Understanding and Representing Ratios

Lesson 16

Math

Unit 1

6th Grade

Lesson 16 of 18

Objective


Solve part:whole ratio problems using tape diagrams.

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."
  • 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. Represent a ratio using a tape diagram.
  2. Use tape diagrams to solve ratio problems when a ratio and the value of the whole are given.
  3. Compare the strategy of using a tape diagram to other strategies learned so far (double number line and table).
  4. Given a ratio of a:b, in like units, reason about the ratio of a units to total units, b units to total units, and the fractional amounts of the total that represent a and b. For example, “For every vote candidate A received, candidate C received nearly three votes,” meaning that candidate C received 3 out of every 4 votes, or $$\frac{3}{4}$$ of all votes.”

Tips for Teachers


Review and recall from Lesson 12 how students used tables of equivalent ratios to solve problems involving a total or whole amount. Introduce tape diagrams as another method to solve these problems.

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Anchor Problems


Problem 1

Sammy and David were selling water bottles to raise money for new soccer uniforms. Sammy sold 5 water bottles for every 3 water bottles David sold. Together they sold 160 water bottles. How many did each person sell? Draw a tape diagram and use it to show your answer.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic A > Lesson 5Exercise 2

Grade 6 Mathematics > Module 1 > Topic A > Lesson 5 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

The ratio of the number of boys to the number of girls at school is 4:5. There are 270 students at this school. For each of the following statements, explain whether the statement is true or false and why:

a.   The number of boys at school is $$\frac{4}{5}$$ the number of girls.

b.    $$\frac{4}{5}$$ of the students in the school are boys.

c.   There are exactly 30 more girls than boys.

d.   There are exactly 30 boys at the school.

e.    $$\frac{5}{9}$$ of the students in the school are girls.

Guiding Questions

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References

Illustrative Mathematics Evaluating Ratio Statements

Evaluating Ratio Statements, accessed on July 19, 2017, 11:42 a.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.

Problem Set

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Target Task


In a jigsaw puzzle, there are edge or corner pieces that have at least one straight edge, as well as inside pieces that have no straight edges. The ratio of edge/corner pieces to inside pieces is 3 to 5. If the puzzle has 96 pieces, how many are inside pieces?

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 lot of practice solving ratio problems with like units using tape diagrams. Mix in problems that are part:part and part:whole. 
  • Revisit problems from Lesson 12; have students compare and contrast their solutions using a table and using a tape diagram. 
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Lesson 15

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Lesson 17

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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