent rules 3. Identify equivalent exponential expressions I 4. Identify equivalent exponential expressions II Exponential expressions 5. Simplify exponential expressions using the multiplication rule 6. Simplify exponential expressions using the division rule 7. Simplify exponential expressions using the multiplication and division rules 8. Simplify exponential expressions using the power rule Polynomial expressions 9. Simplify variable expressions involving like terms and the distributive property 10. Factor out a monomial Quadratic expressions 11. Factor quadratics with leading coefficient 1 12. Factor quadratics with other leading coefficients 13. Factor quadratics: special cases 14. Factor by grouping 15. Factor using a quadratic pattern Radical expressions 16. Simplify radical expressions 17. Simplify radical expressions with variables 18. Simplify radical expressions involving fractions 19. Simplify radical expressions: mixed review

A-SSE.B Write expressions and equations in equivalent forms to solve problems.
A-SSE.B Write expressions and equations in equivalent forms to solve problems.

A1.A-SSE.B.3: Choose and produce an equivalent form of an expression or equation to reveal and explain properties of the quantity represented by the expression.
A1.A-SSE.B.3: Choose and produce an equivalent form of an expression or equation to reveal and explain properties of the quantity represented by the expression.

A1.A-SSE.B.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.		Factor quadratics 1. Factor quadratics using algebra tiles 2. Factor quadratics with leading coefficient 1 3. Factor quadratics with other leading coefficients 4. Factor quadratics: special cases Zeros of a function 5. Solve a quadratic equation by factoring 6. Find the roots of factored quadratic functions
A1.A-SSE.B.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics 1. Factor quadratics using algebra tiles 2. Factor quadratics with leading coefficient 1 3. Factor quadratics with other leading coefficients 4. Factor quadratics: special cases Zeros of a function 5. Solve a quadratic equation by factoring 6. Find the roots of factored quadratic functions
A1.A-SSE.B.3.b: Complete the square in a quadratic equation to reveal the maximum or minimum value of the function it defines.		1. Characteristics of quadratic functions: equations 2. Write a quadratic function in vertex form 3. Complete the square
A1.A-SSE.B.3.b: Complete the square in a quadratic equation to reveal the maximum or minimum value of the function it defines.
1. Characteristics of quadratic functions: equations 2. Write a quadratic function in vertex form 3. Complete the square
A1.A-SSE.B.3.c: Use the properties of exponents to transform expressions for exponential functions.		1. Evaluate expressions using exponent rules 2. Evaluate an exponential function
A1.A-SSE.B.3.c: Use the properties of exponents to transform expressions for exponential functions.
1. Evaluate expressions using exponent rules 2. Evaluate an exponential function

Checkpoint opportunity		1. Checkpoint: Quadratic and exponential expressions
Checkpoint opportunity
1. Checkpoint: Quadratic and exponential expressions
A1.A-CED Creating Equation
A1.A-CED.A Create equations that describe numbers or relationships.
A1.A-CED.A Create equations that describe numbers or relationships.

