IXL Skill Plan | Next Generation Learning Standards: Algebra I

Next Generation Learning Standards: Algebra I

Skills available for New York Algebra 1 standards

Domain

Number and Quantity
Algebra
Functions
Statistics and Probability

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

AI-N.RN.3: Use properties and operations to understand the different forms of rational and irrational numbers.
AI-N.RN.3: Use properties and operations to understand the different forms of rational and irrational numbers.

AI-N.RN.3a: Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.		Equivalent forms 1. Write fractions in lowest terms 2. Convert between decimals and fractions Square roots 3. Square roots Integers 4. Add, subtract, multiply, and divide integers 5. Evaluate numerical expressions involving integers 6. Evaluate variable expressions involving integers Rational numbers 7. Add and subtract rational numbers 8. Multiply and divide rational numbers 9. Evaluate numerical expressions involving rational numbers 10. Evaluate variable expressions involving rational numbers
AI-N.RN.3a: Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.
Equivalent forms 1. Write fractions in lowest terms 2. Convert between decimals and fractions Square roots 3. Square roots Integers 4. Add, subtract, multiply, and divide integers 5. Evaluate numerical expressions involving integers 6. Evaluate variable expressions involving integers Rational numbers 7. Add and subtract rational numbers 8. Multiply and divide rational numbers 9. Evaluate numerical expressions involving rational numbers 10. Evaluate variable expressions involving rational numbers
AI-N.RN.3b: Categorize the sum or product of rational or irrational numbers.		1. Sort rational and irrational numbers 2. Classify rational and irrational numbers 3. Properties of operations on rational and irrational numbers
AI-N.RN.3b: Categorize the sum or product of rational or irrational numbers.
1. Sort rational and irrational numbers 2. Classify rational and irrational numbers 3. Properties of operations on rational and irrational numbers
AI-N.Q Quantities
Reason quantitatively and use units to solve problems.
Reason quantitatively and use units to solve problems.

AI-N.Q.1: Select quantities and use units as a way to:
AI-N.Q.1: Select quantities and use units as a way to:

AI-N.Q.1.i: interpret and guide the solution of multi-step problems;		1. Multi-step word problems 2. Scale drawings: word problems 3. Rate of travel: word problems 4. Weighted averages: word problems
AI-N.Q.1.i: interpret and guide the solution of multi-step problems;
1. Multi-step word problems 2. Scale drawings: word problems 3. Rate of travel: word problems 4. Weighted averages: word problems
AI-N.Q.1.ii: choose and interpret units consistently in formulas; and		1. Convert between customary and metric systems 2. Convert between Celsius and Fahrenheit 3. Convert rates and measurements: customary units 4. Convert rates and measurements: metric units 5. Unit prices with unit conversions 6. Multi-step problems with unit conversions
AI-N.Q.1.ii: choose and interpret units consistently in formulas; and
1. Convert between customary and metric systems 2. Convert between Celsius and Fahrenheit 3. Convert rates and measurements: customary units 4. Convert rates and measurements: metric units 5. Unit prices with unit conversions 6. Multi-step problems with unit conversions
AI-N.Q.1.iii: choose and interpret the scale and the origin in graphs and data displays.		1. Coordinate plane review
AI-N.Q.1.iii: choose and interpret the scale and the origin in graphs and data displays.
1. Coordinate plane review
AI-N.Q.3: Choose a level of accuracy appropriate to limitations on measurement and context 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
AI-N.Q.3: Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities.
Precision 1. Precision Greatest possible error 2. Greatest possible error 3. Minimum and maximum area and volume Percent error 4. Percent error 5. Percent error: area and volume
Checkpoint opportunity		1. Checkpoint: Units and quantities
Checkpoint opportunity
1. Checkpoint: Units and quantities

AI-A	Algebra
AI-A.SSE Seeing Structure in Expressions
Interpret the structure of expressions.
Interpret the structure of expressions.

