# Fraction Operations

## Objective

Add and subtract fractions within 1 with the same units.

## Common Core Standards

### Core Standards

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• 4.NF.B.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

• 4.NF.B.3.B — Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

## Criteria for Success

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1. Understand that when adding or subtracting quantities with like units, one adds or subtracts the values and the unit stays the same, which in the case of fraction addition and subtraction means adding or subtracting the numerators while the denominator does not change.
2. Estimate whether sums and differences will be greater than or less than 1 half when adding or subtracting fractions less than 1 with the same units.
3. Add and subtract fractions with like units where the total is less than 1.
4. Add and subtraction fractions with like units where the total is 1, requiring regrouping.
5. (Optional) Simplify solutions by rewriting them using the largest possible unit.
6. Assess the reasonableness of answers based on estimates (MP.1).

## Tips for Teachers

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Since it is possible to overemphasize the importance of simplifying fractions, the corresponding criteria for success and questions in the Anchor Tasks are optional. If you want the focus for today to solely be on adding and subtracting fractions within 1, you may decide to cut this aspect of the lesson, but be sure to touch on the idea at some point in the unit.

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## Anchor Tasks

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### Problem 1

1. Solve.
1. 5 ones + 2 ones = ___________
2. 5 dogs + 2 dogs = ___________
3. 5 meters + 2 meters = ___________
4. 5 tenths + 2 tenths = ___________
2. What do you notice about the problems in #1? What do you wonder?
3. Use what you observed in #1 to think about what the solution to 5 tenths – 2 tenths would be.

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 16Concept Development

Grade 4 Mathematics > Module 5 > Topic D > Lesson 16 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 The Match Foundation, Inc.

### Problem 2

First, estimate the following sums. Then add.

a.   ${{2\over8}+{3\over8}}$

b.   ${{1\over6}+{3\over6}}$

#### Guiding Questions

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### Problem 3

First, estimate the following differences. Then subtract.

a.   ${{4\over5}-{1\over5}}$

b.   ${{7\over12}-{3\over12}}$

#### Guiding Questions

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### Problem 4

First, estimate the following solutions. Then add or subtract.

a.   ${{3\over4}+{1\over4}}$

b.   ${1-{3\over10}}$

#### Guiding Questions

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## Discussion of Problem Set

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• How do #1 and #7 help you understand how to subtract or add fractions?
• What was difficult about #3?
• What error(s) did the student make in #6? How could you know, just by looking at the sum they came up with, that it’s incorrect?
• How did you solve #9?
• How did you subtract from 1 in #11?
• What made #12 different from previous problems? How did you solve?
• How is the number line helpful in showing how we can subtract and add fractions with like units?

## Target Task

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Solve.

1.   ${{7\over8}-{4\over8}}$

2.   ${{5\over10}+{3\over10}}$

3.   ${1-{2\over5}}$

### Mastery Response

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