# Proportional Relationships

## Objective

Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.

## 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.

• 7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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• 6.RP.A.3

## Criteria for Success

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1. Write a proportion of two equivalent ratios, either part:part or part:whole.
2. Identify situations when a part:whole ratio is required, compared to a part:part.
3. Attend to precision with units when setting up a proportion (MP.6).
4. Solve ratio and rate problems using proportions or other strategies such as tape diagrams.

## Tips for Teachers

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#### 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

Macaroni and cheese is made by combining noodles and cheese in a ratio of 4:1. A pan must be big enough to hold the total amount of food. The table below shows 3 different variations of the recipe and the size pan that is needed.

 Noodles (cups) Cheese (cups) Pan Size (cups) $4$ $1$ $5$ $\frac{2}{3}$ $3\frac{3}{4}$
1.  If you have ${{2\over3}}$ cups of noodles, how many cups of cheese should you add? What size pan do you need?
2. If you have a pan that holds ${3{3\over4}}$ cups, how many cups of noodles and cheese should you use to fill this pan?

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 13Exercise

Grade 7 Mathematics > Module 1 > Topic C > Lesson 13 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..

Modified by The Match Foundation, Inc.

### Problem 2

Gus is painting a large bookshelf to match a desk in his office. The desk is painted a color orange, in the ratio of 1 part red to 2 parts yellow. If Gus thinks he will need 2 gallons of the orange paint, how many gallons of each color paint should he mix to get the right shade of orange?

## Problem Set

? 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 a variety of problems from Lessons 13-16

 Flour (cups) Salt (cups) Total (cups) $1$ $2$ $\frac{3}{4}$ $4\frac{1}{2}$ $7\frac{1}{3}$