Standard #: MAFS.8.EE.3.7 (Archived Standard)

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!

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.

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.

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

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

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

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

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

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.

This lesson allows students to solve two-step equations involving a mythological story line in which the princess (variable) is protected by a bodyguard (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 to steal the “valuable” princess. Using this story line, students must then decide who the Ninja must eliminate first 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.

• 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.

• 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.

In this lesson, 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 which elements of equations affect the number of possible solutions. This lesson is guided by a PowerPoint presentation.

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Students will practice and create problems solving linear equations that involve one solution, no solution, infinitely many solutions. There will be class discussion so students can verbalize their thoughts. In addition, students will create their own real-world problems that can be used for the next day’s extension exercise.

• 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.

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?

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?

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?

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?

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?

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.

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.

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.

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.

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

Use the Distributive Property while solving equations 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.

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

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

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

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

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.

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.

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

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

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

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.

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.

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.

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

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

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.

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?

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?

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?

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?

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?

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!

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.

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.

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.

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.

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.

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.

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

Use the Distributive Property while solving equations 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.

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

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

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

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

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.

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.

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

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

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

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.

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.

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.

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

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

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.

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.

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.

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.

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