# Multi-Digit and Fraction Computation

## Objective

Solve problems involving division with fractions.

## Common Core Standards

### Core Standards

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• 6.NS.A.1 — Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

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• 5.NF.B.6

• 5.NF.B.7

## Criteria for Success

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• Solve fraction division problems using a variety of strategies including visual models and computation.

## Tips for Teachers

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The Problem Set Guidance includes many great resources for problems. The focus of this lesson is on students internalizing the concepts from the previous lessons and beginning to develop fluency with solving fraction division problems. Ensure students have ample time to solve a variety of problems and to engage in conversation with each other around solutions. It may be valuable to include any unused problems from previous lessons to reinforce the conceptual understanding. Any problems not used from the Problem Set Guidance in this lesson can be used for review at the end of the unit prior to the Unit Test.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

It requires ${\frac {1}{4}}$ of a credit to play a video game for one minute.

1. Emma has ${{\frac {7}{8}}}$ credits. Can she play for more or less than one minute? Explain how you know.
2. How long can Emma play the video game with her ${{\frac {7}{8}}}$ credits? How many different ways can you show the solution?

#### References

Illustrative Mathematics Video Game Credits

Video Game Credits, accessed on Sept. 28, 2017, 2:04 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 The Match Foundation, Inc.

### Problem 2

Solve the two problems below using a visual diagram and computation. Compare and contrast the two problems.

Problem 1:

Alisa had ${\frac {1}{2}}$ liter of juice in a bottle. She drank ${{\frac{3}{8}}}$ liters of juice. What fraction of the juice in the bottle did Alisa drink?

Problem 2:

Alisa had some juice in a bottle. Then she drank ${{\frac{3}{8}}}$ liters of juice. If this was ${\frac{3}{4}}$ of the juice that was originally in the bottle, how much juice was there to start?

#### References

Illustrative Mathematics Drinking Juice, Variation 2

Drinking Juice, Variation 2, accessed on Sept. 28, 2017, 2:07 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.

Illustrative Mathematics Drinking Juice, Variation 3

Drinking Juice, Variation 3, accessed on Sept. 28, 2017, 2:07 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.

## 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.

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You are stuck in a big traffic jam on the freeway and you are wondering how long it will take to get to the next exit, which is ${1 \frac {1}{2}}$ miles away. You are timing your progress and find that you can travel ${\frac{2}{3}}$ of a mile in one hour. If you continue to make progress at this rate, how long will it be until you reach the exit?

Solve the problem with a diagram and explain your answer. Then find the answer using an equation and show that it is the same as what you got in your diagram.

#### References

Illustrative Mathematics Traffic Jam

Traffic Jam, accessed on Sept. 14, 2017, 1:31 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 The Match Foundation, Inc.

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