A1.A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.		Linear equations 1. Write variable equations 2. Model and solve linear equations using algebra tiles Inequalities 3. Write inequalities from graphs 4. Write compound inequalities from graphs Word problems 5. Solve one-step and two-step linear equations: word problems 6. Consecutive integer problems 7. Solve linear equations with variables on both sides: word problems 8. Weighted averages: word problems 9. Write exponential functions: word problems 10. Solve quadratic equations: word problems
A1.A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Linear equations 1. Write variable equations 2. Model and solve linear equations using algebra tiles Inequalities 3. Write inequalities from graphs 4. Write compound inequalities from graphs Word problems 5. Solve one-step and two-step linear equations: word problems 6. Consecutive integer problems 7. Solve linear equations with variables on both sides: word problems 8. Weighted averages: word problems 9. Write exponential functions: word problems 10. Solve quadratic equations: word problems
A1.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.		Direct variation 1. Write direct variation equations Slope-intercept form 2. Slope-intercept form: graph an equation 3. Slope-intercept form: write an equation from a graph 4. Slope-intercept form: write an equation 5. Slope-intercept form: write an equation from a table 6. Write a linear function: word problems Standard form 7. Write linear equations in standard form 8. Standard form: graph a line from an equation Point-slope form 9. Point-slope form: graph an equation 10. Point-slope form: write an equation Exponential equations 11. Graph exponential functions 12. Write exponential functions: word problems Quadratic equations 13. Graph quadratic functions in vertex form 14. Write a quadratic function in vertex form 15. Graph quadratic functions in standard form 16. Write a quadratic function in vertex form from its vertex and another point 17. Write a quadratic function in factored form from its x-intercepts and another point 18. Write a quadratic function in standard form from its x-intercepts and another point Linear, quadratic, and exponential equations 19. Write linear and exponential functions: word problems 20. Write linear and exponential functions from tables 21. Write linear, quadratic, and exponential functions from tables
A1.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Direct variation 1. Write direct variation equations Slope-intercept form 2. Slope-intercept form: graph an equation 3. Slope-intercept form: write an equation from a graph 4. Slope-intercept form: write an equation 5. Slope-intercept form: write an equation from a table 6. Write a linear function: word problems Standard form 7. Write linear equations in standard form 8. Standard form: graph a line from an equation Point-slope form 9. Point-slope form: graph an equation 10. Point-slope form: write an equation Exponential equations 11. Graph exponential functions 12. Write exponential functions: word problems Quadratic equations 13. Graph quadratic functions in vertex form 14. Write a quadratic function in vertex form 15. Graph quadratic functions in standard form 16. Write a quadratic function in vertex form from its vertex and another point 17. Write a quadratic function in factored form from its x-intercepts and another point 18. Write a quadratic function in standard form from its x-intercepts and another point Linear, quadratic, and exponential equations 19. Write linear and exponential functions: word problems 20. Write linear and exponential functions from tables 21. Write linear, quadratic, and exponential functions from tables
A1.A-CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.		Linear equations 1. Write a linear function: word problems Linear inequalities 2. Write two-variable inequalities: word problems Systems of equations 3. Solve a system of equations by graphing: word problems 4. Solve a system of equations using substitution: word problems 5. Solve a system of equations using elimination: word problems 6. Solve a system of equations using any method: word problems
A1.A-CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
Linear equations 1. Write a linear function: word problems Linear inequalities 2. Write two-variable inequalities: word problems Systems of equations 3. Solve a system of equations by graphing: word problems 4. Solve a system of equations using substitution: word problems 5. Solve a system of equations using elimination: word problems 6. Solve a system of equations using any method: word problems
A1.A-CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.		1. Rearrange multi-variable equations 2. Linear equations: solve for y
A1.A-CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
1. Rearrange multi-variable equations 2. Linear equations: solve for y

Checkpoint opportunity		1. Checkpoint: Modeling with linear equations and inequalities 2. Checkpoint: Modeling with linear, quadratic, and exponential equations and inequalities
Checkpoint opportunity
1. Checkpoint: Modeling with linear equations and inequalities 2. Checkpoint: Modeling with linear, quadratic, and exponential equations and inequalities
A1.A-REI Reasoning with Equations and Inequalities
A1.A-REI.A Understand solving equations as a process of reasoning and explain the reasoning.
A1.A-REI.A Understand solving equations as a process of reasoning and explain the reasoning.

A1.A-REI.A.1: Explain each step-in solving equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.		1. Properties of equality 2. Identify equivalent equations 3. Solve linear equations: complete the solution
A1.A-REI.A.1: Explain each step-in solving equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
1. Properties of equality 2. Identify equivalent equations 3. Solve linear equations: complete the solution
A1.A-REI.A.2: Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise.		1. Solve radical equations I 2. Solve radical equations II 3. Solve rational equations
A1.A-REI.A.2: Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise.
1. Solve radical equations I 2. Solve radical equations II 3. Solve rational equations

A1.A-REI.B Solve equations and inequalities in one variable.
A1.A-REI.B Solve equations and inequalities in one variable.

