# Fraction Operations

## Objective

Solve word problems involving addition, subtraction, and multiplication of fractions.

## Common Core Standards

### Core Standards

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• 4.NF.B.3.D — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

• 4.NF.B.4.C — Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

## Criteria for Success

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1. Make sense of a three-act task and persevere in solving it (MP.1).
2. Solve two- and multi-step word problems that involve the addition, subtraction, and multiplication of fractions (MP.4).

## Tips for Teachers

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Let students work on each problem in the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram, then allow them to try again on their own.

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## Anchor Tasks

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### Problem 1

Act 1: Watch the slideshow of images listed under Act 1 in Cans of Paint.

How much paint is in the display?

#### Guiding Questions

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#### References

The Mind of an April Fool Cans of Paint

Cans of Paint is made available on The Mind of an April Fool under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Act 2: Use the following information to solve.

• There are 12 cans of red paint that are each $3\frac{10}{16}$ quarts.
• There are 14 cans of green paint that are each $3\frac{11}{16}$ quarts.
• There are 4 cans of blue paint that are each $3\frac{10}{16}$ quarts.
• Do you have all the information you need to solve?

#### Guiding Questions

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#### References

The Mind of an April Fool Cans of Paint

Cans of Paint is made available on The Mind of an April Fool under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

Act 3: Reveal the answer.

There are $109\frac{5}{8}$ quarts of paint.

#### Guiding Questions

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#### References

The Mind of an April Fool Cans of Paint

Cans of Paint is made available on The Mind of an April Fool under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by The Match Foundation, Inc.

### Problem 4

Act 4 (the sequel): If a quart of paint costs \$8, how much does each color of paint in the display cost? What about all of them together?

#### Guiding Questions

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#### References

The Mind of an April Fool Cans of Paint

Cans of Paint is made available on The Mind of an April Fool under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by The Match Foundation, Inc.

## Discussion of Problem Set

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• How much land would be left unused in #1? How did you subtract from a whole?
• How did you determine what could be the amount Jake added to his bottle in #3(b)?
• How many tubes of paint are used for each shirt in #4? 2 or 18? How do you know?
• When you check for reasonableness, do you look at your equations and model? How do you figure out if your answer is reasonable?

## Target Task

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The table below shows the sizes and weights of containers of potato salad sold at a store.

Potato Salad

 Size Weight (pounds) Small ${{2\over8}}$ Medium ${{3\over8}}$ Large ${{6\over8}}$ Extra-large ${1{1\over8}}$

Kim purchased 6 small containers of potato salad and Seth purchased 2 extra-large containers of potato salad. What is the diference in the weights, in pounds, of Kim's and Seth's purchases?

### Mastery Response

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