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MAFS.8.EE.3.7

Solve linear equations in one variable.
  1. 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).
  2. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Clarifications

Fluency Expectations or Examples of Culminating Standards

Students have been working informally with one-variable linear equations since as early as kindergarten. This important line of development culminates in grade 8 with the solution of general one-variable linear equations, including cases with infinitely many solutions or no solutions as well as cases requiring algebraic manipulation using properties of operations. Coefficients and constants in these equations may be any rational numbers.

Examples of Opportunities for In-Depth Focus

This is a culminating standard for solving one-variable linear equations.

General Information

Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Expressions & Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. (Major Cluster) -

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.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

Test Item Specifications


  • Assessment Limits :

    Numbers in items must be rational numbers

  • Calculator :

    Yes

  • Context :

    Allowable

Sample Test Items (6)






  • Test Item #: Sample Item 6
  • Question:

    Select whether each equation has no solution, one solution, or infinitely many solutions.

     



     

  • Difficulty: N/A
  • Type: MI: Matching Item

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1204000: M/J Intensive Mathematics (MC) (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.8.EE.3.AP.7a: Simplify linear equations and solve for one variable.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 3 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 2 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 1 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Educational Games

Solving Equations: Same Variable, Both Sides, One Solution:

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

Algebra Meltdown: A Function Machine Game:

This fun and interactive game challenges you to input numbers into a Mad Scientist function machine in order to get a desired output number. The machine gets more complicated as you level up (equations begin with one variable and include only positive numbers, but quickly become more difficult including negatives and multiple variables and continue to get progressively more challenging). Be careful! Scientists are impatient and get very mad if you do not deliver fast enough!

Type: Educational Game

Timed Algebra Quiz:

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

Algebra Four:

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

Formative Assessments

Linear Equations - 2:

Students are asked to solve a linear equation in one variable with rational coefficients.

Type: Formative Assessment

Linear Equations - 1:

Students are asked to solve a linear equation in one variable with rational coefficients.

Type: Formative Assessment

Equation Prototypes:

Students are asked to write examples of equations with one solution, no solutions, and infinitely many solutions.

Type: Formative Assessment

Counting Solutions:

Students are asked to identify and explain whether given equations have one solution, no solutions, or infinitely many solutions.

Type: Formative Assessment

Linear Equations - 3:

Students are asked to solve a linear equation in one variable with rational coefficients and variables on both sides of the equation.

Type: Formative Assessment

Lesson Plans

How Low Can You Go?:

Land is becoming scarce. With the diminishing amount of viable land available for humans, animals, and vegetation, we must start exploring other options as populations expand. You will investigate the thousands of miles of land below sea-level and create a structure to withstand applied pressure, imitating the pressure felt in deep water.

Students attempt to avoid an "egg-splosion" by creating a model to withstand the pressure felt by objects as if they are at varying depths below sea-level.

Type: Lesson Plan

How Will the Ninja Capture the Valuable Princess?:

This lesson allowed students to solve two step equations involving a mythological story line in which the princess (variable) is protected by a body guard (number added or subtracted in an equation) and by a protector (number multiplied or divided by the variable). The three characters live in a castle, surrounded by the moat (equal sign) and an innocent bystander that lives outside the castle (number on the opposite side of the variable). However, Ninjas are infiltrating the castle in order to steal the "valuable" princess. Using this story line, students must then decide who the Ninja must eliminate first in order to get to the princess. This lesson can also be used to solve equations with like terms on the same side and equations with the same variable on each side.

Type: Lesson Plan

Building and Solving Equations 1:

This 90-minute lesson helps teachers assess how well students are able to create and solve linear equations with one variable and in more than one way. Students will work individually and in pairs on collaborative activities. They will evaluate and sample student work and create linear equations for each other to solve. In order to complete this lesson, students will need copies of the assessment tasks, paper, mini-whiteboards, pens, and erasers.