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

AI-A.SSE.1a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.		1. Sort factors of variable expressions 2. Polynomial vocabulary 3. Interpret parts of quadratic expressions: word problems
AI-A.SSE.1a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
1. Sort factors of variable expressions 2. Polynomial vocabulary 3. Interpret parts of quadratic expressions: word problems
AI-A.SSE.1b: Interpret expressions by viewing one or more of their parts as a single entity.		1. Interpret parts of quadratic expressions: word problems
AI-A.SSE.1b: Interpret expressions by viewing one or more of their parts as a single entity.
1. Interpret parts of quadratic expressions: word problems
AI-A.SSE.2: Recognize and 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
AI-A.SSE.2: Recognize and 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

Write expressions in equivalent forms to reveal their characteristics.
Write expressions in equivalent forms to reveal their characteristics.

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

AI-A.SSE.3c: Use the properties of exponents to rewrite exponential expressions.		1. Evaluate expressions using exponent rules 2. Evaluate an exponential function
AI-A.SSE.3c: Use the properties of exponents to rewrite exponential expressions.
1. Evaluate expressions using exponent rules 2. Evaluate an exponential function
Checkpoint opportunity		1. Checkpoint: Interpret equivalent expressions
Checkpoint opportunity
1. Checkpoint: Interpret equivalent expressions
AI-A.APR Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials.
Perform arithmetic operations on polynomials.

AI-A.APR.1: Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.		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
AI-A.APR.1: Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
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
Checkpoint opportunity		1. Checkpoint: Polynomial operations
Checkpoint opportunity
1. Checkpoint: Polynomial operations

Understand the relationship between zeros and factors of polynomials.
Understand the relationship between zeros and factors of polynomials.

AI-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.		1. Characteristics of quadratic functions: equations 2. Match quadratic functions and graphs 3. Solve a quadratic equation using the zero product property
AI-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.
1. Characteristics of quadratic functions: equations 2. Match quadratic functions and graphs 3. Solve a quadratic equation using the zero product property
AI-A.CED Creating Equations
Create equations that describe numbers or relationships.
Create equations that describe numbers or relationships.

AI-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.		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
AI-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.
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
AI-A.CED.2: Create equations and linear inequalities in two variables to represent a real-world context.		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
AI-A.CED.2: Create equations and linear inequalities in two variables to represent a real-world context.
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
AI-A.CED.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
AI-A.CED.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
AI-A.CED.4: Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.		1. Rearrange multi-variable equations 2. Linear equations: solve for y
AI-A.CED.4: Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
1. Rearrange multi-variable equations 2. Linear equations: solve for y
Checkpoint opportunity		1. Checkpoint: Modeling with linear equations and inequalities 2. Checkpoint: Modeling with linear, quadratic, and exponential equations and inequalities
Checkpoint opportunity
1. Checkpoint: Modeling with linear equations and inequalities 2. Checkpoint: Modeling with linear, quadratic, and exponential equations and inequalities
AI-A.REI Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
Understand solving equations as a process of reasoning and explain the reasoning.

AI-A.REI.1a: Explain each step when solving a linear or quadratic 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
AI-A.REI.1a: Explain each step when solving a linear or quadratic 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

Solve equations and inequalities in one variable.
Solve equations and inequalities in one variable.

AI-A.REI.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
AI-A.REI.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
AI-A.REI.4: Solve quadratic equations in one variable.
AI-A.REI.4: Solve quadratic equations in one variable.

AI-A.REI.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. Understand that the quadratic formula is a derivative of this process.		1. Complete the square
AI-A.REI.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. Understand that the quadratic formula is a derivative of this process.
1. Complete the square
AI-A.REI.4b: Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in a + bi form.		Square roots 1. Solve a quadratic equation using square roots Factoring 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring Complete the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant Any method 8. Solve quadratic equations: word problems
AI-A.REI.4b: Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in a + bi form.
Square roots 1. Solve a quadratic equation using square roots Factoring 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring Complete the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant Any method 8. Solve quadratic equations: word problems
Checkpoint opportunity		1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Quadratic equations
Checkpoint opportunity
1. Checkpoint: Solve linear equations and inequalities 2. Checkpoint: Quadratic equations

Solve systems of equations.
Solve systems of equations.

AI-A.REI.6a: Solve systems of linear equations in two variables both algebraically and graphically.		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 5. Classify a system of equations Graphing 6. Solve a system of equations by graphing 7. Solve a system of equations by graphing: word problems Substitution 8. Solve a system of equations using substitution 9. Solve a system of equations using substitution: word problems Elimination 10. Solve a system of equations using elimination 11. Solve a system of equations using elimination: word problems Any method 12. Solve a system of equations using any method 13. Solve a system of equations using any method: word problems
AI-A.REI.6a: Solve systems of linear equations in two variables both algebraically and graphically.
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 5. Classify a system of equations Graphing 6. Solve a system of equations by graphing 7. Solve a system of equations by graphing: word problems Substitution 8. Solve a system of equations using substitution 9. Solve a system of equations using substitution: word problems Elimination 10. Solve a system of equations using elimination 11. Solve a system of equations using elimination: word problems Any method 12. Solve a system of equations using any method 13. Solve a system of equations using any method: word problems
AI-A.REI.7a: Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.		1. Solve a system of linear and quadratic equations by graphing 2. Solve a system of linear and quadratic equations
AI-A.REI.7a: Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.
1. Solve a system of linear and quadratic equations by graphing 2. Solve a system of linear and quadratic equations

Represent and solve equations and inequalities graphically.
Represent and solve equations and inequalities graphically.

AI-A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.		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
AI-A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
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
AI-A.REI.11: Given the equations y = f(x) and y = g(x):
AI-A.REI.11: Given the equations y = f(x) and y = g(x):

AI-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
AI-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);

AI-A.REI.11.ii: find the solutions approximately using technology to graph the functions or make tables of values; and		Tables 1. Find solutions using a table 2. Approximate solutions using a table Graphs 3. Solve a system of equations by graphing 4. Find the number of solutions to a system of equations by graphing
AI-A.REI.11.ii: find the solutions approximately using technology to graph the functions or make tables of values; and
Tables 1. Find solutions using a table 2. Approximate solutions using a table Graphs 3. Solve a system of equations by graphing 4. Find the number of solutions to a system of equations by graphing
AI-A.REI.11.iii: interpret the solution in context.		1. Solve a system of equations by graphing: word problems
AI-A.REI.11.iii: interpret the solution in context.
1. Solve a system of equations by graphing: word problems
AI-A.REI.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
AI-A.REI.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
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

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

AI-F.IF.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
AI-F.IF.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
AI-F.IF.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
AI-F.IF.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
AI-F.IF.3: Recognize that a sequence is a function whose domain is a subset of the integers.		Arithmetic sequences 1. Arithmetic sequences 2. Write variable expressions for arithmetic sequences Geometric sequences 3. Geometric sequences 4. Write variable expressions for geometric sequences Recursive formulas 5. Evaluate recursive formulas for sequences 6. Write a formula for a recursive sequence Explicit and recursive sequences 7. Identify a sequence as explicit or recursive Mixed sequences 8. Identify arithmetic and geometric sequences 9. Evaluate variable expressions for number sequences 10. Sequences: mixed review
AI-F.IF.3: Recognize that a sequence is a function whose domain is a subset of the integers.
Arithmetic sequences 1. Arithmetic sequences 2. Write variable expressions for arithmetic sequences Geometric sequences 3. Geometric sequences 4. Write variable expressions for geometric sequences Recursive formulas 5. Evaluate recursive formulas for sequences 6. Write a formula for a recursive sequence Explicit and recursive sequences 7. Identify a sequence as explicit or recursive Mixed sequences 8. Identify arithmetic and geometric sequences 9. Evaluate variable expressions for number sequences 10. Sequences: mixed review

Interpret functions that arise in applications in terms of the context.
Interpret functions that arise in applications in terms of the context.

AI-F.IF.4: For a function that models a relationship between two quantities:
AI-F.IF.4: For a function that models a relationship between two quantities:

