End of Course Specifications: Benchmarks

MA.912.A: Algebra

MA.912.A.2: Draw and interpret graphs of relations. Understand the notation and concept of a function, find domains and ranges, and link equations to functions.

MA.912.A.2.3: Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.

Introduction to Functions

Linear Functions

Points, Lines, and Equations

MA.912.A.2.4: Determine the domain and range of a relation.

MA.912.A.3: Solve linear equations and inequalities.

MA.912.A.3.1: Solve linear equations in one variable that include simplifying algebraic expressions.

Solving Algebraic Equations II

MA.912.A.3.2: Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Square Roots

MA.912.A.3.3: Solve literal equations for a specified variable.

Area of Triangles

Solving Formulas for any Variable

MA.912.A.3.4: Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.

Absolute Value Equations and Inequalities

Comparing and Ordering Decimals

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Quadratic Inequalities

Solving Linear Inequalities in One Variable

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.5: Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

Compound Inequalities

Linear Inequalities in Two Variables

Solving Equations by Graphing Each Side

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.7: Rewrite equations of a line into slope-intercept form and standard form.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.8: Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.9: Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.

Cat and Mouse (Modeling with Linear Systems)

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.10: Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.11: Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

Least-Squares Best Fit Lines

Solving Using Trend Lines

MA.912.A.3.12: Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.

Absolute Value with Linear Functions

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Quadratic Inequalities

Slope-Intercept Form of a Line

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.13: Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

Solving Linear Systems (Slope-Intercept Form)

MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.

Cat and Mouse (Modeling with Linear Systems)

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.15: Solve real-world problems involving systems of linear equations and inequalities in two and three variables.

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.4: Perform operations on polynomials. Find factors of polynomials, learning special techniques for factoring quadratics. Understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the factors of a polynomial.

MA.912.A.4.1: Simplify monomials and monomial expressions using the laws of integral exponents.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions II

MA.912.A.4.2: Add, subtract, and multiply polynomials.

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

MA.912.A.4.3: Factor polynomial expressions.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

MA.912.A.4.4: Divide polynomials by monomials and polynomials with various techniques, including synthetic division.

Dividing Exponential Expressions

Dividing Polynomials Using Synthetic Division

MA.912.A.5: Simplify rational expressions and solve rational equations using what they have learned about factoring polynomials.

MA.912.A.5.4: Solve algebraic proportions.

MA.912.A.6: Simplify and perform operations on radical expressions and equations. Rationalize square root expressions and understand and use the concepts of negative and rational exponents. Add, subtract, multiply, divide, and simplify radical expressions and expressions with rational exponents. Solve radical equations and equations with terms that have rational exponents.

MA.912.A.6.1: Simplify radical expressions.

Operations with Radical Expressions

Simplifying Radical Expressions

MA.912.A.6.2: Add, subtract, multiply and divide radical expressions (square roots and higher).

Operations with Radical Expressions

MA.912.A.7: Draw graphs of quadratic functions. Solve quadratic equations and solve these equations by factoring, completing the square and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadratic equations.

MA.912.A.7.1: Graph quadratic equations with and without graphing technology.

Parabolas

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

MA.912.A.7.2: Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Roots of a Quadratic

MA.912.A.7.8: Use quadratic equations to solve real-world problems.

Addition and Subtraction of Functions

MA.912.A.10: In a general sense, all of mathematics is problem solving. In all of mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results

MA.912.A.10.1: Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guessing- and-checking, solving a simpler problem, writing an equation, working backwards, and creating a table.

Absolute Value Equations and Inequalities

Solving Equations on the Number Line

Using Algebraic Equations

MA.912.A.10.3: Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions).

MA.912.D: Discrete Mathematics

MA.912.D.7: Operate with sets and use set theory to solve problems.

MA.912.D.7.1: Perform set operations such as union and intersection, complement, and cross product.

MA.912.G.1: Understand geometric concepts, applications, and their representations with coordinate systems. Find lengths and midpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass and straightedge, patty paper, a drawing program or other techniques, students also construct lines and angles, explaining and justifying the processes used.

MA.912.G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Point-Slope Form of a Line

Points, Lines, and Equations

Correlation last revised: 1/22/2020

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