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# Numerical and Algebraic Expressions

## Objective

Model real-world problems involving rational numbers using reasoned estimates.

## 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.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

## Criteria for Success

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1. Develop a strategy, in collaboration with peers, to solve real-world problems involving computation with rational numbers.
2. Use reasonable estimates as part of a strategy to solve a more complicated problem.
3. Use properties and order of operations to compute with rational numbers in any form.
4. Make sense of problems and persevere through solving them (MP.1).
5. Analyze and critique the work of others (MP.3).

## Tips for Teachers

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• In terms of pacing, this lesson may be extended over 2 days.
• This lesson is designed as a whole-class activity where students work in small groups to apply the math they know to solve real-world problems (MP.4). There are five problems that students can either be assigned to or choose from. Students should work collaboratively to discuss and execute on a solution pathway (MP.1). Allow students to request any tools they may find valuable to solve their problems (MP.5).  Once they are done, students should make a poster or visual of their problem and solution and post it in the classroom for others to see. The Target Task involves students looking at other problems solved by their peers and analyzing and critiquing their work (MP.3).

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Choose Anchor Problem 1 per group (benefits from discussion). This lesson was designed to be completed in small groups. Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Option #1 (Students choose or are assigned one of the five anchor problems to work on with a group of peers. After collaboratively deciding their approach and solution, students can prepare a poster to show their response.)

Trophy stand
Central High School won the league softball championship game last weekend. The team would like to make a display stand for the trophy. The stand will be a rectangular prism. The players plan to paint the stand white so they can each paint a handprint on the stand in different colors.

The players want to fit each of their handprints on the stand without overlapping with any other handprints. There are 24 players on the team.

Design a display stand that meets the requirements above. What are its dimensions? Show or explain how you found the dimensions using words, pictures, and/or numbers.

#### References

Achieve the Core Grade 7 Micro Models and Reasoned Estimates Mini Assessment

Grade 7 Micro Models and Reasoned Estimates Mini Assessment by is made available by Achieve the Core under the CC0 1.0 license. Accessed Oct. 9, 2017, 11:49 a.m..

### Problem 2

Option #2 (Students choose or are assigned one of the five anchor problems to work on with a group of peers. After collaboratively deciding their approach and solution, students can prepare a poster to show their response.)

How many students are there?

1. Which number is closest to the number of people in the United States?
1. 3,000
2. 30,000
3. 300,000
4. 3,000,000
5. 30,000,000
6. 300,000,000
2. Describe how you would go about estimating the number of Americans who are in grade 7.

#### References

Achieve the Core Grade 7 Micro Models and Reasoned Estimates Mini Assessment

Grade 7 Micro Models and Reasoned Estimates Mini Assessment by is made available by Achieve the Core under the CC0 1.0 license. Accessed Oct. 9, 2017, 11:49 a.m..

### Problem 3

Option #3 (Students choose or are assigned one of the five anchor problems to work on with a group of peers. After collaboratively deciding their approach and solution, students can prepare a poster to show their response.)

Jonah started listening to an album just as he clicked to download it. The screen image shows the download progress at the end of the first song.

Jonah continues listening to the album in order. Which song will Jonah be listening to when the download of the full album is complete? Show your work or explain your answer

#### References

Achieve the Core Grade 7 Micro Models and Reasoned Estimates Mini Assessment

Grade 7 Micro Models and Reasoned Estimates Mini Assessment by is made available by Achieve the Core under the CC0 1.0 license. Accessed Oct. 9, 2017, 11:49 a.m..

### Problem 4

Option #4 (Students choose or are assigned one of the five anchor problems to work on with a group of peers. After collaboratively deciding their approach and solution, students can prepare a poster to show their response.)

Will owning an NBA Team make you rich?
The graph below shows the earnings (the amount the team made or lost) for the Charlotte Bobcats from 2005–2013.

What are the estimated average yearly earnings? Show or explain your work.

#### References

Achieve the Core Grade 7 Micro Models and Reasoned Estimates Mini Assessment

Grade 7 Micro Models and Reasoned Estimates Mini Assessment by is made available by Achieve the Core under the CC0 1.0 license. Accessed Oct. 9, 2017, 11:49 a.m..

### Problem 5

Option #5 (Students choose or are assigned one of the five anchor problems to work on with a group of peers. After collaboratively deciding their approach and solution, students can prepare a poster to show their response.)

You are marketing Bus Buzzz, a new headphone designed specifically for people riding a bus. Market research shows that teenagers and senior citizens are the two biggest markets for your product.

You will be advertising on television. After doing some research, you find that 0.3% of teenagers and 0.31% of senior citizens who see a commercial will buy Bus Buzzz.

1. If you can afford to run daily commercials on two shows for one week, on which two shows will you choose to advertise? Explain your answer.
2. Estimate the number of people you expect to buy Bus Buzzz based on the commercials you run. Show your work.
3. Evaluate your model. The CEO of Bus Buzzz is worried that you are double-counting people, because the two shows you selected are on TV at different times. Explain whether or not her concern will make you revise your model.

#### References

Achieve the Core Grade 7 Micro Models and Reasoned Estimates Mini Assessment

Grade 7 Micro Models and Reasoned Estimates Mini Assessment by is made available by Achieve the Core under the CC0 1.0 license. Accessed Oct. 9, 2017, 11:49 a.m..

## 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.

There is no problem set for this lesson, as the activity will take the whole class period. If there is extra time, spiral in review problems from earlier in the unit or previous two units.