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.7.EE.2

**Title:**Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics

**Grade:**7

**Domain-Subdomain:**Expressions & Equations

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Assessments

## Educational Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Experts

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Teaching Ideas

## Tutorials

## Unit/Lesson Sequences

## Video/Audio/Animations

## Virtual Manipulative

## Student Resources

## Original Student Tutorials

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. **Click HERE to open Part 1.**

Type: Original Student Tutorial

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. **Click HERE to open Part 2.**

Type: Original Student Tutorial

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

## Educational Games

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

In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Type: Problem-Solving Task

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Type: Problem-Solving Task

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Type: Problem-Solving Task

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Type: Problem-Solving Task

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Type: Problem-Solving Task

The student is asked to write and solve an inequality to match the context.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Type: Problem-Solving Task

Students are asked to solve an inequality in order to answer a real-world question.

Type: Problem-Solving Task

## Tutorials

Many real world problems involve involve percentages. This lecture shows how algebra is used in solving problems of percent change and profit-and-loss.

Type: Tutorial

Students will learn how to solve a consecutive integer problem. Checking the solution will be left to the student.

Type: Tutorial

This tuptorial shows students how to set up and solve an age word problem. The tutorial also shows how tp check your work using substitution.

Type: Tutorial

This video demonstrates how to factor a linear expression by taking a common factor.

Type: Tutorial

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

In this example, you will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

This video teaches about combining like terms in linear equations.

Type: Tutorial

Students will solve the inequality and graph the solution.

Type: Tutorial

We're putting a little algebra to work to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

Type: Tutorial

This tutorial will help you to solve one-step equations using multiplication and division. For practice, take the quiz after the lesson!

Type: Tutorial

This short video uses both an equation and a visual model to explain why the same steps must be used on both sides of the equation when solving for the value of a variable.

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/Animations

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Type: Video/Audio/Animation

How do we create linear equations to solve real-world problems? The video explains the process.

Type: Video/Audio/Animation

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

## Virtual Manipulative

In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. 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: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Type: Problem-Solving Task

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Type: Problem-Solving Task

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Type: Problem-Solving Task

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Type: Problem-Solving Task

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Type: Problem-Solving Task

The student is asked to write and solve an inequality to match the context.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Type: Problem-Solving Task

Students are asked to solve an inequality in order to answer a real-world question.

Type: Problem-Solving Task

## Tutorial

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

Type: Tutorial

## Video/Audio/Animation

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation