# Proportional Relationships

## Objective

Find the unit rate of ratios involving fractions.

## Common Core Standards

### Core Standards

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• 7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

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• 6.RP.A.2

• 6.RP.A.3.B

• 6.NS.A.1

## Criteria for Success

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1. Recall a rate, associated with a ratio $a:b$, as $a/b$ units of the first quantity per 1 unit of the second quantity, especially in the case where $a$ and $b$ are both fractions. For example, if a person walks $6\frac{3}{4}$ miles in $2\frac{1}{4}$ hours, the person is traveling at a rate of 3 miles per hour.
2. Recall a unit rate as the numerical part of a rate. For example, in the rate of 3 miles per hour, the 3 represents the unit rate.
3. Identify two unit rates for a ratio $a:b$, as $a/b$  and $b/a$.
4. Compute the value of a complex fraction.
5. Use precision in communicating with units (MP.6).

## Tips for Teachers

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• In the last few lessons of this unit, students use their understanding of proportional relationships to solve problems. They learn strategies, including using a unit rate and using proportions, to efficiently solve problems, and they make connections back to the representations of proportional relationships.
• In order to fully access this lesson, students may need to review or recall concepts and skills from 6.NS.1 and 6.RP.2, particularly dividing two fractions and finding the unit rate of whole numbers.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). 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

Find the unit rate in each situation below in miles per hour.

1. Andy drives 180 miles in 3 hours.
2. Brianna bikes ${36{1 \over 2}}$ miles in 2 hours.
3. Chris walks ${4{1 \over 2}}$ miles in ${1{1 \over 4}}$ hours.
4. Deandre runs ${6{1 \over 3}}$miles in 50 minutes.

### Problem 2

Angel and Jayden were at track practice. The track is ${{2 \over 5}}$ kilometers around.

• Angel ran 1 lap in 2 minutes.
• Jayden ran 3 laps in 5 minutes.
1. How many minutes does it take Angel to run one kilometer? What about Jayden?
2. How far does Angel run in one minute? What about Jayden?
3. Who is running faster? Explain your reasoning.

#### References

Illustrative Mathematics Track Practice

Track Practice, accessed on Aug. 2, 2017, 11:06 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

### Problem 3

Which is the better deal? Justify your response.

3${1 \over3}$ lb. of turkey for $10.50 OR 2${1 \over2}$ lb. of turkey for$6.25

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 11Exit Ticket

Grade 7 Mathematics > Module 1 > Topic C > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.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.

• Include problems where students are given two ratios and asked to find the difference between the rates. For example, in Anchor Problem #1, how much faster, in mph, is Brianna biking than Chris is walking?
• Include problems where students are given a list of items with amounts and cost, and are asked to determine which item has the lowest or highest cost per unit.

On rollerskates, Ian can travel $\frac{3}{4}$ of a mile in 5 minutes. On his bike, he can travel $3 \frac{1}{2}$ miles in 12 minutes. How fast, in miles per hour, can Ian travel on rollerskates and on his bike?