AI-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and		Rate of change 1. Rate of change: tables 2. Rate of change: graphs Proportional relationships 3. Identify proportional relationships by graphing 4. Find the constant of proportionality from tables and graphs Linear functions 5. Find the slope of a graph 6. Slope-intercept form: find the slope and y-intercept 7. Standard form: find x- and y-intercepts 8. Slopes of parallel and perpendicular lines 9. Identify linear functions from graphs and equations 10. Identify linear functions from tables Quadratic functions 11. Characteristics of quadratic functions: graphs 12. Match quadratic functions and graphs Exponential functions 13. Match exponential functions and graphs I 14. Match exponential functions and graphs II Rational functions 15. Rational functions: asymptotes and excluded values Linear, quadratic, and exponential functions 16. Identify linear, quadratic, and exponential functions from graphs 17. Identify linear, quadratic, and exponential functions from tables Word problems 18. Evaluate a linear function from its graph: word problems
AI-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and
Rate of change 1. Rate of change: tables 2. Rate of change: graphs Proportional relationships 3. Identify proportional relationships by graphing 4. Find the constant of proportionality from tables and graphs Linear functions 5. Find the slope of a graph 6. Slope-intercept form: find the slope and y-intercept 7. Standard form: find x- and y-intercepts 8. Slopes of parallel and perpendicular lines 9. Identify linear functions from graphs and equations 10. Identify linear functions from tables Quadratic functions 11. Characteristics of quadratic functions: graphs 12. Match quadratic functions and graphs Exponential functions 13. Match exponential functions and graphs I 14. Match exponential functions and graphs II Rational functions 15. Rational functions: asymptotes and excluded values Linear, quadratic, and exponential functions 16. Identify linear, quadratic, and exponential functions from graphs 17. Identify linear, quadratic, and exponential functions from tables Word problems 18. Evaluate a linear function from its graph: word problems
AI-F.IF.4.ii: sketch graphs showing key features given a verbal description of the relationship.		Proportional relationships 1. Graph a proportional relationship Linear functions 2. Complete a table and graph a linear function Quadratic functions 3. Graph quadratic functions in vertex form 4. Use zeros to match quadratic functions and graphs Absolute value functions 5. Graph an absolute value function Exponential functions 6. Graph exponential functions
AI-F.IF.4.ii: sketch graphs showing key features given a verbal description of the relationship.
Proportional relationships 1. Graph a proportional relationship Linear functions 2. Complete a table and graph a linear function Quadratic functions 3. Graph quadratic functions in vertex form 4. Use zeros to match quadratic functions and graphs Absolute value functions 5. Graph an absolute value function Exponential functions 6. Graph exponential functions
AI-F.IF.5: Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.		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
AI-F.IF.5: Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
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
AI-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.		1. Rate of change: tables 2. Rate of change: graphs
AI-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.
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

Analyze functions using different representations.
Analyze functions using different representations.

AI-F.IF.7: Graph functions and show key features of the graph by hand and by using technology where appropriate.
AI-F.IF.7: Graph functions and show key features of the graph by hand and by using technology where appropriate.

AI-F.IF.7a: Graph linear, quadratic, and exponential functions and show key features.		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
AI-F.IF.7a: Graph linear, quadratic, and exponential functions and show key features.
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
AI-F.IF.7b: Graph square root and piecewise-defined functions, including step functions and absolute value functions, and show key features.		1. Graph piecewise-defined functions 2. Graph an absolute value function 3. Graph square root functions 4. Graph cube root functions
AI-F.IF.7b: Graph square root and piecewise-defined functions, including step functions and absolute value functions, and show key features.
1. Graph piecewise-defined functions 2. Graph an absolute value function 3. Graph square root functions 4. Graph cube root functions
AI-F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.
AI-F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.

AI-F.IF.8a: For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of 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
AI-F.IF.8a: For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of 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
AI-F.IF.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
AI-F.IF.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
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
AI-F.BF Building Functions
Build a function that models a relationship between two quantities.
Build a function that models a relationship between two quantities.

AI-F.BF.1: Write a function that describes a relationship between two quantities.
AI-F.BF.1: Write a function that describes a relationship between two quantities.

AI-F.BF.1a: Determine a function from context. Define a sequence explicitly 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
AI-F.BF.1a: Determine a function from context. Define a sequence explicitly 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

Build new functions from existing functions.
Build new functions from existing functions.

AI-F.BF.3a: Using f(x) + k, k f(x), and f(x + k):
AI-F.BF.3a: Using f(x) + k, k f(x), and f(x + k):

AI-F.BF.3a.i: identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative);		1. Function transformation rules 2. Describe function transformations
AI-F.BF.3a.i: identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative);
1. Function transformation rules 2. Describe function transformations
AI-F.BF.3a.ii: find the value of k given the graphs;		1. Translations of functions 2. Reflections of functions 3. Dilations of functions
AI-F.BF.3a.ii: find the value of k given the graphs;
1. Translations of functions 2. Reflections of functions 3. Dilations of functions
AI-F.BF.3a.iii: write a new function using the value of k; and		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
AI-F.BF.3a.iii: write a new function using the value of k; and
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
AI-F.BF.3a.iv: use technology to experiment with cases and explore the effects on the graph.
AI-F.BF.3a.iv: use technology to experiment with cases and explore the effects on the graph.

