IXL Skill Plan | Illinois Priority Learning Standards: Mathematics III

Illinois Priority Learning Standards: Mathematics III

Skills available for Illinois Integrated 3 math standards

Section

Algebra
Functions
Statistics and Probability

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

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

9-12.HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.		1. Polynomial vocabulary
9-12.HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
1. Polynomial vocabulary
9-12.HSA-SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.		1. Factor using a quadratic pattern
9-12.HSA-SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
1. Factor using a quadratic pattern
9-12.HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.		Polynomial expressions 1. Factor out a monomial 2. Factor using a quadratic pattern 3. Factor by grouping 4. Factor sums and differences of cubes 5. Factor polynomials Binomial Theorem 6. Pascal's triangle and the Binomial Theorem 7. Binomial Theorem I 8. Binomial Theorem II Radical expressions 9. Simplify radical expressions with variables I 10. Simplify radical expressions with variables II 11. Simplify radical expressions using conjugates Rational expressions 12. Simplify rational expressions
9-12.HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Polynomial expressions 1. Factor out a monomial 2. Factor using a quadratic pattern 3. Factor by grouping 4. Factor sums and differences of cubes 5. Factor polynomials Binomial Theorem 6. Pascal's triangle and the Binomial Theorem 7. Binomial Theorem I 8. Binomial Theorem II Radical expressions 9. Simplify radical expressions with variables I 10. Simplify radical expressions with variables II 11. Simplify radical expressions using conjugates Rational expressions 12. Simplify rational expressions

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

9-12.HSA-SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.		1. Find the sum of a finite geometric series
9-12.HSA-SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
1. Find the sum of a finite geometric series
9-12.HSA-APR Arithmetic with Polynomials and Rational Expressions
9-12.HSA-APR.A Perform arithmetic operations on polynomials
9-12.HSA-APR.A Perform arithmetic operations on polynomials

9-12.HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.		1. Add and subtract polynomials 2. Multiply polynomials
9-12.HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
1. Add and subtract polynomials 2. Multiply polynomials

9-12.HSA-APR.B Understand the relationship between zeros and factors of polynomials
9-12.HSA-APR.B Understand the relationship between zeros and factors of polynomials

9-12.HSA-APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.		Quadratics 1. Solve a quadratic equation using the zero product property 2. Use zeros to match quadratic functions and graphs Polynomials 3. Find the roots of factored polynomials 4. Match polynomials and graphs using zeros
9-12.HSA-APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Quadratics 1. Solve a quadratic equation using the zero product property 2. Use zeros to match quadratic functions and graphs Polynomials 3. Find the roots of factored polynomials 4. Match polynomials and graphs using zeros
9-12.HSA-CED Creating Equations
9-12.HSA-CED.A Create equations that describe numbers or relationships
9-12.HSA-CED.A Create equations that describe numbers or relationships

9-12.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.		1. Solve quadratic equations: word problems 2. Write exponential functions: word problems
9-12.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
1. Solve quadratic equations: word problems 2. Write exponential functions: word problems
9-12.HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.		Linear equations 1. Write the equation of a linear function Absolute value equations 2. Graph an absolute value function Quadratic equations 3. Graph a quadratic function 4. Write a quadratic function in vertex form from its vertex and another point 5. Write a quadratic function in factored form from its x-intercepts and another point Radical equations 6. Graph square root functions 7. Graph cube root functions Exponential and logarithmic equations 8. Write exponential functions: word problems 9. Graph exponential functions 10. Graph logarithmic functions Trigonometric equations 11. Write equations of sine functions from graphs 12. Write equations of sine functions using properties 13. Graph sine functions 14. Write equations of cosine functions from graphs 15. Write equations of cosine functions using properties 16. Graph cosine functions 17. Write equations of sine and cosine functions from graphs 18. Write equations of sine and cosine functions using properties 19. Graph sine and cosine functions
9-12.HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Linear equations 1. Write the equation of a linear function Absolute value equations 2. Graph an absolute value function Quadratic equations 3. Graph a quadratic function 4. Write a quadratic function in vertex form from its vertex and another point 5. Write a quadratic function in factored form from its x-intercepts and another point Radical equations 6. Graph square root functions 7. Graph cube root functions Exponential and logarithmic equations 8. Write exponential functions: word problems 9. Graph exponential functions 10. Graph logarithmic functions Trigonometric equations 11. Write equations of sine functions from graphs 12. Write equations of sine functions using properties 13. Graph sine functions 14. Write equations of cosine functions from graphs 15. Write equations of cosine functions using properties 16. Graph cosine functions 17. Write equations of sine and cosine functions from graphs 18. Write equations of sine and cosine functions using properties 19. Graph sine and cosine functions
9-12.HSA-CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.		Linear inequalities 1. Write two-variable linear inequalities: word problems Systems of equations 2. Solve a system of equations by graphing: word problems 3. Solve a system of equations using substitution: word problems 4. Solve a system of equations using elimination: word problems 5. Solve a system of equations using any method: word problems
9-12.HSA-CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
Linear inequalities 1. Write two-variable linear inequalities: word problems Systems of equations 2. Solve a system of equations by graphing: word problems 3. Solve a system of equations using substitution: word problems 4. Solve a system of equations using elimination: word problems 5. Solve a system of equations using any method: word problems
9-12.HSA-REI Reasoning with Equations and Inequalities
9-12.HSA-REI.D Represent and solve equations and inequalities graphically
9-12.HSA-REI.D Represent and solve equations and inequalities graphically

