IXL Skill Plan | Maine Learning Results: Algebra 1

Maine Learning Results: Algebra 1

Skills available for Maine Algebra 1 standards

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Quantitative Reasoning
Algebraic Reasoning
Statistical Reasoning

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Quantitative Reasoning
Number and Quantity: The Real Number System
9-12.QR.A.1 Extend the properties of exponents to rational exponents.
9-12.QR.A.1 Extend the properties of exponents to rational exponents.

HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)³ = 5^(1/3)3 to hold, so (5^1/3)³ must equal 5.		1. Evaluate integers raised to positive rational exponents 2. Evaluate integers raised to rational exponents 3. Convert between rational exponents and radicals
HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)³ = 5^(1/3)3 to hold, so (5^1/3)³ must equal 5.
1. Evaluate integers raised to positive rational exponents 2. Evaluate integers raised to rational exponents 3. Convert between rational exponents and radicals
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
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.QR.A.2 Use properties of rational and irrational numbers.
9-12.QR.A.2 Use properties of rational and irrational numbers.

HSN.RN.B.3: Explain when and why the sum or product of two rational and/or irrational numbers is rational or irrational.		1. Sort rational and irrational numbers 2. Classify rational and irrational numbers 3. Properties of operations on rational and irrational numbers
HSN.RN.B.3: Explain when and why the sum or product of two rational and/or irrational numbers is rational or irrational.
1. Sort rational and irrational numbers 2. Classify rational and irrational numbers 3. Properties of operations on rational and irrational numbers
Checkpoint opportunity		1. Checkpoint: Radicals and rational exponents
Checkpoint opportunity
1. Checkpoint: Radicals and rational exponents
Number and Quantity: Quantities
9-12.QR.A.3 Reason quantitatively and use units to solve problems.
9-12.QR.A.3 Reason quantitatively and use units to solve problems.

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 5 displays. Example: Marlena made a scale drawing of the sand volleyball court at her summer camp. The drawing of the volleyball court is 6 cm long by 3 cm wide. The actual volleyball court is 18 meters long. What scale did Marlena use for the drawing?		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
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 5 displays. Example: Marlena made a scale drawing of the sand volleyball court at her summer camp. The drawing of the volleyball court is 6 cm long by 3 cm wide. The actual volleyball court is 18 meters long. What scale did Marlena use for the drawing?
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
HSN.Q.A.2: Define appropriate quantities for the purpose of descriptive modeling. Example: If a town in Aroostook county with a population of 1254 people is projected to double in size every 105 years, what will the population be 315 years from now?		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
HSN.Q.A.2: Define appropriate quantities for the purpose of descriptive modeling. Example: If a town in Aroostook county with a population of 1254 people is projected to double in size every 105 years, what will the population be 315 years from now?
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
HSN.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Example: The label on a ½ - liter bottle of flavored water bottled in Maine indicates that one serving of 8 ounce contains 60 calories. The label also says that the full bottle contains 130 calories. Is this the actual amount or the estimated amount of calories in this bottle? How would you explain any discrepancy?		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
HSN.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Example: The label on a ½ - liter bottle of flavored water bottled in Maine indicates that one serving of 8 ounce contains 60 calories. The label also says that the full bottle contains 130 calories. Is this the actual amount or the estimated amount of calories in this bottle? How would you explain any discrepancy?
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

Algebraic Reasoning
Algebra: Seeing Structure in Expressions
9-12.AR.A.1 Interpret the structure of expressions.
9-12.AR.A.1 Interpret the structure of expressions.

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

SSE.A.1a: 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
SSE.A.1a: 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
SSE.A.1b: Interpret multi-part expressions by viewing one or more of their parts as a single entity. For example, view P(1+r)ⁿ as the product of P and a factor not depending on P and interpret the parts.		1. Interpret parts of quadratic expressions: word problems
SSE.A.1b: Interpret multi-part expressions by viewing one or more of their parts as a single entity. For example, view P(1+r)ⁿ as the product of P and a factor not depending on P and interpret the parts.
1. Interpret parts of quadratic expressions: word problems
HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ - y⁴ as (x²)² - (y²)², allowing for it to be recognized as a difference of squares that can be factored as (x² - y²)(x² + y²)		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
HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ - y⁴ as (x²)² - (y²)², allowing for it to be recognized as a difference of squares that can be factored as (x² - y²)(x² + y²)
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.AR.A.2 Write expressions in equivalent forms to reveal information and to solve problems.
9-12.AR.A.2 Write expressions in equivalent forms to reveal information and to solve problems.