A1.A-REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.		Multi-variable equations 1. Rearrange multi-variable equations Equations with models 2. Model and solve linear equations using algebra tiles One- and two-step linear equations 3. Solve one-step linear equations 4. Solve two-step linear equations 5. Solve one-step and two-step linear equations: word problems Multi-step linear equations 6. Solve linear equations with variables on one side 7. Solve linear equations with variables on both sides 8. Solve linear equations: mixed review 9. Solve linear equations: complete the solution 10. Solve linear equations with variables on both sides: word problems Solutions to linear equations 11. Create linear equations with no solutions or infinitely many solutions Linear inequalities 12. Identify solutions to inequalities 13. Solve one-step linear inequalities: addition and subtraction 14. Solve one-step linear inequalities: multiplication and division 15. Solve one-step linear inequalities 16. Solve two-step linear inequalities 17. Solve advanced linear inequalities Compound inequalities 18. Solve compound inequalities
A1.A-REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Multi-variable equations 1. Rearrange multi-variable equations Equations with models 2. Model and solve linear equations using algebra tiles One- and two-step linear equations 3. Solve one-step linear equations 4. Solve two-step linear equations 5. Solve one-step and two-step linear equations: word problems Multi-step linear equations 6. Solve linear equations with variables on one side 7. Solve linear equations with variables on both sides 8. Solve linear equations: mixed review 9. Solve linear equations: complete the solution 10. Solve linear equations with variables on both sides: word problems Solutions to linear equations 11. Create linear equations with no solutions or infinitely many solutions Linear inequalities 12. Identify solutions to inequalities 13. Solve one-step linear inequalities: addition and subtraction 14. Solve one-step linear inequalities: multiplication and division 15. Solve one-step linear inequalities 16. Solve two-step linear inequalities 17. Solve advanced linear inequalities Compound inequalities 18. Solve compound inequalities
A1.A-REI.B.4: Solve quadratic equations in one variable.
A1.A-REI.B.4: Solve quadratic equations in one variable.

A1.A-REI.B.4.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.		1. Complete the square
A1.A-REI.B.4.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.
1. Complete the square
A1.A-REI.B.4.b: Solve quadratic equations with real solutions using any method.		Square roots 1. Solve a quadratic equation using square roots Factoring 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 Any method 8. Solve quadratic equations: word problems
A1.A-REI.B.4.b: Solve quadratic equations with real solutions using any method.
Square roots 1. Solve a quadratic equation using square roots Factoring 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 Any method 8. Solve quadratic equations: word problems

Checkpoint opportunity		1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Quadratic equations
Checkpoint opportunity
1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Quadratic equations

A-REI.C Solve systems of equations.
A-REI.C Solve systems of equations.

A1.A-REI.C.5: Explain how the strategy of elimination results in finding solution(s) to a system of equations.		1. Solve a system of equations using elimination 2. Solve a system of equations using elimination: word problems
A1.A-REI.C.5: Explain how the strategy of elimination results in finding solution(s) to a system of equations.
1. Solve a system of equations using elimination 2. Solve a system of equations using elimination: word problems
A1.A-REI.C.6: Solve systems of linear equations exactly and approximately.		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.A-REI.C.6: Solve systems of linear equations exactly and approximately.
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.A-REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.		1. Solve a system of linear and quadratic equations by graphing 2. Solve a system of linear and quadratic equations
A1.A-REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
1. Solve a system of linear and quadratic equations by graphing 2. Solve a system of linear and quadratic equations

A1.A-REI.D Represent and solve equations and inequalities graphically.
A1.A-REI.D Represent and solve equations and inequalities graphically.