9-12.HSA-REI.D.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
9-12.HSA-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Tables 1. Find solutions using a table 2. Approximate solutions using a table Graphs 3. Solve a system of equations by graphing 4. Solve a system of equations by graphing: word problems 5. Find the number of solutions to a system of equations

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

9-12.HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.		Linear functions 1. Find the slope of a linear function 2. Graph a linear function Absolute value functions 3. Graph an absolute value function Quadratic functions 4. Characteristics of quadratic functions: graphs 5. Characteristics of quadratic functions: equations 6. Graph a quadratic function 7. Match quadratic functions and graphs Polynomial functions 8. Match polynomials and graphs Radical functions 9. Graph square root functions 10. Graph cube root functions Rational functions 11. Rational functions: asymptotes and excluded values Exponential and logarithmic functions 12. Graph exponential functions 13. Match exponential functions and graphs 14. Graph logarithmic functions Word problems 15. Identify graphs: word problems
9-12.HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Linear functions 1. Find the slope of a linear function 2. Graph a linear function Absolute value functions 3. Graph an absolute value function Quadratic functions 4. Characteristics of quadratic functions: graphs 5. Characteristics of quadratic functions: equations 6. Graph a quadratic function 7. Match quadratic functions and graphs Polynomial functions 8. Match polynomials and graphs Radical functions 9. Graph square root functions 10. Graph cube root functions Rational functions 11. Rational functions: asymptotes and excluded values Exponential and logarithmic functions 12. Graph exponential functions 13. Match exponential functions and graphs 14. Graph logarithmic functions Word problems 15. Identify graphs: word problems
9-12.HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.		Absolute value functions 1. Domain and range of absolute value functions: graphs 2. Domain and range of absolute value functions: equations Quadratic functions 3. Domain and range of quadratic functions: graphs 4. Domain and range of quadratic functions: equations Polynomial functions 5. Domain and range of polynomials Radical functions 6. Domain and range of radical functions Exponential and logarithmic functions 7. Domain and range of exponential functions 8. Domain and range of logarithmic functions
9-12.HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Absolute value functions 1. Domain and range of absolute value functions: graphs 2. Domain and range of absolute value functions: equations Quadratic functions 3. Domain and range of quadratic functions: graphs 4. Domain and range of quadratic functions: equations Polynomial functions 5. Domain and range of polynomials Radical functions 6. Domain and range of radical functions Exponential and logarithmic functions 7. Domain and range of exponential functions 8. Domain and range of logarithmic functions
9-12.HSF-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.		1. Average rate of change
9-12.HSF-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
1. Average rate of change

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

9-12.HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

9-12.HSF-IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.		1. Match polynomials and graphs
9-12.HSF-IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
1. Match polynomials and graphs
9-12.HSF-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.		Exponential functions 1. Match exponential functions and graphs Sine functions 2. Find properties of sine functions 3. Graph sine functions 4. Graph translations of sine functions Cosine functions 5. Find properties of cosine functions 6. Graph cosine functions 7. Graph translations of cosine functions
9-12.HSF-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Exponential functions 1. Match exponential functions and graphs Sine functions 2. Find properties of sine functions 3. Graph sine functions 4. Graph translations of sine functions Cosine functions 5. Find properties of cosine functions 6. Graph cosine functions 7. Graph translations of cosine functions
9-12.HSF-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
9-12.HSF-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

9-12.HSF-IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.		1. Solve a quadratic equation by factoring 2. Solve a quadratic equation by completing the square
9-12.HSF-IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
1. Solve a quadratic equation by factoring 2. Solve a quadratic equation by completing the square
9-12.HSF-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.		1. Evaluate exponential functions 2. Solve exponential equations by rewriting the base
9-12.HSF-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
1. Evaluate exponential functions 2. Solve exponential equations by rewriting the base
9-12.HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
9-12.HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

9-12.HSF-BF Building Functions
9-12.HSF-BF.A Build a function that models a relationship between two quantities
9-12.HSF-BF.A Build a function that models a relationship between two quantities

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

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

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

9-12.HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.		Translations 1. Translations of functions Reflections 2. Reflections of functions Dilations 3. Dilations of functions Mixed transformations 4. Transformations of absolute value functions 5. Function transformation rules 6. Transformations of functions 7. Describe function transformations
9-12.HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Translations 1. Translations of functions Reflections 2. Reflections of functions Dilations 3. Dilations of functions Mixed transformations 4. Transformations of absolute value functions 5. Function transformation rules 6. Transformations of functions 7. Describe function transformations

9-12.HSS	Statistics and Probability
9-12.HSS-IC Making Inferences and Justifying Conclusions
9-12.HSS-IC.A Understand and evaluate random processes underlying statistical experiments
9-12.HSS-IC.A Understand and evaluate random processes underlying statistical experiments

9-12.HSS-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.		1. Identify biased samples
9-12.HSS-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
1. Identify biased samples

9-12.HSS-IC.B Make inferences and justify conclusions from sample surveys, experiments, and observational studies
9-12.HSS-IC.B Make inferences and justify conclusions from sample surveys, experiments, and observational studies

9-12.HSS-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.		1. Experiment design
9-12.HSS-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
1. Experiment design