AR.Math.Content.8.NS: The Number System

AR.Math.Content.8.NS.A: Know that there are numbers that are not rational, and approximate them by rational numbers.

AR.Math.Content.8.NS.A.1: Know that numbers that are not rational are called irrational. Understand that every number has a decimal expansion. Write a fraction a/b as a repeating decimal. Write a repeating decimal as a fraction.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

AR.Math.Content.8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²).

Circumference and Area of Circles
Ordering and Approximating Square Roots

AR.Math.Content.8.EE: Expressions and Equations

AR.Math.Content.8.EE.A: Work with radicals and integer exponents.

AR.Math.Content.8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions using product, quotient, power to a power, or expanded form.

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

AR.Math.Content.8.EE.A.2: Use square root and cube root symbols to represent solutions to equations. Use square root symbols to represent solutions to equations of the form x² = p, where p is a positive rational number. Evaluate square roots of small perfect squares. Use cube root symbols to represent solutions to equations of the form x³ = p, where p is a rational number. Evaluate square roots and cube roots of small perfect cubes.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

AR.Math.Content.8.EE.A.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Unit Conversions 2 - Scientific Notation and Significant Digits

AR.Math.Content.8.EE.A.4: Perform operations with numbers expressed in scientific notation, including problems where both standard form and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

AR.Math.Content.8.EE.B: Understand the connections between proportional relationships, lines, and linear equations.

AR.Math.Content.8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways (graphs, tables, equations).

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

AR.Math.Content.8.EE.B.6: Using a non-vertical or non-horizontal line, show why the slope m is the same between any two distinct points by creating similar triangles. Write the equation y = mx for a line through the origin. Be able to write the equation y = mx + b for a line intercepting the vertical axis at b.

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

AR.Math.Content.8.EE.C: Analyze and solve linear equations and pairs of simultaneous linear equations.

AR.Math.Content.8.EE.C.7: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

AR.Math.Content.8.EE.C.8: Analyze and solve pairs of simultaneous linear equations. Find solutions to a system of two linear equations in two variables so they correspond to points of intersection of their graphs. Solve systems of equations in two variables algebraically using simple substitution and by inspection (e.g., 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6). Solve real-world mathematical problems by utilizing and creating two linear equations in two variables.

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)

AR.Math.Content.8.F: Functions

AR.Math.Content.8.F.A: Define, evaluate, and compare functions.

AR.Math.Content.8.F.A.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Points, Lines, and Equations

AR.Math.Content.8.F.A.2: Compare properties (e.g., y-intercept/initial value, slope/rate of change) of two functions each represented in a different way (e.g., algebraically, graphically, numerically in tables, or by verbal descriptions).

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Graphs of Polynomial Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Slope-Intercept Form of a Line

AR.Math.Content.8.F.A.3: Identify the unique characteristics of functions (e.g., linear, quadratic, and exponential) by comparing their graphs, equations, and input/output tables.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

AR.Math.Content.8.F.B: Use functions to model relationships between quantities.

AR.Math.Content.8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a verbal description of a relationship, two (x, y) values, a table, a graph. 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.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Translating and Scaling Functions

AR.Math.Content.8.F.B.5: Describe the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the features of a function that has been described verbally.

Arithmetic Sequences
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

AR.Math.Content.8.G: Geometry

AR.Math.Content.8.G.A: Understand congruence and similarity using physical models, transparencies, or geometry software.

AR.Math.Content.8.G.A.1: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines.

Circles
Holiday Snowflake Designer
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures
Translations

AR.Math.Content.8.G.A.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that exhibits the congruence between them.

Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

AR.Math.Content.8.G.A.3: Given a two-dimensional figure on a coordinate plane, identify and describe the effect (rule or new coordinates) of a transformation (dilation, translation, rotation, and reflection). Image to pre-image, Pre-image to image.

Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

AR.Math.Content.8.G.A.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Dilations
Similar Figures

AR.Math.Content.8.G.A.5: Use informal arguments to establish facts about: The angle sum and exterior angle of triangles. The angles created when parallel lines are cut by a transversal. The angle-angle criterion for similarity of triangles.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

AR.Math.Content.8.G.B: Understand and apply the Pythagorean Theorem.

AR.Math.Content.8.G.B.6: Model or explain an informal proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

AR.Math.Content.8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

AR.Math.Content.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Distance Formula
Pythagorean Theorem

AR.Math.Content.8.SP: Statistics and Probability

AR.Math.Content.8.SP.A: Investigate patterns of association in bivariate data.

AR.Math.Content.8.SP.A.1: 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
Solving Using Trend Lines
Trends in Scatter Plots

AR.Math.Content.8.SP.A.2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Correlation
Solving Using Trend Lines

AR.Math.Content.8.SP.A.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.

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

AR.Math.Content.8.SP.A.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Histograms