Type: Lesson Plan

Classifying Solutions to Systems of Equations:

This lesson unit is intended to help you assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help you identify and assist students who have difficulties in:

  • Using substitution to complete a table of values for a linear equation.
  • Identifying a linear equation from a given table of values.
  • Graphing and solving linear equations.

Type: Lesson Plan

Solving Linear Equations in One Variable:

This lesson is intended to help you assess how well students are able to:

  • Solve linear equations in one variable with rational number coefficients.
  • Collect like terms.
  • Expand expressions using the distributive property.
  • Categorize linear equations in one variable as having one, none, or infinitely many solutions.
It also aims to encourage discussion on some common misconceptions about algebra.

Type: Lesson Plan

Solving Real-Life Problems: Baseball Jerseys:

This lesson unit is intended to help you assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, interpret and evaluate the data generated and identify the break-even point, checking it for confirmation and communicate their reasoning clearly.

Type: Lesson Plan

Repeating Decimals:

This lesson unit is intended to help you assess how well students are able to translate between decimal and fraction notation, particularly when the decimals are repeating, create and solve simple linear equations to find the fractional equivalent of a repeating decimal, and understand the effect of multiplying a decimal by a power of 10.

Type: Lesson Plan

The Yo-Yo Problem: Solving Linear Equations:

In this lesson, students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation, and the graphing calculator.
The lesson starts with the presentation of the yo-yo purchase problem. Students then complete a hands-on activity involving a design created with pennies that allows them to explore a linear pattern and express that pattern in symbolic form. Algebra tiles are introduced as the students practice solving linear equations. Working from the concrete to the abstract is especially important for students who have difficulty with mathematics, and algebra tiles help students make this transition. In addition to using algebra tiles, students also use symbolic manipulation and the graphing calculator. Finally, the students return to solve the yo-yo problem.
A feature of this lesson is the effective use of peer tutors in this inclusion classroom. Student worksheets are included to print.

Type: Lesson Plan

Company Charges:

In this lesson the students will learn how to write and solve linear equations that have one solution, infinitely many solutions and no solutions. As the students decipher word problems, they will recognize what elements of the equations effect the number of possible solutions. This lesson is guided by a Powerpoint presentation.

Type: Lesson Plan

Determining the density of regular and irregular objects:

This MEA provides students with opportunities to practice solving one-step equations while learning about density. Students will calculate density of regular and irregular objects.

Type: Lesson Plan

The Variable Stands Alone:

Students will practice and create problems solving linear equations that involve one solution, no solution, infinitely many solutions. There will be class think aloud portions so students can discuss their thoughts. In addition, students will create their own real-world problems that can be used for the next days extension exercise.

Type: Lesson Plan

Solving Linear Equations in One Variable:

This lesson unit is intended to help you assess how well students are able to:

  • Solve linear equations in one variable with rational number coefficients.
  • Collect like terms.
  • Expand expressions using the distributive property.
  • Categorize linear equations in one variable as having one, none, or infinitely many solutions.
It also aims to encourage discussion on some common misconceptions about algebra.

Type: Lesson Plan

Original Student Tutorials

Multi-Step Equations: Part 5 How Many Solutions?:

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

Multi-Step Equations: Part 4 Putting it All Together:

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

Multi-step Equations: Part 3 Variables on Both Sides:

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

Multi-Step Equations: Part 2 Distributive Property:

Explore how to solve multi-step equations using the distributive property 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
  • [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

Multi-Step Equations: Part 1 Combining Like Terms:

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

Problem-Solving Tasks

Coupon Versus Discount:

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

Solving Equations:

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

The Sign of Solutions:

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

Student Center Activity

Edcite: Mathematics Grade 8:

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

Distributive Property to Simplify Equations:

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

Type: Tutorial

Introduction to solving an equation with variables on both sides:

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

Application of the Distributive Property to Solve a Multi-Step Equation:

