# Understanding and Representing Ratios

Lesson 15

Math

Unit 1

Lesson 15 of 18

## Objective

Solve part:part 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 part:part ratio is given and the value of one of the quantities is given.
3. Compare the strategy of using a tape diagram to other strategies learned so far (double number line and table).

## Tips for Teachers

• Students have just learned about tables as a very effective tool to use for solving ratio problems. Tape diagrams may feel like a step backward in the progression of representations; however, in the next two lessons, students will see more complicated examples where a tape diagram is a very effective tool.
• With tape diagrams, it's important to ensure the units are the same. A common misuse of tape diagrams is to represent quantities measured in different units. For example, if you were working with two ingredients from a recipe, one that used cups and another that used teaspoons, a table would be the more appropriate tool.
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## Anchor Problems

### Problem 1

Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3.

a.   Name two possible lengths of Shanni’s and Mel’s ribbons.

b.   Draw a tape diagram to represent the ratio of ribbon length.

c.   If each block in the tape diagram represented 1 inch, what are the lengths of the ribbons?

d.   What if each block in the tape diagram represented 2 yards, what are the lengths of the ribbons?

e.   Could Shanni’s ribbon be 21 inches and Mel’s ribbon be 9 yards? Why or why not?

#### References

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic A > Lesson 3Exercise 2

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

Mason and Laney ran laps to train for the long-distance running team. The ratio of the number of laps Mason ran to the number of laps Laney ran was 2 to 3.

a.   If Mason ran 4 miles, how far did Laney run?

b.   If Laney ran 930 meters, how far did Mason run?

#### References

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

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

Fishtank Plus Content

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

Your school's office manager surveyed the entire sixth grade to find out what transportation students use to get to school. She determined that the ratio of students who took the bus to students who walked to school to students who got a ride was 5:3:2.

If 27 students walked to school, how many students are in the sixth grade? Draw a tape diagram and use it to show your answer.

### Student Response

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 examples similar to Anchor Problem #2, where students can use a tape diagram to find a missing part.
• Include examples similar to the Target Task, where students can use a tape diagram to find missing parts and add them to determine the total.
• Include review problems from earlier in the unit, where students may use any of the strategies they know to solve a problem.
• EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic A > Lesson 3Exercise 4 & Problem Set: Students may have seen these problems from earlier lessons in this unit; they may solve these now with tape diagrams and compare their solutions to methods used earlier.

Lesson 14

Lesson 16

## Lesson Map

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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