Curriculum  /  Math  /  7th Grade  /  Unit 1: Proportional Relationships  /  Lesson 16

Proportional Relationships

Lesson 16

Math

Unit 1

7th Grade

Lesson 16 of 18

Objective

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.
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Anchor Problems

25-30 minutes

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)
$$4$$ $$1$$ $$5$$
$$\frac{2}{3}$$    
    $$3\frac{3}{4}$$

a.    If you have $${{2\over3}}$$ cups of noodles, how many cups of cheese should you add? What size pan do you need?

b.   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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Student Response

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References

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

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 Fishtank Learning, 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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Student Response

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

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)
$$1$$    
$$2$$ $$\frac{3}{4}$$  
  $$4\frac{1}{2}$$  
    $$7\frac{1}{3}$$

Student Response

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Additional Practice

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

  • Include a variety of problems from Lessons 13-16

Next

Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.

Lesson 17
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Lesson Map

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Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Topic B: Non-Proportional Relationships

Topic C: Connecting Everything Together

Topic D: Solving Ratio & Rate Problems with Fractions

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