# Equations and Inequalities

## Objective

Model with equations in the form ${px+q=r}$ and ${p(x+q)=r}$.

## Common Core Standards

### Core Standards

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• 7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

• 7.EE.B.4.A — 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?

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• 6.EE.B.7

## Criteria for Success

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1. Analyze real-world situations and identify important information needed to solve a problem.
2. Create equations to model real-world applications and efficiently solve a problem (MP.4).

## Tips for Teachers

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• In this lesson, students have the opportunity to tackle novel challenges and discover how equations are effective tools to model and solve problems. In place of Anchor Problems, the Problem Set Guidance includes four options for activities, two of which require students to have computers. Choose one or two activities to use.
• In terms of pacing, and depending on the number of activities used, this lesson may extend over more than one day.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Andrew Stadel's 3-Act Math Tasks Styrofoam CupsStudents guess how many Styrofoam cups it will take to reach the top of a doorway. Then, given measurements, they use equations to determine a way to find an exact answer.
• Desmos Picture PerfectUsing computers, students explore placing pictures on hooks that are equally spaced from one another. They develop equations to find efficient ways to solve the challenges. This is similar to Central Park.
• Desmos Central ParkUsing computers, students explore creating equally spaced parking spaces by dragging dividers into the right locations. They eventually use variables and equations to find efficient ways to tackle the challenges.
• SERP Poster Problems On the DownloadThis problem explores speed and delayed start time in the context of downloading files on different cell phones. Students write and solve equations and create posters to share and discuss student work.

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A batch of 8 cookie ice cream sandwiches weighs 1,092 grams. On average, each cookie weighs 12 grams, and the same amount of ice cream is used for each sandwich. A pint of ice cream has approximately 450–460 grams of ice cream. How many pints of ice cream would you need to make another batch of 8 cookie ice cream sandwiches?

#### References

Wikimedia Commons Photo: Toll House Chocolate Chip Cookie Sandwich.jpg by Thomson200

Toll House Chocolate Chip Cookie Sandwich.jpg is made available on Wikimedia Commons under the CC0 1.0 license. Accessed May 14, 2018, 4:44 p.m..

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