- Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
*For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?* - Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
*For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.*

### Clarifications

**Fluency Expectations or Examples of Culminating Standards**

In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, students solve the equations fluently. This will require fluency with rational number arithmetic (7.NS.1.1–1.3), as well as fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.1.1).

**Examples of Opportunities for In-Depth Focus**

Work toward meeting this standard builds on the work that led to meeting 6.EE.2.7 and prepares students for the work that will lead to meeting 8.EE.3.7.

**Subject Area:**Mathematics

**Grade:**7

**Domain-Subdomain:**Expressions & Equations

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Solve real-life and mathematical problems using numerical and algebraic expressions and 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

**Assessment Limits :**

Inequalities must have context. Inequalities may use ≤ or ≥. Inequalities may not be compound inequalities**Calculator :**Yes

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**The perimeter of a rectangular garden is 37.5 feet (ft). The width is x, and the length is 15 ft. What is the width, in feet, of the garden?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**A community is planning to build a rectangular garden. The width of the garden is feet (ft), and the perimeter of the garden is 37.5 ft. The community planners want to spread mulch on the entire garden.How many square feet of mulch will be needed?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 3**Question:**At her job, Jessie earns $9.50 per hour. She also earns a $60 bonus every month.

Jessie needs to earn more than $460 every month.

A. Create an inequality that represents the situation, where h represents the number of hours that Jessie needs to work in a month in order to earn more than $460.

B. Enter the minimum whole number of hours Jessie would have to work to earn $460 in a month.

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 4**Question:**This question has

**three**parts.Vanessa has added 40 gallons of water to her new fish pond in her backyard and wants to add more water. Her pond can hold a maximum of 256 gallons. Her garden hose can add 48 gallons of water in 2 minutes.

**Part A**. Create an inequality to represent the number of minutes, m, Vanessa could run the garden hose to add more water to the pond without adding the maximum amount in case of rain.**Part B.**Drag the appropriate arrow and circle to the number line to graph the solution to the inequality from Part A.**Part C.**Select all the amounts of time, in minutes, that Vanessa could leave the house running.**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## 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

## STEM Lessons - Model Eliciting Activity

The principal of Central Middle School is thinking of adding pizza to the lunch menu on Mondays and Fridays but needs help deciding the costs per slice and what students think is important about the pizza. After the students' initial decision about the pizza the principal remembers that there is a delivery charge.The students must revisit their decision and do additional calculations to see if their original process still works.

In this MEA, students must select which material to use in the development of an advanced military scout robot. Students must analyze data about each material’s individual properties that would make it a valid choice for military or police service. Students must complete calculations to determine material density as well as the overall mass and weight of the robot. This lesson focuses on the characteristic properties of density, unit conversion, and differentiating between mass and weight.

## MFAS Formative Assessments

Students are asked to compare an arithmetic solution to an algebraic solution of a word problem.

Students are asked to solve a real-world problem by writing and solving an inequality.

Students are asked to write and solve an equation of the form *p*(*x* + *q*) = *r* in the context of a problem about the perimeter of a square.

Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario.

Students are asked to write, solve, and graph a two-step inequality.

## Original Student Tutorials Science - Grades K-8

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

## Original Student Tutorials Mathematics - Grades 6-8

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.**

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.**

## 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

## 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

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

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

This video teaches about combining like terms in linear equations.

Type: Tutorial

Students will solve the inequality and graph the solution.

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

## 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

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

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