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Common Core Mapping for Grade 8

In Grade 8, instructional time should focus on three critical areas:
(1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations;
(2) grasping the concept of a function and using functions to describe quantitative relationships;
(3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Related Topics:
Common Core Math Worksheets and Lesson Plans for Grade 8
Common Core for Mathematics

The Number System





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.

Irrational Numbers

Recognizing rational and irrational numbers

Writing fractions as repeating decimals

Converting decimals to fractions

Convert 1-digit repeating decimals

Convert multi-digit repeating decimals

Rational & Irrational Numbers Games


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). For example, by truncating the decimal expansion of √ 2, show that √ 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Approximate Irrational Numbers

Approximate Irrational Numbers

Approximate Irrational Numbers

Rational & Irrational Numbers Games

Expressions and Equations





Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,
32x 3-5= 3-3= 1/33= 1/27.

Integer Exponents

Negative exponents

Exponent rules

Properties of Exponents

Exponent Games


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 2 is irrational.

Square Roots & Cube Roots

Square roots of perfect squares

Estimating square roots

Cube roots

Cube roots 2

Square Root Games


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. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

Scientific Notation

Scientific notation

Orders of magnitude

Scientific Notation Games


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

Multiply & Divide Scientific Notation

Scientific Notation Intuition

Scientific Notation

Multiply & divide scientific notation

Computing in scientific notation

Scientific Notation Games


Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Graph Proportional Relationships

Graphing proportional relationships

Rates and proportional relationships


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

Slope & Similar Triangles

Slope & triangle similarity

Equation of Line Games


Solve linear equations in one variable.

See Below


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 = aa = a, or a = b results (where a and b are different numbers).

Solutions to Linear Equations

Solutions to equations

Equations with variables on both sides

Multi-step equations with distribution


Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Solve Equations

One-Step Equations

Multistep equations with distribution

Equations with variables on both sides

Solve Equation Games


Analyze and solve pairs of simultaneous linear equations.

See Below



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.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Types of Solution for Systems of Equations

Solve Systems of Equations Graphically

Solve Systems of Equations by Substitution

Solve Systems of Equations by Elimination

Systems of Equations

Solutions to systems of equations

Constructing consistent and inconsistent systems

Graphical solutions to systems

Graphing systems of equations

Systems of equations with substitution

Systems of equations with simple elimination

Systems of equations with elimination

Systems of equations


Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Systems of Equations Word Problems

Understanding systems of equations word problems

Systems of equations word problems






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.


Recognizing functions

Views of a function

Function Games


Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Compare Functions

Comparing linear functions

Comparing linear functions applications

Function Games


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. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Linear & Nonlinear Functions

NonLinear Functions

Linear & nonlinear functions

Function Games


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.

Construct Functions

Modeling Linear Relationships

Interpret Rate of Change

Representations of a Line

Linear Models

Constructing and interpreting linear functions

Graphing linear equations

Identifying slope of a line

Interpreting and finding intercepts of linear functions

Interpreting features of linear functions

Linear function intercepts

Solving for the x-intercept

Solving for the y-intercept


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.

Interpret graphs of functions

Increasing and Decreasing Functions

Constructing and interpreting linear functions

Interpreting graphs of linear and nonlinear functions






Verify experimentally the properties of rotations, reflections, and translations:

A. Lines are taken to lines, and line segments to line segments of the same length.

B. Angles are taken to angles of the same measure.

C. Parallel lines are taken to parallel lines.

Transformations- rotations, reflections, and translations

Reflections and Translations

Sequence of Translations

Sequences of Rigid Motions

Precisely define rigid transformations

Identify the Transformation

Transformation Games


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.

Congruence & Transformation

Congruence and Rigid Motion

Exploring Rigid Transformations and Congruence

Describe the Transformation

Transformation Games


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

Coordinate Transformations

Define translations on the Coordinate Plane

Perform translations on the Coordinate Plane

Rotate about the origin

Rotate about arbitrary point



Transformations (Give the Coordinates)

Transformation Games


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.

Similarity & Transformations

Transformations and Similarity

Describe the sequence of transformations

Transformation Games


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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Angle Relationships

Angles Associated with Parallel Lines

Angle Sum of a Triangle

Find Angles

Angles 1

Angles 2

Congruent angles

Parallel lines 1

Parallel lines 2


Explain a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem

Pythagorean Theorem

Pythagorean Theorem Proofs

Pythagorean Theorem Games


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

Apply Pythagorean Theorem

Pythagorean theorem

Special right triangles

Pythagorean Theorem Word Problems

Pythagorean Theorem Games


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

Distance Formula

Distance formula

Distance formula


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

Volume Formulas

Find the Volumes

Volume word problems

Volume Games

Statistics and Probability





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.

Scatter Plots

Constructing scatter plots

Interpreting scatter plots

Statistics Games


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.

Scatter Plots - Line of Best Fit

Estimating the line of best fit

Statistics Games


Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

Linear Model Equations

Linear models of bivariate data


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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Two-Way Tables

Bivariate Categorical Data

Association Between Categorical Variables

Frequencies of bivariate data

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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