A1.A-REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).		1. Relate the graph of a linear equation to its solutions 2. Find values using function graphs 3. Complete a function table from a graph 4. Complete a function table from an equation 5. Complete a table and graph a linear function
A1.A-REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
1. Relate the graph of a linear equation to its solutions 2. Find values using function graphs 3. Complete a function table from a graph 4. Complete a function table from an equation 5. Complete a table and graph a linear function
A1.A-REI.D.11: Explain why the solution(s) of a system of equations are the point(s) of intersection(s) on a coordinate plane. Find the solutions approximately, using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value functions.		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 6. Solve a system of linear and quadratic equations by graphing
A1.A-REI.D.11: Explain why the solution(s) of a system of equations are the point(s) of intersection(s) on a coordinate plane. Find the solutions approximately, using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value functions.
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 6. Solve a system of linear and quadratic equations by graphing
A1.A-REI.D.12: Graph and interpret (with the use of technology) the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.		1. Does (x, y) satisfy the inequality? 2. Graph a two-variable linear inequality 3. Write a linear inequality from a graph 4. Is (x, y) a solution to the system of linear inequalities? 5. Solve systems of linear inequalities by graphing
A1.A-REI.D.12: Graph and interpret (with the use of technology) the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
1. Does (x, y) satisfy the inequality? 2. Graph a two-variable linear inequality 3. Write a linear inequality from a graph 4. Is (x, y) a solution to the system of linear inequalities? 5. 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

A1.F	Functions
A1.F-IF Interpreting Functions
A1.F-IF.A Understand the concept of a function and use function notation.
A1.F-IF.A Understand the concept of a function and use function notation.

A1.F-IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input f. The graph of f is the graph of the equation y = f(x).		Independent and dependent variables 1. Identify independent and dependent variables Identify functions 2. Identify functions 3. Identify functions: vertical line test Function tables and graphs 4. Find values using function graphs 5. Complete a function table from a graph 6. Complete a function table from an equation Relations 7. Domain and range of relations Linear functions 8. Domain and range of linear functions: graphs Exponential functions 9. Domain and range of exponential functions: graphs 10. Domain and range of exponential functions: equations Quadratic functions 11. Domain and range of quadratic functions: graphs 12. Domain and range of quadratic functions: equations Absolute value functions 13. Domain and range of absolute value functions: graphs 14. Domain and range of absolute value functions: equations Square root functions 15. Domain and range of square root functions: graphs 16. Domain and range of square root functions: equations
A1.F-IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input f. The graph of f is the graph of the equation y = f(x).
Independent and dependent variables 1. Identify independent and dependent variables Identify functions 2. Identify functions 3. Identify functions: vertical line test Function tables and graphs 4. Find values using function graphs 5. Complete a function table from a graph 6. Complete a function table from an equation Relations 7. Domain and range of relations Linear functions 8. Domain and range of linear functions: graphs Exponential functions 9. Domain and range of exponential functions: graphs 10. Domain and range of exponential functions: equations Quadratic functions 11. Domain and range of quadratic functions: graphs 12. Domain and range of quadratic functions: equations Absolute value functions 13. Domain and range of absolute value functions: graphs 14. Domain and range of absolute value functions: equations Square root functions 15. Domain and range of square root functions: graphs 16. Domain and range of square root functions: equations
A1.F-IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.		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.F-IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
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.F-IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.		Arithmetic sequences 1. Arithmetic sequences 2. Write variable expressions for arithmetic sequences Geometric sequences 3. Geometric sequences 4. Write variable expressions for geometric sequences Recursive formulas 5. Evaluate recursive formulas for sequences 6. Write a formula for a recursive sequence Explicit and recursive sequences 7. Identify a sequence as explicit or recursive Mixed sequences 8. Identify arithmetic and geometric sequences 9. Evaluate variable expressions for number sequences 10. Sequences: mixed review
A1.F-IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Arithmetic sequences 1. Arithmetic sequences 2. Write variable expressions for arithmetic sequences Geometric sequences 3. Geometric sequences 4. Write variable expressions for geometric sequences Recursive formulas 5. Evaluate recursive formulas for sequences 6. Write a formula for a recursive sequence Explicit and recursive sequences 7. Identify a sequence as explicit or recursive Mixed sequences 8. Identify arithmetic and geometric sequences 9. Evaluate variable expressions for number sequences 10. Sequences: mixed review

