Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Number:**MAFS.8.EE.3

**Title:**Analyze and solve linear equations and pairs of simultaneous linear equations. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**8

**Domain-Subdomain:**Expressions & Equations

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Games

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Student Center Activity

## Tutorials

## Video/Audio/Animation

## Student Resources

## Original Student Tutorials

Learn how equations can have 1 solution, no solution or infinitely many solutions in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - Click
**HERE**to open Part 2: The Distributive Property - Click
**HERE**to open Part 3: Variables on Both Sides - Click
**HERE**to open Part 4: Putting It All Together - [CURRENT TUTORIAL] Part 5: How Many Solutions?

Type: Original Student Tutorial

Learn alternative methods of solving multi-step equations in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - Click
**HERE**to open Part 2: The Distributive Property - Click
**HERE**to open Part 3: Variables on Both Sides - [CURRENT TUTORIAL] Part 4: Putting It All Together
- Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Learn how to solve multi-step equations that contain variables on both sides of the equation in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - Click
**HERE**to open Part 2: The Distributive Property - [CURRENT TUTORIAL] Part 3: Variables on Both Sides
- Click
**HERE**to open Part 4: Putting It All Together - Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Explore how to solve multi-step equations using the distributive property in this interactive tutorial.

This is part two of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - [CURRENT TUTORIAL] Part 2: The Distributive Property
- Click
**HERE**to open Part 3: Variables on Both Sides - Click
**HERE**to open Part 4: Putting It All Together - Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Learn how to solve multi-step equations that contain like terms in this interactive tutorial.

This is part one of five in a series on solving multi-step equations.

- [CURRENT TUTORIAL] Part 1: Combining Like Terms
- Click
**HERE**to open Part 2: The Distributive Property - Click
**HERE**to open Part 3: Variables on Both Sides - Click
**HERE**to open Part 4: Putting It All Together - Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

## Educational Games

In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!

Type: Educational Game

In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Educational Game

## Problem-Solving Tasks

The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.

Type: Problem-Solving Task

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task

This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns. This progression of tasks helps distinguish between 8th grade and high school expectations related to systems of linear equations.

Type: Problem-Solving Task

In this activity, the student is asked to solve a variety of equations (one solution, infinite solutions, no solution) in the traditional algebraic manner and to use pictures of a pan balance to show the solution process.

Type: Problem-Solving Task

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations. The students are required to find the solution algebraically to complete the task.

Type: Problem-Solving Task

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Type: Problem-Solving Task

In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.

Type: Problem-Solving Task

The task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.

Type: Problem-Solving Task

Students are asked to create and graph linear equations to compare the savings of two individuals. The purpose of the table in (a) is to help students complete (b) by noticing regularity in the repeated reasoning required to complete the table (Standard for Mathematical Practice, ).

Type: Problem-Solving Task

Students are asked to write equations to model the repair costs of three different companies and determine the conditions for which each company would be least expensive. This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts. The solution can be determined in multiple ways, including either a graphical or algebraic approach.

Type: Problem-Solving Task

The student is given the equation 5x-2y=3 and asked, if possible, to write a second linear equation creating systems resulting in one, two, infinite, and no solutions.

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

This example demonstrates solving a system of equations algebraically and graphically.

Type: Tutorial

This video demonstrates a system of equations with no solution.

Type: Tutorial

This video shows how to solve a system of equations using the substitution method.

Type: Tutorial

This video demonstrates testing a solution (coordinate pair) for a system of equations

Type: Tutorial

This video demonstrates analyzing solutions to linear systems using a graph.

Type: Tutorial

This video shows how to algebraically analyze a system that has no solutions.

Type: Tutorial

This video will show how to solve a consecutive integer problem.

Type: Tutorial

Use the Distributive Property while solving equations with variables on both sides.

Type: Tutorial

Students will learn how to solve an equation with variables on both sides. This tutorial shows a final answer expressed as an improper fraction and mixed number.

Type: Tutorial

This video shows how to solve the equation (3/4)x + 2 = (3/8)x - 4 using the Distributive Property.

Type: Tutorial

This video shows how to solve an equation involving the Distributive Property.

Type: Tutorial

This example involves a variable in the denominator on both sides of the equation.

Type: Tutorial

Students will learn how to solve an equation with variables on both sides. Students will also learn how to distribute and combine like terms.

Type: Tutorial

Learn how to solve a word problem by writing an equation to model the situation. In this video, we use the linear equation 210(t-5) = 41,790.

Type: Tutorial

This tutorial shows a word problem in which students will find the dimensions of a garden given only the perimeter. Students will create an equation to solve.

Type: Tutorial

This example demonstrates how to solve an equation expressed in the form ax + b = c.

Type: Tutorial

This video shows how to solve an equation by isolating the variable in the numerator.

Type: Tutorial

Students will practice two step equations, some of which require combining like terms and using the distributive property.

Type: Tutorial

This video shows how to solve a two step equation. It begins with the concept of equality, what is done to one side of an equation, must be done to the other side of an equation.

Type: Tutorial

This short video explains how to solve multi-step equations with variables on both sides and why it is necessary to complete the same steps on both sides of the equation.

Type: Tutorial

When solving a system of linear equations in x and y with a single solution, we get a unique pair of values for x and y. But what happens when try to solve a system with no solutions or an infinite number of solutions?

Type: Tutorial

This lesson introduces students to linear equations in one variable, shows how to solve them using addition, subtraction, multiplication, and division properties of equalities, and allows students to determine if a value is a solution, if there are infinitely many solutions, or no solution at all. The site contains an explanation of equations and linear equations, how to solve equations in general, and a strategy for solving linear equations. The lesson also explains contradiction (an equation with no solution) and identity (an equation with infinite solutions). There are five practice problems at the end for students to test their knowledge with links to answers and explanations of how those answers were found. Additional resources are also referenced.

Type: Tutorial

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

## Video/Audio/Animation

Mixture problems can involve mixtures of things other than liquids. This video shows how Algebra can be used to solve problems involving mixtures of different types of items.

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.

Type: Problem-Solving Task

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task

This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns. This progression of tasks helps distinguish between 8th grade and high school expectations related to systems of linear equations.

Type: Problem-Solving Task

In this activity, the student is asked to solve a variety of equations (one solution, infinite solutions, no solution) in the traditional algebraic manner and to use pictures of a pan balance to show the solution process.

Type: Problem-Solving Task

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations. The students are required to find the solution algebraically to complete the task.

Type: Problem-Solving Task

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Type: Problem-Solving Task

In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.

Type: Problem-Solving Task

The task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.

Type: Problem-Solving Task

Students are asked to create and graph linear equations to compare the savings of two individuals. The purpose of the table in (a) is to help students complete (b) by noticing regularity in the repeated reasoning required to complete the table (Standard for Mathematical Practice, ).

Type: Problem-Solving Task

Students are asked to write equations to model the repair costs of three different companies and determine the conditions for which each company would be least expensive. This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts. The solution can be determined in multiple ways, including either a graphical or algebraic approach.

Type: Problem-Solving Task

The student is given the equation 5x-2y=3 and asked, if possible, to write a second linear equation creating systems resulting in one, two, infinite, and no solutions.

Type: Problem-Solving Task

## Tutorial

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial