IXL Skill Plan | Illinois Priority Learning Standards: Algebra 1

Illinois Priority Learning Standards: Algebra 1

Skills available for Illinois Algebra 1 standards

Section

Number and Quantity
Algebra
Functions
Statistics and Probability

Print skill plan

9-12.HSN	Number and Quantity
9-12.HSN-RN The Real Number System
9-12.HSN-RN.A Extend the properties of exponents to rational exponents.
9-12.HSN-RN.A Extend the properties of exponents to rational exponents.

9-12.HSN-RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.		Rational exponents 1. Multiplication with rational exponents 2. Division with rational exponents 3. Power rule with rational exponents 4. Simplify expressions involving rational exponents 5. Convert between rational exponents and radicals Radical expressions 6. Simplify radical expressions 7. Simplify radical expressions with variables 8. Simplify radical expressions involving fractions 9. Multiply radical expressions 10. Add and subtract radical expressions 11. Simplify radical expressions using the distributive property 12. Simplify radical expressions using conjugates 13. Simplify radical expressions: mixed review
9-12.HSN-RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents 1. Multiplication with rational exponents 2. Division with rational exponents 3. Power rule with rational exponents 4. Simplify expressions involving rational exponents 5. Convert between rational exponents and radicals Radical expressions 6. Simplify radical expressions 7. Simplify radical expressions with variables 8. Simplify radical expressions involving fractions 9. Multiply radical expressions 10. Add and subtract radical expressions 11. Simplify radical expressions using the distributive property 12. Simplify radical expressions using conjugates 13. Simplify radical expressions: mixed review
9-12.HSN-Q Quantities
9-12.HSN-Q.A Reason quantitatively and use units to solve problems.
9-12.HSN-Q.A Reason quantitatively and use units to solve problems.

9-12.HSN-Q.A.1: Use units as a way 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
9-12.HSN-Q.A.1: Use units as a way 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
9-12.HSN-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
9-12.HSN-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
9-12.HSN-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
9-12.HSN-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

9-12.HSA	Algebra
9-12.HSA-SSE Seeing Structure in Expressions
9-12.HSA-SSE.A Interpret the structure of expressions
9-12.HSA-SSE.A Interpret the structure of expressions

9-12.HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
9-12.HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.

9-12.HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.		1. Sort factors of variable expressions 2. Polynomial vocabulary
9-12.HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
1. Sort factors of variable expressions 2. Polynomial vocabulary
9-12.HSA-SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
9-12.HSA-SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

9-12.HSA-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
9-12.HSA-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

9-12.HSA-SSE.B Write expressions in equivalent forms to solve problems
9-12.HSA-SSE.B Write expressions in equivalent forms to solve problems

9-12.HSA-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
9-12.HSA-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

9-12.HSA-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.		Factor quadratics 1. Factor quadratics with leading coefficient 1 2. Factor quadratics with other leading coefficients 3. Factor quadratics: special cases Solve quadratics 4. Solve a quadratic equation by factoring
9-12.HSA-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics 1. Factor quadratics with leading coefficient 1 2. Factor quadratics with other leading coefficients 3. Factor quadratics: special cases Solve quadratics 4. Solve a quadratic equation by factoring
9-12.HSA-SSE.B.3b: Complete the square in a quadratic expression 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
9-12.HSA-SSE.B.3b: Complete the square in a quadratic expression 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
9-12.HSA-SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.		1. Evaluate expressions using exponent rules 2. Evaluate an exponential function
9-12.HSA-SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
1. Evaluate expressions using exponent rules 2. Evaluate an exponential function
9-12.HSA-APR Arithmetic with Polynomials and Rational Expressions
9-12.HSA-APR.A Perform arithmetic operations on polynomials
9-12.HSA-APR.A Perform arithmetic operations on polynomials

9-12.HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.		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
9-12.HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
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
9-12.HSA-CED Creating Equations
9-12.HSA-CED.A Create equations that describe numbers or relationships
9-12.HSA-CED.A Create equations that describe numbers or relationships

