Proportional Relationships

Lesson 16


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

Common Core Standards

Core Standards


  • 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.

Foundational Standards


  • 6.RP.A.3

Criteria for Success


  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


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.

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Anchor Problems


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)
$$4$$ $$1$$ $$5$$
  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?

Guiding Questions

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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?

Guiding Questions

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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 a variety of problems from Lessons 13-16

Target Task


A preschool makes their own playdoh using flour, salt, and water. The table below shows the relationship between the amount of flour and salt that is needed for the recipe before the water is added. Complete the table.

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

Mastery Response


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