MAFS.8.EE: Expressions and Equations

MAFS.8.EE.1: Work with radicals and integer exponents.

MAFS.8.EE.1.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

MAFS.8.EE.1.2: 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.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Square Roots

MAFS.8.EE.1.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal 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

MAFS.8.EE.2: Understand the connections between proportional relationships, lines, and linear equations.

MAFS.8.EE.2.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Polling: Neighborhood
Road Trip (Problem Solving)
Slope - Activity B

MAFS.8.EE.2.6: 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.

Perimeters and Areas of Similar Figures
Point-Slope Form of a Line - Activity A
Points, Lines, and Equations
Similar Figures - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity B

MAFS.8.EE.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

MAFS.8.EE.3.7: Solve linear equations in one variable.

MAFS.8.EE.3.7.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 and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

MAFS.8.EE.3.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Chocomatic (Multiplication, Arrays, and Area)
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

MAFS.8.EE.3.8: Analyze and solve pairs of simultaneous linear equations.

MAFS.8.EE.3.8.a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MAFS.8.EE.3.8.b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MAFS.8.EE.3.8.c: Solve real-world and mathematical problems leading to two linear equations in two variables.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MAFS.8.F: Functions

MAFS.8.F.1: Define, evaluate, and compare functions.

MAFS.8.F.1.1: 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)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

MAFS.8.F.1.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Fourth-Degree Polynomials - Activity A
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
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Using Algebraic Equations
Using Algebraic Expressions

MAFS.8.F.1.3: 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.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B

MAFS.8.F.2: Use functions to model relationships between quantities.

MAFS.8.F.2.4: 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.

Direct and Inverse Variation
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
Point-Slope Form of a Line - Activity A
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B

MAFS.8.F.2.5: Describe qualitatively 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 qualitative features of a function that has been described verbally.

Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Slope-Intercept Form of a Line - Activity B
Using Algebraic Equations
Using Algebraic Expressions

MAFS.8.G: Geometry

MAFS.8.G.1: Understand congruence and similarity using physical models, transparencies, or geometry software.

MAFS.8.G.1.1: Verify experimentally the properties of rotations, reflections, and translations:

MAFS.8.G.1.1.a: Lines are taken to lines, and line segments to line segments of the same length.

Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations

MAFS.8.G.1.1.b: Angles are taken to angles of the same measure.

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

MAFS.8.G.1.1.c: Parallel lines are taken to parallel lines.

Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations

MAFS.8.G.1.2: 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.

Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations

MAFS.8.G.1.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Dilations
Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations

MAFS.8.G.1.4: 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
Perimeters and Areas of Similar Figures
Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Similar Figures - Activity A
Translations

MAFS.8.G.1.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Segment and Angle Bisectors
Similar Figures - Activity A

MAFS.8.G.2: Understand and apply the Pythagorean Theorem.

MAFS.8.G.2.6: Explain a proof of the Pythagorean Theorem and its converse.

Distance Formula - Activity A
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard

MAFS.8.G.2.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Distance Formula - Activity A
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard

MAFS.8.G.2.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

City Tour (Coordinates)
Distance Formula - Activity A
Points in the Coordinate Plane - Activity A
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard

MAFS.8.G.3: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

MAFS.8.G.3.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Prisms and Cylinders - Activity A

MAFS.8.SP: Statistics and Probability

MAFS.8.SP.1: Investigate patterns of association in bivariate data.

MAFS.8.SP.1.1: 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.

Arithmetic and Geometric Sequences
Correlation
Finding Patterns
Geometric Sequences
Scatter Plots - Activity A
Solving Using Trend Lines

MAFS.8.SP.1.2: 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
Lines of Best Fit Using Least Squares - Activity A
Scatter Plots - Activity A
Solving Using Trend Lines

MAFS.8.SP.1.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B

MAFS.8.SP.1.4: 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 summarizing data 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.

Arithmetic and Geometric Sequences
Box-and-Whisker Plots
Describing Data Using Statistics
Finding Patterns
Geometric Sequences
Histograms
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Scatter Plots - Activity A
Stem-and-Leaf Plots

MAFS.8.NS: The Number System

MAFS.8.NS.1: Know that there are numbers that are not rational, and approximate them by rational numbers.

MAFS.8.NS.1.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Improper Fractions and Mixed Numbers
Percents, Fractions, and Decimals