Checkpoint opportunity		1. Checkpoint: Function transformations 2. Checkpoint: Build functions
Checkpoint opportunity
1. Checkpoint: Function transformations 2. Checkpoint: Build functions
AI-F.LE Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems.
Construct and compare linear, quadratic, and exponential models and solve problems.

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

AI-F.LE.1a: Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows 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
AI-F.LE.1a: Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows 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
AI-F.LE.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.		1. Identify linear and exponential functions from graphs 2. Identify linear and exponential functions from tables 3. Write linear and exponential functions: word problems
AI-F.LE.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
1. Identify linear and exponential functions from graphs 2. Identify linear and exponential functions from tables 3. Write linear and exponential functions: word problems
AI-F.LE.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.		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
AI-F.LE.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.
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
AI-F.LE.2: Construct a linear or exponential function symbolically given:
AI-F.LE.2: Construct a linear or exponential function symbolically given:

AI-F.LE.2.i: a graph;		Linear functions 1. Slope-intercept form: write an equation from a graph 2. Point-slope form: write an equation from a graph Exponential functions 3. Match exponential functions and graphs II
AI-F.LE.2.i: a graph;
Linear functions 1. Slope-intercept form: write an equation from a graph 2. Point-slope form: write an equation from a graph Exponential functions 3. Match exponential functions and graphs II
AI-F.LE.2.ii: a description of the relationship;		Linear functions 1. Slope-intercept form: write an equation 2. Point-slope form: write an equation 3. Write a linear function: word problems Arithmetic and geometric sequences 4. Write variable expressions for arithmetic sequences 5. Write variable expressions for geometric sequences 6. Write a formula for a recursive sequence
AI-F.LE.2.ii: a description of the relationship;
Linear functions 1. Slope-intercept form: write an equation 2. Point-slope form: write an equation 3. Write a linear function: word problems Arithmetic and geometric sequences 4. Write variable expressions for arithmetic sequences 5. Write variable expressions for geometric sequences 6. Write a formula for a recursive sequence
AI-F.LE.2.iii: two input-output pairs (include reading these from a table).		1. Slope-intercept form: write an equation from a table 2. Write linear and exponential functions from tables
AI-F.LE.2.iii: two input-output pairs (include reading these from a table).
1. Slope-intercept form: write an equation from a table 2. Write linear and exponential functions from tables
AI-F.LE.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
AI-F.LE.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

Interpret expressions for functions in terms of the situation they model.
Interpret expressions for functions in terms of the situation they model.

AI-F.LE.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
AI-F.LE.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

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

AI-S.ID.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
AI-S.ID.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
AI-S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample 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
AI-S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample 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
AI-S.ID.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
AI-S.ID.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

Summarize, represent, and interpret data on two categorical and quantitative variables.
Summarize, represent, and interpret data on two categorical and quantitative variables.

AI-S.ID.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
AI-S.ID.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
AI-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variables' values are related.
AI-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variables' values are related.

AI-S.ID.6a: Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.		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
AI-S.ID.6a: Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
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
Checkpoint opportunity		1. Checkpoint: Two-way frequency tables
Checkpoint opportunity
1. Checkpoint: Two-way frequency tables

Interpret linear models.
Interpret linear models.

AI-S.ID.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
AI-S.ID.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
AI-S.ID.8: Calculate (using technology) and interpret the correlation coefficient of a linear fit.		1. Match correlation coefficients to scatter plots 2. Calculate correlation coefficients
AI-S.ID.8: Calculate (using technology) and interpret the correlation coefficient of a linear fit.
1. Match correlation coefficients to scatter plots 2. Calculate correlation coefficients
AI-S.ID.9: Distinguish between correlation and causation.		1. Correlation and causation
AI-S.ID.9: Distinguish between correlation and causation.
1. Correlation and causation
Checkpoint opportunity		1. Checkpoint: Linear modeling
Checkpoint opportunity
1. Checkpoint: Linear modeling