A1.F-IF.B Interpret functions that arise in applications in terms of the context.
A1.F-IF.B Interpret functions that arise in applications in terms of the context.

A1.F-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features may include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximum and minimum; and symmetries.		Linear functions 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. Slope-intercept form: graph an equation 6. Standard form: find x- and y-intercepts 7. Standard form: graph a line from an equation 8. Point-slope form: graph an equation 9. Identify linear functions from graphs and equations 10. Identify linear functions from tables 11. Complete a table and graph a linear function Exponential functions 12. Graph exponential functions 13. Match exponential functions and graphs I 14. Match exponential functions and graphs II Quadratic functions 15. Characteristics of quadratic functions: graphs 16. Characteristics of quadratic functions: equations 17. Graph quadratic functions in vertex form 18. Graph quadratic functions in standard form 19. Match quadratic functions and graphs Linear, quadratic, and exponential functions 20. Identify linear, quadratic, and exponential functions from graphs 21. Identify linear, quadratic, and exponential functions from tables Absolute value functions 22. Graph an absolute value function Word problems 23. Identify graphs: word problems 24. Evaluate a linear function from its graph: word problems
A1.F-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features may include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximum and minimum; and symmetries.
Linear functions 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. Slope-intercept form: graph an equation 6. Standard form: find x- and y-intercepts 7. Standard form: graph a line from an equation 8. Point-slope form: graph an equation 9. Identify linear functions from graphs and equations 10. Identify linear functions from tables 11. Complete a table and graph a linear function Exponential functions 12. Graph exponential functions 13. Match exponential functions and graphs I 14. Match exponential functions and graphs II Quadratic functions 15. Characteristics of quadratic functions: graphs 16. Characteristics of quadratic functions: equations 17. Graph quadratic functions in vertex form 18. Graph quadratic functions in standard form 19. Match quadratic functions and graphs Linear, quadratic, and exponential functions 20. Identify linear, quadratic, and exponential functions from graphs 21. Identify linear, quadratic, and exponential functions from tables Absolute value functions 22. Graph an absolute value function Word problems 23. Identify graphs: word problems 24. Evaluate a linear function from its graph: word problems
A1.F-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.		Linear functions 1. Domain and range of linear functions: graphs 2. Domain and range of linear functions: word problems Exponential functions 3. Domain and range of exponential functions: graphs 4. Domain and range of exponential functions: equations Quadratic functions 5. Domain and range of quadratic functions: graphs 6. Domain and range of quadratic functions: equations Absolute value functions 7. Domain and range of absolute value functions: graphs 8. Domain and range of absolute value functions: equations Square root functions 9. Domain and range of square root functions: graphs 10. Domain and range of square root functions: equations
A1.F-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Linear functions 1. Domain and range of linear functions: graphs 2. Domain and range of linear functions: word problems Exponential functions 3. Domain and range of exponential functions: graphs 4. Domain and range of exponential functions: equations Quadratic functions 5. Domain and range of quadratic functions: graphs 6. Domain and range of quadratic functions: equations Absolute value functions 7. Domain and range of absolute value functions: graphs 8. Domain and range of absolute value functions: equations Square root functions 9. Domain and range of square root functions: graphs 10. Domain and range of square root functions: equations
A1.F-IF.B.6: Calculate and interpret the average rate of change of a nonlinear function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.		1. Rate of change: tables 2. Rate of change: graphs
A1.F-IF.B.6: Calculate and interpret the average rate of change of a nonlinear function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
1. Rate of change: tables 2. Rate of change: graphs

Checkpoint opportunity		1. Checkpoint: Function concepts 2. Checkpoint: Average rate of change
Checkpoint opportunity
1. Checkpoint: Function concepts 2. Checkpoint: Average rate of change

A1.F-IF.C Analyze functions using different representations.
A1.F-IF.C Analyze functions using different representations.