9-12.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.		Linear equations 1. Write variable equations 2. Model and solve linear equations using algebra tiles 3. Solve one-step and two-step linear equations: word problems 4. Consecutive integer problems 5. Solve linear equations with variables on both sides: word problems 6. Rate of travel: word problems 7. Weighted averages: word problems Inequalities 8. Write inequalities from graphs 9. Write compound inequalities from graphs Exponential and quadratic equations 10. Write exponential functions: word problems 11. Solve quadratic equations: word problems
9-12.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
Linear equations 1. Write variable equations 2. Model and solve linear equations using algebra tiles 3. Solve one-step and two-step linear equations: word problems 4. Consecutive integer problems 5. Solve linear equations with variables on both sides: word problems 6. Rate of travel: word problems 7. Weighted averages: word problems Inequalities 8. Write inequalities from graphs 9. Write compound inequalities from graphs Exponential and quadratic equations 10. Write exponential functions: word problems 11. Solve quadratic equations: word problems
9-12.HSA-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
9-12.HSA-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
9-12.HSA-CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable 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
9-12.HSA-CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable 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
9-12.HSA-REI Reasoning with Equations and Inequalities
9-12.HSA-REI.A Understand solving equations as a process of reasoning and explain the reasoning
9-12.HSA-REI.A Understand solving equations as a process of reasoning and explain the reasoning

9-12.HSA-REI.A.1: Explain each step in solving a simple equation 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
9-12.HSA-REI.A.1: Explain each step in solving a simple equation 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

9-12.HSA-REI.B Solve equations and inequalities in one variable
9-12.HSA-REI.B Solve equations and inequalities in one variable

9-12.HSA-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
9-12.HSA-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
9-12.HSA-REI.B.4: Solve quadratic equations in one variable.
9-12.HSA-REI.B.4: Solve quadratic equations in one variable.

9-12.HSA-REI.B.4a: 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. Derive the quadratic formula from this form.		1. Complete the square
9-12.HSA-REI.B.4a: 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. Derive the quadratic formula from this form.
1. Complete the square
9-12.HSA-REI.B.4b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.		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. Solve a quadratic equation by completing the square Quadratic formula 5. Solve a quadratic equation using the quadratic formula
9-12.HSA-REI.B.4b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
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. Solve a quadratic equation by completing the square Quadratic formula 5. Solve a quadratic equation using the quadratic formula

9-12.HSA-REI.C Solve systems of equations
9-12.HSA-REI.C Solve systems of equations

9-12.HSA-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.		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
9-12.HSA-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
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

9-12.HSA-REI.D Represent and solve equations and inequalities graphically
9-12.HSA-REI.D Represent and solve equations and inequalities graphically

9-12.HSA-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
9-12.HSA-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
9-12.HSA-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., 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, polynomial, rational, absolute value, exponential, and logarithmic 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
9-12.HSA-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., 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, polynomial, rational, absolute value, exponential, and logarithmic 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
9-12.HSA-REI.D.12: Graph 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
9-12.HSA-REI.D.12: Graph 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

9-12.HSF	Functions
9-12.HSF-IF Interpreting Functions
9-12.HSF-IF.A Understand the concept of a function and use function notation
9-12.HSF-IF.A Understand the concept of a function and use function notation

9-12.HSF-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 x. 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
9-12.HSF-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 x. 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
9-12.HSF-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
9-12.HSF-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

9-12.HSF-IF.B Interpret functions that arise in applications in terms of the context
9-12.HSF-IF.B Interpret functions that arise in applications in terms of the context

9-12.HSF-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.		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
9-12.HSF-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.
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
9-12.HSF-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
9-12.HSF-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
9-12.HSF-IF.B.6: Calculate and interpret the average rate of change of a 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
9-12.HSF-IF.B.6: Calculate and interpret the average rate of change of a 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

9-12.HSF-IF.C Analyze functions using different representations
9-12.HSF-IF.C Analyze functions using different representations

9-12.HSF-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.
9-12.HSF-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.

9-12.HSF-IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.		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. Graph quadratic functions in vertex form 5. Graph quadratic functions in standard form
9-12.HSF-IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
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. Graph quadratic functions in vertex form 5. Graph quadratic functions in standard form
9-12.HSF-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.		1. Match exponential functions and graphs II
9-12.HSF-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
1. Match exponential functions and graphs II
9-12.HSF-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
9-12.HSF-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

9-12.HSF-IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.		1. Write a quadratic function in vertex form 2. Solve a quadratic equation by factoring 3. Solve a quadratic equation by completing the square
9-12.HSF-IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
1. Write a quadratic function in vertex form 2. Solve a quadratic equation by factoring 3. Solve a quadratic equation by completing the square
9-12.HSF-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.		1. Exponential functions over unit intervals
9-12.HSF-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
1. Exponential functions over unit intervals
9-12.HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).		1. Compare linear functions: graphs and equations 2. Compare linear functions: tables, graphs, and equations
9-12.HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
1. Compare linear functions: graphs and equations 2. Compare linear functions: tables, graphs, and equations
9-12.HSF-BF Building Functions
9-12.HSF-BF.A Build a function that models a relationship between two quantities
9-12.HSF-BF.A Build a function that models a relationship between two quantities

9-12.HSF-BF.A.1: Write a function that describes a relationship between two quantities.
9-12.HSF-BF.A.1: Write a function that describes a relationship between two quantities.

