MA.912.A: Algebra

MA.912.A.1: Expand and deepen understanding of real and complex numbers by comparing expressions and performing arithmetic computations, especially those involving square roots and exponents. Use the properties of real numbers to simplify algebraic expressions and equations, and they convert between different measurement units using dimensional analysis.

MA.912.A.1.1: Know equivalent forms of real numbers (including integer exponents and radicals, percents, scientific notation, absolute value, rational numbers, irrational numbers).

 Rational Numbers, Opposites, and Absolute Values
 Square Roots
 Unit Conversions
 Unit Conversions 2 - Scientific Notation and Significant Digits

MA.912.A.1.4: Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real-world problems.

 Percent of Change
 Rational Numbers, Opposites, and Absolute Values
 Square Roots
 Unit Conversions

MA.912.A.1.5: Use dimensional (unit) analysis to perform conversions between units of measure, including rates.

 Unit Conversions

MA.912.A.1.6: Identify the real and imaginary parts of complex numbers and perform basic operations.

 Points in the Complex Plane
 Roots of a Quadratic

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.2.1: Create a graph to represent a real-world situation.

 Quadratics in Polynomial Form

MA.912.A.2.2: Interpret a graph representing a real-world situation.

 Quadratics in Polynomial Form

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.

 Introduction to Functions

MA.912.A.2.5: Graph absolute value equations and inequalities in two variables.

 Absolute Value Equations and Inequalities
 Absolute Value with Linear Functions
 Compound Inequalities

MA.912.A.2.6: Identify and graph common functions (including but not limited to linear, rational, quadratic, cubic, radical, absolute value).

 Absolute Value with Linear Functions
 Addition and Subtraction of Functions
 Arithmetic Sequences
 Compound Interest
 Exponential Functions
 General Form of a Rational Function
 Introduction to Exponential Functions
 Linear Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Rational Functions
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Translating and Scaling Functions
 Zap It! Game

MA.912.A.2.7: Perform operations (addition, subtraction, division and multiplication) of functions algebraically, numerically, and graphically.

 Addition and Subtraction of Functions

MA.912.A.2.9: Recognize, interpret, and graph functions defined piece-wise, with and without technology.

 Absolute Value with Linear Functions

MA.912.A.2.10: Describe and graph transformations of functions.

 Absolute Value with Linear Functions
 Exponential Functions
 Introduction to Exponential Functions
 Quadratics in Vertex Form
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Translations
 Zap It! Game

MA.912.A.2.11: Solve problems involving functions and their inverses.

 Linear Functions
 Logarithmic Functions
 Points, Lines, and Equations

MA.912.A.2.12: Solve problems using direct, inverse, and joint variations.

 Determining a Spring Constant
 Direct and Inverse Variation

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.3.6: Solve and graph the solutions of absolute value equations and inequalities with one variable.

 Absolute Value with Linear Functions
 Compound Inequalities

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 x2+bx+c

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

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+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.4.5: Graph polynomial functions with and without technology and describe end behavior.

 Graphs of Polynomial Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form
 Quadratics in Vertex Form

MA.912.A.4.6: Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes? Rule of Signs, and the Conjugate Root Theorem) to find the zeros of a polynomial function.

 Graphs of Polynomial Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form

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.

 Direct and Inverse Variation

MA.912.A.5.6: Identify removable and non-removable discontinuities and vertical, horizontal, and oblique asymptotes of a graph of a rational function, find the zeros, and graph the function.

 General Form of a Rational Function

MA.912.A.5.7: Solve real-world problems involving rational equations (mixture, distance, work, interest, and ratio).

 Cat and Mouse (Modeling with Linear Systems)
 Compound Interest
 Earthquakes 1 - Recording Station
 Rational Functions

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.6.5: Solve equations that contain radical expressions.

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

MA.912.A.7.3: Solve quadratic equations over the real numbers by completing the square.

 Roots of a Quadratic

MA.912.A.7.4: Use the discriminant to determine the nature of the roots of a quadratic equation.

 Roots of a Quadratic

MA.912.A.7.5: Solve quadratic equations over the complex number system.

 Points in the Complex Plane
 Roots of a Quadratic

MA.912.A.7.6: Identify the axis of symmetry, vertex, domain, range and intercept(s) for a given parabola.

 Parabolas
 Roots of a Quadratic
 Zap It! Game

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

 Addition and Subtraction of Functions

MA.912.A.8: Understand the concepts of logarithmic and exponential functions. Graph exponential functions and solve problems of growth and decay. Understand the inverse relationship between exponents and logarithms and use it to prove laws of logarithms and to solve equations. Convert logarithms between bases and simplify logarithmic expressions.

MA.912.A.8.1: Define exponential and logarithmic functions and determine their relationship.

 Compound Interest
 Exponential Functions
 Logarithmic Functions

MA.912.A.8.3: Graph exponential and logarithmic functions.

 Compound Interest
 Exponential Functions
 Introduction to Exponential Functions
 Logarithmic Functions

MA.912.A.8.5: Solve logarithmic and exponential equations.

 Exponential Functions

MA.912.A.8.7: Solve applications of exponential growth and decay.

 Compound Interest

MA.912.A.9: Write equations and draw graphs of conic sections (circle, ellipse, parabola, and hyperbola), thus relating an algebraic representation to a geometric one.

MA.912.A.9.1: Write the equations of conic sections in standard form and general form, in order to identify the conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).

 Circles
 Ellipses
 Hyperbolas
 Parabolas

MA.912.A.9.2: Graph conic sections with and without using graphing technology.

 Circles
 Ellipses
 Hyperbolas

MA.912.A.9.3: Solve real-world problems involving conic sections.

 Circles

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).

 Linear Functions

Correlation last revised: 5/10/2018

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