A1.F-IF.C.7: Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.
A1.F-IF.C.7: Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.

A1.F-IF.C.7.a: Graph linear and quadratic functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases, including intercepts, maxima, and minima if they exist.		Linear functions 1. Slope-intercept form: graph an equation 2. Standard form: graph a line from an equation 3. Point-slope form: graph an equation Quadratic functions 4. Characteristics of quadratic functions: graphs 5. Graph quadratic functions in vertex form 6. Graph quadratic functions in standard form 7. Match quadratic functions and graphs
A1.F-IF.C.7.a: Graph linear and quadratic functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases, including intercepts, maxima, and minima if they exist.
Linear functions 1. Slope-intercept form: graph an equation 2. Standard form: graph a line from an equation 3. Point-slope form: graph an equation Quadratic functions 4. Characteristics of quadratic functions: graphs 5. Graph quadratic functions in vertex form 6. Graph quadratic functions in standard form 7. Match quadratic functions and graphs
A1.F-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.		1. Characteristics of quadratic functions: graphs 2. Write a quadratic function in vertex form 3. Solve a quadratic equation by factoring 4. Solve a quadratic equation by completing the square
A1.F-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
1. Characteristics of quadratic functions: graphs 2. Write a quadratic function in vertex form 3. Solve a quadratic equation by factoring 4. Solve a quadratic equation by completing the square

Checkpoint opportunity		1. Checkpoint: Graph and analyze functions
Checkpoint opportunity
1. Checkpoint: Graph and analyze functions
A1.F-BF Building Functions
A1.F-BF.A Build a function that models a relationship between two quantities.
A1.F-BF.A Build a function that models a relationship between two quantities.

A1.F-BF.A.1.a: Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.		Sequences 1. Write variable expressions for arithmetic sequences 2. Write variable expressions for geometric sequences 3. Write a formula for a recursive sequence Linear, quadratic, and exponential functions 4. Write a linear function: word problems 5. Write exponential functions: word problems 6. Write linear and exponential functions from tables 7. Write linear, quadratic, and exponential functions from tables
A1.F-BF.A.1.a: Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences 1. Write variable expressions for arithmetic sequences 2. Write variable expressions for geometric sequences 3. Write a formula for a recursive sequence Linear, quadratic, and exponential functions 4. Write a linear function: word problems 5. Write exponential functions: word problems 6. Write linear and exponential functions from tables 7. Write linear, quadratic, and exponential functions from tables
A1.F-BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.		1. Write variable expressions for arithmetic sequences 2. Write variable expressions for geometric sequences 3. Write a formula for a recursive sequence 4. Convert a recursive formula to an explicit formula 5. Convert an explicit formula to a recursive formula
A1.F-BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
1. Write variable expressions for arithmetic sequences 2. Write variable expressions for geometric sequences 3. Write a formula for a recursive sequence 4. Convert a recursive formula to an explicit formula 5. Convert an explicit formula to a recursive formula

Checkpoint opportunity		1. Checkpoint: Sequences
Checkpoint opportunity
1. Checkpoint: Sequences

A1.F-BF.B Build new functions from existing functions.
A1.F-BF.B Build new functions from existing functions.

