Understanding and Representing Ratios

Lesson 17

Math

Unit 1

6th Grade

Lesson 17 of 18

Objective


Solve more complex ratio problems using tape diagrams.

Common Core Standards


Core Standards

  • 6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Criteria for Success


  1. Use tape diagrams to represent situations with more than one ratio or ratios that change.
  2. Solve ratio problems when given a part:part ratio and a difference between the two quantities.

Tips for Teachers


Students encounter more challenging real-world problems in this lesson providing them with the opportunity to apply their ratio reasoning and strategies to model and solve the problems (MP.4). Tape diagrams are an effective tool to use to solve these problems, however, students may also use other strategies of their choice. 

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Anchor Problems


Problem 1

At a concert, the ratio of the number of people who are local to people who are from out of town is 2:7. If there are 250 more people from out of town than people who are local, how many local people are at the concert?

Guiding Questions

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Problem 2

The Business Direct Hotel serves people who travel for business. On a Saturday night, not many people are traveling, so the ratio of the number of busy rooms to open rooms is 2:5. However, on Sunday night, a lot of people arrive for a conference. The ratio of the number of busy rooms to open rooms is 6:1. 

If the Business Direct Hotel has 432 busy rooms on Sunday night, how many open rooms does it have on Saturday night?

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic A > Lesson 6Exercise 1

Grade 6 Mathematics > Module 1 > Topic A > Lesson 6 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 3

You made green paint by mixing yellow and blue paint in a ratio of 5 to 3. You then added an additional 14 liters of blue paint, and the amount of yellow paint and blue paint in the mixture was equal. How much green paint total was in the mixture at first, before adding the extra blue paint?

Guiding Questions

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References

Institute for Mathematics and Education Draft 6-7 Progression on Ratios and Proportional Relationshipspage 7

Draft 6-7 Progression on Ratios and Proportional Relationships, by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed Sept. 11, 2017, 10:53 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Problem Set

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Target Task


A tee-shirt store sells long sleeve (LS) and short sleeve (SS) tee-shirts. In the fall, they stock 4 LS tee-shirts for every 3 SS tee-shirts. In the spring, they stock only 2 LS tee-shirts for every 5 SS tee-shirts. 

If the store stocks the same number of tee-shirts in the fall and in the spring, and there are 105 SS tee-shirts in the fall, how many SS tee-shirts does the store stock in the spring?

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 problems similar to Anchor Problem #3.
  • Include a variety of review problems using tape diagrams from the previous two lessons.
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Lesson 16

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Lesson 18

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding & Describing Ratios

Topic B: Equivalent Ratios

Topic C: Representing Ratios in Tables

Topic D: Solving Part:Part:Whole Ratio Problems

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