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

Type: Tutorial

Solving Equations with the Distributive Property:

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

Type: Tutorial

Solving a Multi-Step Equation:

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

Type: Tutorial

Solving an equation with variables on both sides:

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

Linear equation word problem:

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

Solving Equations: Word Problem:

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

Solving a more complicated equation:

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

Type: Tutorial

Solving a two-step equation with a numerator of x:

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

Type: Tutorial

Two-Step Equations:

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

Type: Tutorial

Solving two-step equations:

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

Solving Multi-Step Equations:

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

Linear Equations in One Variable:

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

Solving Equations With the Variable on Both Sides.:

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

Type: Tutorial

Solving Equations with One Variable :

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

Type: Tutorial

Video/Audio/Animation

Solving Mixture Problems with Linear Equations:

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

Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative

STEM Lessons - Model Eliciting Activity

Determining the density of regular and irregular objects:

This MEA provides students with opportunities to practice solving one-step equations while learning about density. Students will calculate density of regular and irregular objects.

MFAS Formative Assessments

Counting Solutions:

Students are asked to identify and explain whether given equations have one solution, no solutions, or infinitely many solutions.

Equation Prototypes:

Students are asked to write examples of equations with one solution, no solutions, and infinitely many solutions.

Linear Equations - 1:

Students are asked to solve a linear equation in one variable with rational coefficients.

Linear Equations - 2:

Students are asked to solve a linear equation in one variable with rational coefficients.

Linear Equations - 3:

Students are asked to solve a linear equation in one variable with rational coefficients and variables on both sides of the equation.

Original Student Tutorials Mathematics - Grades 6-8

Multi-Step Equations: Part 1 Combining Like Terms:

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?

 

Multi-Step Equations: Part 2 Distributive Property:

Explore how to solve multi-step equations using the distributive property 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
  • [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?

 

Multi-step Equations: Part 3 Variables on Both Sides:

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?

 

Multi-Step Equations: Part 4 Putting it All Together:

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?

 

Multi-Step Equations: Part 5 How Many Solutions?:

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?

 

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Multi-Step Equations: Part 5 How Many Solutions?:

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

Multi-Step Equations: Part 4 Putting it All Together:

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

Multi-step Equations: Part 3 Variables on Both Sides:

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

Multi-Step Equations: Part 2 Distributive Property:

Explore how to solve multi-step equations using the distributive property 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
  • [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

Multi-Step Equations: Part 1 Combining Like Terms:

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

Solving Equations: Same Variable, Both Sides, One Solution:

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

Timed Algebra Quiz:

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

Algebra Four:

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

Coupon Versus Discount:

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

Solving Equations:

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

The Sign of Solutions:

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

Student Center Activity

Edcite: Mathematics Grade 8:

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

Distributive Property to Simplify Equations:

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

Type: Tutorial

Introduction to solving an equation with variables on both sides:

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

Application of the Distributive Property to Solve a Multi-Step Equation:

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

Type: Tutorial

Solving Equations with the Distributive Property:

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

Type: Tutorial

Solving a Multi-Step Equation:

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

Type: Tutorial

Solving an equation with variables on both sides:

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

Linear equation word problem:

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

Solving Equations: Word Problem:

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

Solving a more complicated equation:

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

Type: Tutorial

Solving a two-step equation with a numerator of x:

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

Type: Tutorial

Two-Step Equations:

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

Type: Tutorial

Solving two-step equations:

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

Solving Multi-Step Equations:

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

Linear Equations in One Variable:

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

Solving Equations With the Variable on Both Sides.:

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

Type: Tutorial

Solving Equations with One Variable :

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

Type: Tutorial

Video/Audio/Animation

Solving Mixture Problems with Linear Equations:

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

Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Coupon Versus Discount:

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

Solving Equations:

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

The Sign of Solutions:

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

Tutorial

Solving Equations With the Variable on Both Sides.:

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

Type: Tutorial

Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative