# Multi-Digit and Fraction Computation

## Objective

Solve and write story 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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1. Model a real-world application using division of fractions (MP.4).
2. Solve fraction division problems using visual models and computation.
3. Write story problems for fraction division situations involving a remainder and no remainder.

## Tips for Teachers

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• This lesson follows the format of the lesson plan for the Poster Problem “No Matter How You Slice It” by SERP. The components of the lesson plan are broken into two parts for Anchor Problems #1 and #2: Anchor Problem #1 includes the Launch and Handout #1. Anchor Problem #2 includes the Workshop activity (Handout #2) and class discussion. There is no Problem Set Guidance due to the length of time of the Workshop activity.
• Students were introduced to the fraction division algorithm in Lesson 4; however, students should continue to use visual models to make sense of fraction division and to confirm the answers they get via calculations.
• The following tools or materials are useful for this lesson: computer to show videos, markers and poster paper for creating posters.

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## Anchor Problems

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### Problem 1

Do the Launch and Pose a Problem sections SERP's Poster Problem "No Matter How you Slice It."

Launch:

• Watch the video on slide 1.
• Can you explain how the slicer works?
• According to the video, what is the thinnest slice this slicer can make?
• If you know the length of a block of cheese, can you determine how many slices it can make?
• Suppose you get a new block and you know how thick you want your slices. What do you need to know in order to tell how many sandwiches you can make?

Pose a Problem:

• Discuss slides 2, 3, and 4.
• Complete Handout #1.

#### Guiding Questions

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#### References

SERP Poster Problems No Matter How You Slice ItLaunch and Pose a Problem

No Matter How You Slice It from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed Sept. 28, 2017, 1:18 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Do the Workshop section of SERP's Poster Problem "No Matter How You Slice It", including Handout #2. Students can work in pairs or in small groups.

Handout #2:

Make up and solve two of your own slicing problems. In problem A, you should not have any cheese left over, and in problem B, you one must have some cheese left over.

For each problem, you need to determine how much cheese you start off with: how long is your block of cheese? You also need to say how thick you want the slices of cheese to be—or you can decide how many slices you will need in total. Keep in mind that the thickness of each slice should be between ${\frac{1}{32}}$ and ${\frac{1}{2}}$ inches thick.

After you create your problems, make a poster showing each problem and its solution. Each solution should include an explanation, at least one calculation, and a diagram.

#### Guiding Questions

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#### References

SERP Poster Problems No Matter How You Slice ItWorkshop

No Matter How You Slice It from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed Sept. 28, 2017, 1:18 p.m..

Modified by The Match Foundation, Inc.

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There are other ways to think about division of fractions. Try these two questions. They both use division, but why? And how do you know what to divide by what?

1. The water level in the reservoir has gone down ${2 \frac{1}{2}}$ feet in the last month and a half. How fast is the water level going down per month?
2. Farmer Schmidt owns ${\frac{3}{4}}$ of a square mile of land. Her field is a rectangle. One side is ${\frac{2}{3}}$ of a mile. How long is the other side?

#### References

SERP Poster Problems No Matter How You Slice ItSlide #7

No Matter How You Slice It from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed Sept. 28, 2017, 1:18 p.m..

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