9-12.HSF-BF.A.1b: Combine standard function types using arithmetic operations.		1. Add and subtract functions 2. Multiply functions
9-12.HSF-BF.A.1b: Combine standard function types using arithmetic operations.
1. Add and subtract functions 2. Multiply functions

9-12.HSF-BF.B Build new functions from existing functions
9-12.HSF-BF.B Build new functions from existing functions

9-12.HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), 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.		Linear functions 1. Transformations of linear functions Quadratic functions 2. Transformations of quadratic functions Absolute value functions 3. Transformations of absolute value functions: translations and reflections 4. Transformations of absolute value functions: translations, reflections, and dilations Function transformations 5. Function transformation rules 6. Translations of functions 7. Reflections of functions 8. Dilations of functions 9. Transformations of functions 10. Describe function transformations
9-12.HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), 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.
Linear functions 1. Transformations of linear functions Quadratic functions 2. Transformations of quadratic functions Absolute value functions 3. Transformations of absolute value functions: translations and reflections 4. Transformations of absolute value functions: translations, reflections, and dilations Function transformations 5. Function transformation rules 6. Translations of functions 7. Reflections of functions 8. Dilations of functions 9. Transformations of functions 10. Describe function transformations
9-12.HSF-LE Linear, Quadratic, and Exponential Models
9-12.HSF-LE.A Construct and compare linear, quadratic, and exponential models and solve problems
9-12.HSF-LE.A Construct and compare linear, quadratic, and exponential models and solve problems

9-12.HSF-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
9-12.HSF-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

9-12.HSF-LE.A.1a: 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
9-12.HSF-LE.A.1a: 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
9-12.HSF-LE.A.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.		Linear rate of change 1. Solve one-step and two-step linear equations: word problems 2. Rate of travel: word problems Identify linear functions 3. Identify linear and exponential functions from graphs
9-12.HSF-LE.A.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Linear rate of change 1. Solve one-step and two-step linear equations: word problems 2. Rate of travel: word problems Identify linear functions 3. Identify linear and exponential functions from graphs
9-12.HSF-LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.		Exponential growth and decay 1. Exponential growth and decay: word problems Identify exponential functions 2. Identify linear and exponential functions from graphs
9-12.HSF-LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Exponential growth and decay 1. Exponential growth and decay: word problems Identify exponential functions 2. Identify linear and exponential functions from graphs
9-12.HSF-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
9-12.HSF-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
9-12.HSF-LE.A.3: Observe using graphs and tables 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
9-12.HSF-LE.A.3: Observe using graphs and tables 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

9-12.HSF-LE.B Interpret expressions for functions in terms of the situation they model
9-12.HSF-LE.B Interpret expressions for functions in terms of the situation they model

9-12.HSF-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
9-12.HSF-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

9-12.HSS	Statistics and Probability
9-12.HSS-ID Interpreting Categorical and Quantitative Data
9-12.HSS-ID.A Summarize, represent, and interpret data on a single count or measurement variable
9-12.HSS-ID.A Summarize, represent, and interpret data on a single count or measurement variable

9-12.HSS-ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).		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
9-12.HSS-ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
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
9-12.HSS-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
9-12.HSS-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
9-12.HSS-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
9-12.HSS-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

9-12.HSS-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables
9-12.HSS-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables

9-12.HSS-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
9-12.HSS-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

9-12.HSS-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.		1. Find the equation of a regression line 2. Analyze a regression line of a data set
9-12.HSS-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
1. Find the equation of a regression line 2. Analyze a regression line of a data set

9-12.HSS-ID.C Interpret linear models
9-12.HSS-ID.C Interpret linear models

9-12.HSS-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
9-12.HSS-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
9-12.HSS-ID.C.9: Distinguish between correlation and causation.		1. Correlation and causation
9-12.HSS-ID.C.9: Distinguish between correlation and causation.
1. Correlation and causation