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.
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.

HSA.SSE.B.3a: Rewrite a quadratic expression (such as by factoring) 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
HSA.SSE.B.3a: Rewrite a quadratic expression (such as by factoring) 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
HSA.SSE.B.3b: Rewrite a quadratic expression (such as by completing the square) 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
HSA.SSE.B.3b: Rewrite a quadratic expression (such as by completing the square) 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
HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.		1. Evaluate expressions using exponent rules 2. Evaluate an exponential function
HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
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
Algebra: Arithmetic with Polynomials & Rational Expressions
9-12.AR.A.3 Perform arithmetic operations on polynomials.
9-12.AR.A.3 Perform arithmetic operations on polynomials.

HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.
HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.

HSA.APR.A.1a: Perform operations on polynomial expressions (addition, subtraction, multiplication, and division), and compare the system of polynomials to the system of integers.		Model 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 Division 10. Divide polynomials by monomials
HSA.APR.A.1a: Perform operations on polynomial expressions (addition, subtraction, multiplication, and division), and compare the system of polynomials to the system of integers.
Model 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 Division 10. Divide polynomials by monomials
HSA.APR.A.1b: Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive Property.		Properties 1. Distributive property 2. Simplify linear expressions using properties 3. Simplify variable expressions involving like terms and the distributive property 4. Identify equivalent linear expressions Factor 5. Sort factors of variable expressions 6. Factor out a monomial 7. Factor quadratics using algebra tiles 8. Factor quadratics with leading coefficient 1 9. Factor quadratics with other leading coefficients 10. Factor quadratics: special cases 11. Factor by grouping 12. Factor polynomials
HSA.APR.A.1b: Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive Property.
Properties 1. Distributive property 2. Simplify linear expressions using properties 3. Simplify variable expressions involving like terms and the distributive property 4. Identify equivalent linear expressions Factor 5. Sort factors of variable expressions 6. Factor out a monomial 7. Factor quadratics using algebra tiles 8. Factor quadratics with leading coefficient 1 9. Factor quadratics with other leading coefficients 10. Factor quadratics: special cases 11. Factor by grouping 12. Factor polynomials
Checkpoint opportunity		1. Checkpoint: Add, subtract, and multiply polynomials
Checkpoint opportunity
1. Checkpoint: Add, subtract, and multiply polynomials
Algebra: Creating Equations and/or Inequalities
9-12.AR.A.7 Create equations and/or inequalities that describe numbers or relationships.
9-12.AR.A.7 Create equations and/or inequalities that describe numbers or relationships.

HSA.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 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
HSA.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 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
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
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
HSA.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods such as lobsters, blueberries, and potatoes.		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
HSA.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods such as lobsters, blueberries, and potatoes.
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
HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.		1. Rearrange multi-variable equations 2. Linear equations: solve for y
HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
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
Algebra: Reasoning with Equations & Inequalities
9-12.AR.A.8 Understand solving equations as a process of reasoning and explain the reasoning.
9-12.AR.A.8 Understand solving equations as a process of reasoning and explain the reasoning.

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 or refute a solution method.		1. Properties of equality 2. Identify equivalent equations 3. Solve linear equations: complete the solution
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 or refute a solution method.
1. Properties of equality 2. Identify equivalent equations 3. Solve linear equations: complete the solution

9-12.AR.A.9 Solve equations and inequalities in one variable.
9-12.AR.A.9 Solve equations and inequalities in one variable.

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

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
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
HSA.REI.B.4b: i): 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.		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 Completing 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
HSA.REI.B.4b: i): 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.
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 Completing the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant
Checkpoint opportunity		1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Quadratic equations
Checkpoint opportunity
1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Quadratic equations

9-12.AR.A.10 Solve systems of equations.
9-12.AR.A.10 Solve systems of equations.

HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.		1. Solve a system of equations using elimination 2. Solve a system of equations using elimination: word problems
HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
1. Solve a system of equations using elimination 2. Solve a system of equations using elimination: word problems
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
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
HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the point(s) of intersection between the line y = -3x and the circle x² + y² = 3.		1. Solve a system of linear and quadratic equations by graphing 2. Solve a system of linear and quadratic equations
HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the point(s) of intersection between the line y = -3x and the circle x² + y² = 3.
1. Solve a system of linear and quadratic equations by graphing 2. Solve a system of linear and quadratic equations

9-12.AR.A.11 Represent and solve equations and inequalities graphically.
9-12.AR.A.11 Represent and solve equations and inequalities graphically.

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). Show that any point on the graph of an equation in two variables is a solution to the equation.		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
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). Show that any point on the graph of an equation in two variables is a solution to the equation.
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
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
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
HSA.REI.D.12: Graph the solutions of 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 of 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
HSA.REI.D.12: Graph the solutions of 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 of 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
Functions: Interpreting Functions
9-12.AR.A.12 Understand the concept of a function and use function notation.
9-12.AR.A.12 Understand the concept of a function and use function notation.

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
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
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
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
HSF.IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.		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
HSF.IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
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

9-12.AR.A.13 Interpret functions that arise in applications in terms of the context.
9-12.AR.A.13 Interpret functions that arise in applications in terms of the context.

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. Key features may include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative and absolute maximums and minimums; symmetries; end behavior; and periodicity.		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
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. Key features may include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative and absolute maximums and minimums; symmetries; end behavior; and periodicity.
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
HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.		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
HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
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
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
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
Checkpoint opportunity		1. Checkpoint: Function concepts 2. Checkpoint: Average rate of change
Checkpoint opportunity
1. Checkpoint: Function concepts 2. Checkpoint: Average rate of change

9-12.AR.A.14 Analyze functions using different representations.
9-12.AR.A.14 Analyze functions using different representations.

HSF.IF.C.7: Graph functions expressed symbolically as well as show and describe key features of the graph, by hand in simple cases and using technology for more complicated cases.
HSF.IF.C.7: Graph functions expressed symbolically as well as show and describe key features of the graph, by hand in simple cases and using technology for more complicated cases.

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. 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
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. 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
HSF.IF.C.7b: i): Graph square root and piecewise-defined functions, (including step functions and absolute value functions), as well as show and describe key features of the graph.		1. Graph piecewise-defined functions 2. Graph an absolute value function 3. Graph square root functions
HSF.IF.C.7b: i): Graph square root and piecewise-defined functions, (including step functions and absolute value functions), as well as show and describe key features of the graph.
1. Graph piecewise-defined functions 2. Graph an absolute value function 3. Graph square root functions
HSF.IF.C.7b: ii): Graph cube root functions, as well as show and describe key features of the graph.
HSF.IF.C.7b: ii): Graph cube root functions, as well as show and describe key features of the graph.

HSF.IF.C.7e: i): Graph exponential functions, showing intercepts and end behavior.		1. Match exponential functions and graphs II
HSF.IF.C.7e: i): Graph exponential functions, showing intercepts and end behavior.
1. Match exponential functions and graphs II
HSF.IF.C.7e: ii): Graph logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline, and amplitude.
HSF.IF.C.7e: ii): Graph logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline, and amplitude.

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.
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.

HSF.IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, maximum and minimum 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
HSF.IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, maximum and minimum 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
HSF.IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions. For example, apply the properties to financial situations such as identifying appreciation and depreciation rate for the value of a house or car sometime after its initial purchase: V_n = P(1 + r)ⁿ.		1. Evaluate an exponential function 2. Match exponential functions and graphs I 3. Match exponential functions and graphs II 4. Exponential functions over unit intervals
HSF.IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions. For example, apply the properties to financial situations such as identifying appreciation and depreciation rate for the value of a house or car sometime after its initial purchase: V_n = P(1 + r)ⁿ.
1. Evaluate an exponential function 2. Match exponential functions and graphs I 3. Match exponential functions and graphs II 4. Exponential functions over unit intervals
HSF.IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.		1. Compare linear functions: graphs and equations 2. Compare linear functions: tables, graphs, and equations
HSF.IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
1. Compare linear functions: graphs and equations 2. Compare linear functions: tables, graphs, and equations
Checkpoint opportunity		1. Checkpoint: Analyze, interpret, and compare functions 2. Checkpoint: Graph and analyze functions
Checkpoint opportunity
1. Checkpoint: Analyze, interpret, and compare functions 2. Checkpoint: Graph and analyze functions
Functions: Building Functions
9-12.AR.A.15 Build a function that models a relationship between two quantities.
9-12.AR.A.15 Build a function that models a relationship between two quantities.

