# Fraction Operations

## Objective

Add and subtract fractions that require regrouping where the total is less than or equal to two.

## 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. Estimate whether sums and differences will be greater than or less than one whole when adding or subtracting fractions where the total is between 1 and 2.
2. Add and subtract fractions with like units that require regrouping where the total is less than or equal to 2 using a variety of strategies, such as:
1. Adding like units, regrouping where necessary, or
2. Using simplifying strategies, such as making a whole, going down over a whole, or counting up over a whole.
3. (Optional) Simplify solutions by rewriting them using the largest possible unit.
4. Assess the reasonableness of answers based on estimates (MP.1).

## Tips for Teachers

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• Similar to Lesson 3, 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 that cross a whole, you may decide to cut this aspect of the lesson, but be sure to touch on the idea at some point in the unit.
• “Calculations with mixed numbers provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 13). While this lesson does not explicitly have students computing with mixed numbers, they will start to see a wider variety of approaches to adding and subtracting with fractions as they get larger in value, allowing them to construct viable arguments and critique the reasoning of others regarding the solution method (MP.3).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

1. Estimate the following sums.

a.  ${{3\over4}+{2\over4}}$

b.  ${{5\over6}+{3\over6}}$

1. Solve for the actual sums in #1 above.

### Problem 2

1. Estimate the following differences.

a.  ${1{1\over3}-{2\over3}}$

b.  ${1{3\over8}-{7\over8}}$

1. Solve for the actual differences in #1 above.

### Problem 3

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

a.   ${{5\over8}+{11\over8}}$

b.   ${2-{2\over5}}$

## Discussion of Problem Set

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• What did Jaissa do to solve in #2? Why do you think she did that?
• What did Frederick do to solve in #4(a)? Why do you think he did that?
• What did Helena do to solve in #4(b)? Why do you think she did that?
• Of Jaissa’s, Frederick’s, and Helena’s strategies, which ones make the most sense to you? Which ones are you still struggling with making sense of?
• What strategies did you use to solve the problems in the Problem Set? Did you use the same strategy each time?

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### Problem 1

What is $\frac{10}{12}+\frac{5}{12}$?

A.  $\frac{15}{24}$

B.  $\frac{5}{12}$

C.  $1\frac{1}{3}$

D.  $1\frac{3}{12}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 16Exit Ticket, Question #2

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

Solve. Show or explain your work.

$1\frac{2}{7} - \frac{5}{7}=$ _________

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 17Exit Ticket, Question #2

Grade 4 Mathematics > Module 5 > Topic D > Lesson 17 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.

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