A1.N: Number & Operations

A1.N.1: Extend the understanding of number and operations to include square roots and cube roots.

A1.N.1.1: Write square roots and cube roots of monomial algebraic expressions in simplest radical form.

Simplifying Radical Expressions

A1.N.1.2: Add, subtract, multiply, and simplify square roots of monomial algebraic expressions and divide square roots of whole numbers, rationalizing the denominator when necessary.

Simplifying Radical Expressions

A1.A: Algebraic Reasoning & Algebra

A1.A.1: Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context.

A1.A.1.1: Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context.

Absolute Value Equations and Inequalities
Solving Algebraic Equations II
Solving Linear Systems (Standard Form)

A1.A.1.2: Solve absolute value equations and interpret the solutions in the original context.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

A1.A.1.3: Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original context.

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

A1.A.2: Represent and solve real-world and mathematical problems using linear inequalities, compound inequalities and systems of linear inequalities; interpret solutions in the original context.

A1.A.2.1: Represent relationships in various contexts with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

A1.A.2.2: Represent relationships in various contexts with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Solving Linear Inequalities in One Variable

A1.A.2.3: Solve systems of linear inequalities with a maximum of two variables; graph and interpret the solutions on a coordinate plane.

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

A1.A.3: Generate equivalent algebraic expressions and use algebraic properties to evaluate expressions and arithmetic and geometric sequences.

A1.A.3.1: Solve equations involving several variables for one variable in terms of the others.

Area of Triangles
Solving Formulas for any Variable

A1.A.3.2: Simplify polynomial expressions by adding, subtracting, or multiplying.

Addition of Polynomials

A1.A.3.3: Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

A1.A.3.4: Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as a ⊙ b= 2a + b.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Solving Equations by Graphing Each Side
Standard Form of a Line

A1.A.3.5: Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term.

Arithmetic and Geometric Sequences

A1.A.3.6: Recognize that geometric sequences are exponential using equations, tables, graphs and verbal descriptions. Given the formula f(x) = a(r)x, find the next term and define the meaning of a and r within the context of the problem.

Arithmetic and Geometric Sequences

A1.A.4: Analyze mathematical change involving linear equations in real-world and mathematical problems.

A1.A.4.1: Calculate and interpret slope and the x- and y-intercepts of a line using a graph, an equation, two points, or a set of data points to solve real-world and mathematical problems.

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

A1.A.4.2: Solve mathematical and real-world problems involving lines that are parallel, perpendicular, horizontal, or vertical.

Linear Functions
Parallel, Intersecting, and Skew Lines
Point-Slope Form of a Line
Standard Form of a Line

A1.A.4.3: Express linear equations in slope-intercept, point-slope, and standard forms and convert between these forms. Given sufficient information (slope and y-intercept, slope and one-point on the line, two points on the line, x- and y-intercept, or a set of data points), write the equation of a line.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

A1.A.4.4: Translate between a graph and a situation described qualitatively.

Points, Lines, and Equations

A1.F: Functions

A1.F.1: Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems.

A1.F.1.1: Distinguish between relations and functions.

Introduction to Functions
Linear Functions
Points, Lines, and Equations

A1.F.2: Recognize functions and understand that families of functions are characterized by their rate of change.

A1.F.2.1: Distinguish between linear and nonlinear (including exponential) functions arising from real-world and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals.

Absolute Value with Linear Functions
Compound Interest
Direct and Inverse Variation
Linear Functions
Slope-Intercept Form of a Line

A1.F.3: Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems.

A1.F.3.1: Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations.

Arithmetic Sequences
Geometric Sequences
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

A1.F.3.2: Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of real-world and mathematical problems.

Logarithmic Functions

A1.D: Data & Probability

A1.D.1: Display, describe, and compare data. For linear relationships, make predictions and assess the reliability of those predictions.

A1.D.1.1: Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

A1.D.1.2: Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

A1.D.2: Calculate probabilities and apply probability concepts.

A1.D.2.1: Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

Binomial Probabilities
Independent and Dependent Events
Permutations and Combinations

A1.D.2.3: Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability