EI: Equations and Inequalities

EI.1: Interpret key features of an expression (i.e., terms, factors, and coefficients).

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

EI.2: Create expressions that can be modeled by a real-world context.

Linear Inequalities in Two Variables
Using Algebraic Expressions

EI.3: Use the structure of an expression to identify ways to rewrite it.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

EI.4: Simplify and evaluate numerical and algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

EI.5: Compare and contrast an expression and an equation and give examples of each.

Compound Interest
Using Algebraic Equations

EI.6: Given an equation, solve for a specified variable of degree one (i.e. isolate a variable).

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

EI.7: Fluently solve and check multi-step equations and inequalities with an emphasis on the distributive property, variables on both sides, and rational coefficients. Explain each step when solving a multi-step equation and inequality. Justify each step using the properties of real numbers.

Compound Inequalities
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side

EI.8: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently.

Solving Equations on the Number Line

EI.10: Graph the solution point of an equation and the solution set of an inequality in one variable on a horizontal number line. For inequalities, be able to interpret and write the solution set in a variety of ways (e.g., set notation).

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

F: Functions

F.12: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. Use function notation, where appropriate.

Introduction to Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Radical Functions

F.13: Compare and contrast a function and a relation. Use appropriate strategies to assess whether a given situation represents a function or a relation (e.g., the vertical line test).

Introduction to Functions
Linear Functions
Points, Lines, and Equations

F.14: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Introduction to Functions
Logarithmic Functions
Radical Functions

F.15: Determine the rate of change of a linear function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Use the rate of change to determine if two lines are parallel, perpendicular, or neither.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side

F.16: Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Slope-Intercept Form of a Line

F.17: Create and graph the equation of a linear function given the rate of change and y-intercept. Compare and contrast up to three linear functions written in a various forms (i.e., point-slope, slope-intercept, standard form).

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

F.18: Given two points, a graph, a table of values, a mapping, or a real-world context determine the linear function that models this information. Fluently convert between the point-slope, slope-intercept, and standard form of a line.

Absolute Value with Linear Functions
Arithmetic Sequences
Exponential Functions
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

F.19: Create and identify the parent function for linear and quadratic functions in the Coordinate Plane.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions
Zap It! Game

F.20: Compare the properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (Limited to linear and quadratic functions only.)

Graphs of Polynomial Functions
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

F.21: Describe the following characteristics of linear and quadratic parent functions by inspection: domain/range, increasing/decreasing intervals, intercepts, symmetry, and asymptotic behavior. Identify each characteristic in set notation or words, where appropriate.

Exponential Functions
Graphs of Polynomial Functions

F.22: Graph a system of two functions, f(x) and g(x), on the same Coordinate Plane by hand for simple cases, and with technology for complicated cases. Explain the relationship between the point(s) of intersection and the solution to the system. Determine the solution(s) using technology, a tables of values, substitution, or successive approximations. (Limited to linear and quadratic functions only.)

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)

F.23: With accuracy, graph the solutions to a linear inequality in two variables as a half-plane, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes on the same Coordinate Plane. Construct graphs of linear inequalities and systems of linear inequalities without technology. Use appropriate strategies to verify points that may or may not belong to the solution set.

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

F.25: Identify when systems of equations and inequalities have constraints.

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

F.26: Perform simple translations on linear functions given in a variety of forms (e.g., two points, a graph, a table of values, a mapping, slope-intercept form, or standard form). Explain the impact on the parent function when the slope is greater than one or less than one and the effect of increasing/decreasing the y-intercept.

Absolute Value with Linear Functions

F.28: Identify and graph real-world contexts that can be modeled by a quadratic equation.

Addition and Subtraction of Functions
Quadratics in Polynomial Form

F.29: Solve quadratic equations in standard form by factoring, graphing, tables, and the Quadratic Formula. Know when the Quadratic Formula might yield complex solutions and the location of the solutions in relationship to the x-axis. Know suitable alternatives for the terminology “solution of a quadratic” and when each is appropriate to use.

Roots of a Quadratic

P: Polynomials

P.31: Describe and identify a polynomial of degree one, two, three and four by examining a polynomial expression or a graph.

Graphs of Polynomial Functions

P.32: Add and subtract polynomials using appropriate strategies (e.g. by using Algebra Tiles).

Addition and Subtraction of Functions
Addition of Polynomials

P.33: Factor polynomials using the greatest common factor and factor quadratics that have only rational zeros.

Factoring Special Products

P.35: Use the zeros of a polynomial to construct a rough graph of the function.

Polynomials and Linear Factors

G: Geometry

G.36: Explain and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function

G.37: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Circles
Distance Formula

G.38: Fluently use formulas and/or appropriate measuring tools to find length and angle measures, perimeter, area, volume, and surface area of polygons, circles, spheres, cones, cylinders, pyramids, and composite or irregular figures. Use them to solve real-world and mathematical problems.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

S: Statistics

S.40: Without technology, fluently calculate the measures of central tendency (mean, median, mode), measures of spread (range, interquartile range), and understand the impact of extreme values (outliers) on each of these values. Justify which measure is appropriate to use when describing a data set or a real-world context.

Box-and-Whisker Plots
Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

S.41: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

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

S.43: For scatter plots that suggest a linear association, informally fit a straight line and predict the equation for the line of best fit.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

S.44: Justify the relationship between the correlation coefficient and the rate of change for the line of best fit.

Correlation
Solving Using Trend Lines

S.45: Understand the difference between correlation and causation and identify real-world contexts that depict each of them.

Correlation

Correlation last revised: 4/9/2018

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