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# MAFS.7.EE.2.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
1. 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?
2. 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.

Subject Area: Mathematics
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 of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Remarks/Examples

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.

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark may be assessed using: MS , EE , GRID item(s)

• Assessment Limits :
Inequalities must have context. Inequalities may use ≤ or ≥. Inequalities may not be compound inequalities
• Calculator :

Yes

• Context :

Allowable

### SAMPLE TEST ITEMS (4)

• 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