8.EE: Expressions and Equations

2.1: Work with radicals and integer exponents.

8.EE.1: Apply the properties (product, quotient, power, zero, negative exponents, and rational exponents) of integer exponents to generate equivalent numerical expressions.

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

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

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.EE.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
Unit Conversions 2 - Scientific Notation and Significant Digits

8.EE.4: Perform operations with numbers expressed in scientific notation, including problems where both standard notation and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

2.2: Understand the connections between proportional relationships, lines, and linear equations.

8.EE.5: Graph linear equations such as y = mx + b, interpreting m as the slope or rate of change of the graph and b as the y-intercept or starting value. Compare two different proportional relationships represented in different ways.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and 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

2.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7: Solve linear equations in one variable.

8.EE.7.a: 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).

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

8.EE.7.b: Solve linear equations with rational coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.

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

8.EE.8: Analyze and solve systems of linear equations.

8.EE.8.a: Show that the solution to a system of two linear equations in two variables is the intersection of the graphs of those equations because points of intersection satisfy both equations simultaneously.

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)

8.EE.8.b: Solve systems of two linear equations in two variables and estimate solutions by graphing the equations. Simple cases may be done by inspection.

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)

8.EE.8.c: Solve real-world and mathematical problems leading to 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)

8.G: Geometry

3.1: Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.1: Through experimentation, verify the properties of rotations, reflections, and translations (transformations) to figures on a coordinate plane).

8.G.1.a: Lines are taken to lines, and line segments to line segments of the same length.

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

8.G.1.b: Angles are taken to angles of the same measure.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

8.G.1.c: Parallel lines are taken to parallel lines.

Reflections
Rotations, Reflections, and Translations
Similar Figures

8.G.2: Demonstrate understanding of congruence by applying a sequence of translations, reflections, and rotations on two-dimensional figures. Given two congruent figures, describe a sequence that exhibits the congruence between them.

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

8.G.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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

8.G.4: Demonstrate understanding of similarity, by applying a sequence of translations, reflections, rotations, and dilations on two-dimensional figures. Describe a sequence that exhibits the similarity between them.

Dilations
Similar Figures

8.G.5: Justify using informal arguments to establish facts about

8.G.5.a: measures of exterior angles of triangles,

Polygon Angle Sum
Triangle Angle Sum

8.G.5.b: angles created when parallel lines are cut be a transversal (e.g., alternate interior angles), and

Triangle Angle Sum

8.G.5.c: angle-angle criterion for similarity of triangles.

Similar Figures
Similarity in Right Triangles

3.2: Understand and apply the Pythagorean Theorem.

8.G.6: Explain the Pythagorean Theorem and its converse.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

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

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

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

Circles
Distance Formula

3.3: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9: Identify and apply the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Prisms and Cylinders
Pyramids and Cones

8.SP: Statistics and Probability

4.1: Investigate patterns of association in bivariate data.

8.SP.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
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

8.SP.2: Explain why 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
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and y-intercept.

Correlation

8.F: Functions

5.1: Define, evaluate, and compare functions.

8.F.1: Understand that a function is a rule that assigns to each input (the domain) exactly one output (the range). The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. For example, use the vertical line test to determine functions and non-functions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

8.F.2: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Graphs of Polynomial Functions
Linear Functions
Quadratics in Polynomial Form

8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

5.2: Use functions to model relationships between quantities.

8.F.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 description of a relationship or from two (x, y) values, including reading these from a table or from 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

8.F.5: Given a verbal description between two quantities, sketch a graph. Conversely, given a graph, describe a possible real-world example.

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

Correlation last revised: 9/24/2019

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