A1.F-BF.B.3: Identify the effect on linear and quadratic graphs of replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.		Linear functions 1. Transformations of linear functions Quadratic functions 2. Transformations of quadratic functions Functions 3. Function transformation rules 4. Translations of functions 5. Reflections of functions 6. Dilations of functions 7. Transformations of functions 8. Describe function transformations
A1.F-BF.B.3: Identify the effect on linear and quadratic graphs of replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Linear functions 1. Transformations of linear functions Quadratic functions 2. Transformations of quadratic functions Functions 3. Function transformation rules 4. Translations of functions 5. Reflections of functions 6. Dilations of functions 7. Transformations of functions 8. Describe function transformations

Checkpoint opportunity		1. Checkpoint: Function transformations
Checkpoint opportunity
1. Checkpoint: Function transformations
A1.F-LE Linear, Quadratic, and Exponential Models
A1.F-LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
A1.F-LE.A Construct and compare linear, quadratic, and exponential models and solve problems.

A1.F-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
A1.F-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

A1.F-LE.A.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.		1. Linear functions over unit intervals 2. Exponential functions over unit intervals 3. Describe linear and exponential growth and decay
A1.F-LE.A.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
1. Linear functions over unit intervals 2. Exponential functions over unit intervals 3. Describe linear and exponential growth and decay
A1.F-LE.A.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.		1. Identify linear and exponential functions from graphs 2. Identify linear and exponential functions from tables 3. Write linear and exponential functions: word problems
A1.F-LE.A.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
1. Identify linear and exponential functions from graphs 2. Identify linear and exponential functions from tables 3. Write linear and exponential functions: word problems
A1.F-LE.A.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.		1. Exponential growth and decay: word problems 2. Identify linear and exponential functions from graphs 3. Identify linear and exponential functions from tables 4. Write linear and exponential functions: word problems
A1.F-LE.A.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
1. Exponential growth and decay: word problems 2. Identify linear and exponential functions from graphs 3. Identify linear and exponential functions from tables 4. Write linear and exponential functions: word problems
A1.F-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).		Arithmetic and geometric sequences 1. Write variable expressions for arithmetic sequences 2. Write variable expressions for geometric sequences Slope-intercept form 3. Slope-intercept form: write an equation from a graph 4. Slope-intercept form: write an equation 5. Slope-intercept form: write an equation from a table 6. Write a linear function: word problems Parallel and perpendicular lines 7. Slopes of parallel and perpendicular lines 8. Write an equation for a parallel or perpendicular line Point-slope form 9. Point-slope form: write an equation 10. Point-slope form: write an equation from a graph Exponential functions 11. Write exponential functions from tables and graphs 12. Write exponential functions: word problems Linear and exponential functions 13. Write linear and exponential functions from tables
A1.F-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Arithmetic and geometric sequences 1. Write variable expressions for arithmetic sequences 2. Write variable expressions for geometric sequences Slope-intercept form 3. Slope-intercept form: write an equation from a graph 4. Slope-intercept form: write an equation 5. Slope-intercept form: write an equation from a table 6. Write a linear function: word problems Parallel and perpendicular lines 7. Slopes of parallel and perpendicular lines 8. Write an equation for a parallel or perpendicular line Point-slope form 9. Point-slope form: write an equation 10. Point-slope form: write an equation from a graph Exponential functions 11. Write exponential functions from tables and graphs 12. Write exponential functions: word problems Linear and exponential functions 13. Write linear and exponential functions from tables
A1.F-LE.A.3: Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.		1. Compare linear and exponential growth 2. Compare linear, exponential, and quadratic growth
A1.F-LE.A.3: Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
1. Compare linear and exponential growth 2. Compare linear, exponential, and quadratic growth

A1.F-LE.B Interpret expressions for functions in terms of the situation they model.
A1.F-LE.B Interpret expressions for functions in terms of the situation they model.

