1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.

1.A: apply mathematics to problems arising in everyday life, society, and the workplace;

Determining a Spring Constant
Estimating Population Size

1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Estimating Population Size

1.C: select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

Estimating Sums and Differences

1.D: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

Biconditional Statements
Using Algebraic Expressions

1.E: create and use representations to organize, record, and communicate mathematical ideas;

Describing Data Using Statistics
Stem-and-Leaf Plots
Using Algebraic Expressions

1.G: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Using Algebraic Expressions

2: The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.

2.A: determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;

Function Machines 3 (Functions and Problem Solving)

2.B: write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y? = m(x - x?), given one point and the slope and given two points;

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

2.C: write linear equations in two variables given a table of values, a graph, and a verbal description;

Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

2.D: write and solve equations involving direct variation;

Direct and Inverse Variation

2.G: write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined;

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

2.H: write linear inequalities in two variables given a table of values, a graph, and a verbal description; and

Linear Inequalities in Two Variables
Systems of Linear Inequalities (Slope-intercept form)

2.I: write systems of two linear equations given a table of values, a graph, and a verbal description.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

3: The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.

3.A: determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y? = m(x - x?);

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

3.B: calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Function Machines 1 (Functions and Tables)
Points, Lines, and Equations
Slope-Intercept Form of a Line

3.C: graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems;

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

3.D: graph the solution set of linear inequalities in two variables on the coordinate plane;

Linear Inequalities in Two Variables
Systems of Linear Inequalities (Slope-intercept form)

3.E: determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d;

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Rational Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions
Translations

3.F: graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Systems of Linear Inequalities (Slope-intercept form)

3.G: estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)

3.H: graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

4: The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.

4.A: calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;

Correlation

4.B: compare and contrast association and causation in real-world problems; and

Correlation

4.C: write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

5: The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

5.A: solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

5.B: solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and

Compound Inequalities
Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

5.C: solve systems of two linear equations with two variables for mathematical and real-world problems.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6: The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.

6.B: write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)²+ k), and rewrite the equation from vertex form to standard form (f(x) = ax²+ bx + c); and

Parabolas

6.C: write quadratic functions when given real solutions and graphs of their related equations.

Quadratics in Polynomial Form

7: The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.

7.A: graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry;

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Translating and Scaling Functions

7.B: describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and

Modeling the Factorization of x2+bx+c
Quadratics in Factored Form

7.C: determine the effects on the graph of the parent function f(x) = x² when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Translating and Scaling Functions
Translations
Zap It! Game

8: The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

8.A: solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and

Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
Roots of a Quadratic

9: The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

9.A: determine the domain and range of exponential functions of the form f(x) = ab to the x power and represent the domain and range using inequalities;

Exponential Functions
Logarithmic Functions

9.B: interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab to the x power in real-world problems;

Compound Interest
Introduction to Exponential Functions

9.C: write exponential functions in the form f(x) = ab to the x power (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

Compound Interest
Introduction to Exponential Functions

9.D: graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; and

Compound Interest
Introduction to Exponential Functions
Logarithmic Functions

10: The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

10.A: add and subtract polynomials of degree one and degree two;

Addition and Subtraction of Functions
Addition of Polynomials

10.B: multiply polynomials of degree one and degree two;

Modeling the Factorization of x2+bx+c

10.C: determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend;

Dividing Polynomials Using Synthetic Division

10.D: rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;

Modeling the Factorization of x2+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

10.E: factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two; and

Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

10.F: decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

Factoring Special Products

11: The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

11.A: simplify numerical radical expressions involving square roots; and

Operations with Radical Expressions
Simplifying Radical Expressions

11.B: simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

12: The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

12.A: decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;

Introduction to Functions
Linear Functions
Points, Lines, and Equations

12.B: evaluate functions, expressed in function notation, given one or more elements in their domains;

Logarithmic Functions

12.C: identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes;

Arithmetic Sequences
Geometric Sequences

12.D: write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; and

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

12.E: solve mathematic and scientific formulas, and other literal equations, for a specified variable.

Area of Triangles
Solving Formulas for any Variable

Correlation last revised: 9/24/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.