Proportional Relationships

Lesson 16

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.

Foundational Standards

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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.

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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?

Guiding Questions

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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?

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

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The table below shows the combination of a dry prepackaged mix and water to make concrete. The mix says for every 1 gallon of water, stir 60 pounds of dry mix. We know that 1 gallon of water is equal to 8 pounds of water. Using the information in the table, complete the remaining parts of the table.

Dry Mix (pounds) Water (pounds) Total (pounds)
  $$8$$  
$$75$$ $$10$$  
    $$14\frac{1}{6}$$
$$4\frac{1}{2}$$    

References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 13Exit Ticket

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..

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