A1.F-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.		1. Solve one-step and two-step linear equations: word problems 2. Solve linear equations with variables on both sides: word problems 3. Interpret the slope and y-intercept of a linear function 4. Exponential growth and decay: word problems 5. Compound interest: word problems
A1.F-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
1. Solve one-step and two-step linear equations: word problems 2. Solve linear equations with variables on both sides: word problems 3. Interpret the slope and y-intercept of a linear function 4. Exponential growth and decay: word problems 5. Compound interest: word problems

Checkpoint opportunity		1. Checkpoint: Compare linear and exponential functions
Checkpoint opportunity
1. Checkpoint: Compare linear and exponential functions

A1.S	Statistics and Probability
A1.S-ID Interpreting Categorical and Quantitative Data
A1.S-ID.A Summarize, represent, and interpret data on a single count or measurement variable.
A1.S-ID.A Summarize, represent, and interpret data on a single count or measurement variable.

A1.S-ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots) in a modeling context.		Line plots 1. Create line plots 2. Interpret line plots Histograms 3. Create histograms 4. Interpret histograms Bar graphs, line graphs, and histograms 5. Create bar graphs, line graphs, and histograms 6. Interpret bar graphs, line graphs, and histograms Box plots 7. Box plots
A1.S-ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots) in a modeling context.
Line plots 1. Create line plots 2. Interpret line plots Histograms 3. Create histograms 4. Interpret histograms Bar graphs, line graphs, and histograms 5. Create bar graphs, line graphs, and histograms 6. Interpret bar graphs, line graphs, and histograms Box plots 7. Box plots
A1.S-ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.		1. Mean, median, mode, and range 2. Calculate quartiles and interquartile range 3. Variance and standard deviation 4. Choose appropriate measures of center and variation
A1.S-ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
1. Mean, median, mode, and range 2. Calculate quartiles and interquartile range 3. Variance and standard deviation 4. Choose appropriate measures of center and variation
A1.S-ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).		1. Box plots 2. Identify an outlier and describe the effect of removing it
A1.S-ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
1. Box plots 2. Identify an outlier and describe the effect of removing it

Checkpoint opportunity		1. Checkpoint: Line plots, histograms, and box plots 2. Checkpoint: Compare data sets
Checkpoint opportunity
1. Checkpoint: Line plots, histograms, and box plots 2. Checkpoint: Compare data sets

A1.S-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.
A1.S-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.

A1.S-ID.B.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.		1. Find probabilities using two-way frequency tables 2. Find conditional probabilities using two-way frequency tables
A1.S-ID.B.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
1. Find probabilities using two-way frequency tables 2. Find conditional probabilities using two-way frequency tables
A1.S-ID.B.6: Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
A1.S-ID.B.6: Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

A1.S-ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.		1. Interpret lines of best fit: word problems 2. Find the equation of a regression line 3. Interpret regression lines 4. Analyze a regression line of a data set
A1.S-ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
1. Interpret lines of best fit: word problems 2. Find the equation of a regression line 3. Interpret regression lines 4. Analyze a regression line of a data set
A1.S-ID.B.6.b: Informally assess the fit of a function by plotting and analyzing residuals.		1. Interpret a scatter plot
A1.S-ID.B.6.b: Informally assess the fit of a function by plotting and analyzing residuals.
1. Interpret a scatter plot
A1.S-ID.B.6.c: Informally assess the fit of a function by plotting and analyzing residuals.		1. Write equations for lines of best fit
A1.S-ID.B.6.c: Informally assess the fit of a function by plotting and analyzing residuals.
1. Write equations for lines of best fit

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

A1.S-ID.C Interpret linear models.
A1.S-ID.C Interpret linear models.

A1.S-ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.		1. Interpret lines of best fit: word problems 2. Interpret regression lines 3. Analyze a regression line of a data set
A1.S-ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
1. Interpret lines of best fit: word problems 2. Interpret regression lines 3. Analyze a regression line of a data set
A1.S-ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.		1. Match correlation coefficients to scatter plots 2. Calculate correlation coefficients
A1.S-ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
1. Match correlation coefficients to scatter plots 2. Calculate correlation coefficients
A1.S-ID.C.9: Distinguish between correlation and causation.		1. Correlation and causation
A1.S-ID.C.9: Distinguish between correlation and causation.
1. Correlation and causation

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