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

HSF.BF.A.1a: 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
HSF.BF.A.1a: 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
HSF.BF.A.1b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.		1. Add and subtract polynomials 2. Multiply polynomials 3. Add and subtract functions 4. Multiply functions
HSF.BF.A.1b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
1. Add and subtract polynomials 2. Multiply polynomials 3. Add and subtract functions 4. Multiply functions
HSF.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.		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
HSF.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.
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

9-12.AR.A.16 Build new functions from existing functions.
9-12.AR.A.16 Build new functions from existing functions.

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 20 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 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
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 20 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 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
HSF.BF.B.4: Find inverse functions.
HSF.BF.B.4: Find inverse functions.

HSF.BF.B.4a: Solve an equation of the form f(x) = c (where c represents the output value of the function) for a simple function f that has an inverse and write an expression for the inverse. For example, if f(x) =2 x³, then solving f(x) = c leads to x = (c/2)^1/3, which is the general formula for finding an input from a specific output, c, for this function.		1. Find the inverse of a linear function
HSF.BF.B.4a: Solve an equation of the form f(x) = c (where c represents the output value of the function) for a simple function f that has an inverse and write an expression for the inverse. For example, if f(x) =2 x³, then solving f(x) = c leads to x = (c/2)^1/3, which is the general formula for finding an input from a specific output, c, for this function.
1. Find the inverse of a linear function
Checkpoint opportunity		1. Checkpoint: Build functions 2. Checkpoint: Function transformations
Checkpoint opportunity
1. Checkpoint: Build functions 2. Checkpoint: Function transformations
Functions: Linear, Quadratic, & Exponential Models
9-12.AR.A.17 Construct and compare linear, quadratic, and exponential models and solve problems.
9-12.AR.A.17 Construct and compare linear, quadratic, and exponential models and solve problems.

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

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
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
HSF.LE.A.1b: 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
HSF.LE.A.1b: 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
HSF.LE.A.1c: 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
HSF.LE.A.1c: 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
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
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
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
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.AR.A.18 Interpret expressions for function in terms of the situation they model.
9-12.AR.A.18 Interpret expressions for function in terms of the situation they model.

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

Statistical Reasoning
Statistics & Probability: Interpreting Categorical & Quantitative Data
9-12.SR.A.1 Summarize, represent, and interpret data on a single count or measurement variable.
9-12.SR.A.1 Summarize, represent, and interpret data on a single count or measurement variable.

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
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
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
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
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
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
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

9-12.SR.A.2 Summarize, represent, and interpret data on two categorical variables and two quantitative variables.
9-12.SR.A.2 Summarize, represent, and interpret data on two categorical variables and two quantitative variables.

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

HSS.ID.B.6a: 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 5. Exponential regression
HSS.ID.B.6a: 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 5. Exponential regression
HSS.ID.B.6b: Informally assess the fit of a function by plotting and analyzing residuals.		1. Interpret a scatter plot
HSS.ID.B.6b: Informally assess the fit of a function by plotting and analyzing residuals.
1. Interpret a scatter plot
HSS.ID.B.6c: Fit a linear function for a scatter plot that suggests a linear association.		1. Write equations for lines of best fit
HSS.ID.B.6c: Fit a linear function for a scatter plot that suggests a linear association.
1. Write equations for lines of best fit
Checkpoint opportunity		1. Checkpoint: Two-way frequency tables
Checkpoint opportunity
1. Checkpoint: Two-way frequency tables

9-12.SR.A.3 Interpret linear models.
9-12.SR.A.3 Interpret linear models.

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
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
HSS.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
HSS.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
HSS.ID.C.9: Distinguish between correlation and causation.		1. Correlation and causation
HSS.ID.C.9: Distinguish between correlation and causation.
1. Correlation and causation
Checkpoint opportunity		1. Checkpoint: Linear modeling
Checkpoint opportunity
1. Checkpoint: Linear modeling