Understanding and Representing Ratios

Lesson 4

Math

Unit 1

6th Grade

Lesson 4 of 18

Objective


Reason with equivalent ratios and determine if two ratios are equivalent.

Common Core Standards


Core Standards

  • 6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

Foundational Standards

  • 5.NF.B.5
  • 5.NF.B.5.A
  • 5.NF.B.5.B

Criteria for Success


  1. Recall and use the definition of equivalent ratios:  The ratio of $$A:B$$ is equivalent to $$c\times A:c\times B$$ for a nonzero number $$c$$. Or, two ratios are equivalent if there is a nonzero number that can be multiplied by both quantities in one ratio to equal the corresponding quantities in the second ratio.
  2. Use the definition of equivalent ratios to find ratios that are equivalent to a given ratio.
  3. Given two ratios, use ratio reasoning and the definition of equivalent ratios to determine if they are equivalent. 
  4. Given a ratio and one value in an equivalent ratio, find the other value in the equivalent ratio.

Tips for Teachers


This is the second of two lessons that introduce equivalent ratios. Students should continue to understand the definition of equivalent ratios and use it in context to determine and/or find equivalent ratios. Diagrams can be used to support understanding where applicable, but students should also see the multiplicative relationship between two ratios, as described in the definition.

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Anchor Problems

25-30 minutes


Problem 1

In a marching band there are 24 trombones and 15 snare drums.

Heather says, “The ratio of trombones to snare drums is 24:15.” Audrey says, “No, the ratio of trombones to snare drums is 8:5.” Who is right and why?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Equivalent Ratios 2

Equivalent Ratios 2, accessed on July 18, 2017, 3:35 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

You are making a mixed bag of walnuts and cashews. The ratio of the number of walnuts to the number of cashews you want to use is 5:6. You have 54 cashews to include in the mix. How many walnuts should you add? Justify your answer by showing that the new ratio you created of the number of walnuts to cashews is equivalent to 5:6.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic A > Lesson 4Exercise 2

Grade 6 Mathematics > Module 1 > Topic A > Lesson 4 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

Which of the ratios in the list below are equivalent to the ratio 12:8? Explain or show how you know each ratio is equivalent.

a.   8:12

b.   3:2

c.   2:3

d.   24:16

e.   6:4

f.   6:2

g.   15:10

h.   20:16

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 store sells water bottles in large and small sizes. There are 24 large water bottles and 18 small water bottles on display in the store. The manager of the store wants there to be 3 large water bottles on display for every 2 small water bottles. Should the manager make any changes to the current display? Explain.

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.

Next

Represent ratios using double number lines and identify equivalent ratios.

Lesson 5
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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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