# Fraction Operations

## Common Core Standards

### Core Standards

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• 4.NF.B.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

## Criteria for Success

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1. Estimate the sum of two mixed numbers, determining whether that estimate will be greater than or less than the actual sum.
2. Add two mixed numbers using a variety of strategies, such as:
1. Converting the mixed numbers to fractions greater than 1 and adding like units,
2. Adding the corresponding whole number and fractional parts of both addends, regrouping a whole if necessary, or
3. Using simplifying strategies, such as making a whole.
3. Assess the reasonableness of answers based on estimates (MP.1).

## Tips for Teachers

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Before the Problem Set, you could have students play a modified version of “Rolling Fractions” found on p. 63 of the Georgia Standards of Excellence Curriculum Frameworks: Mathematics GSE Fourth Grade Unit 4: Operations with Fractions. You should modify it by having students find the sum and not the difference. You may also modify it by giving students more denominators to choose from in #1 of the directions (e.g., include all denominators students are expected to work with in Grade 4, including 2, 3, 4, 5, 6, 8, 10, and 12).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

1. Solve.
1. 2 thousands 1 one + 3 thousands 2 ones = ___________
2. 2 dollars 1 cent + 3 hours 2 cents = ___________
3. 2 ones 1 fifth + 3 ones 2 fifths = ___________
2. What do you notice about the problems in #1? What do you wonder?

### Problem 2

Solve.

a.   ${1{1\over4}+2{2\over4}}$

b.   ${4{1\over10}+5{4\over10}}$

### Problem 3

Solve.

a.   ${2{5\over8}+1{3\over8}}$

b.   ${2{5\over8}+1{5\over8}}$

c.   ${4{7\over12}+16{9\over12}}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic F > Lesson 31Concept Development

Grade 4 Mathematics > Module 5 > Topic F > Lesson 31 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.

## Discussion of Problem Set

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• How did you solve #2(c)?
• What error did the student make in #3? What can help you to avoid that mistake?
• Was anyone able to answer #5 without actually adding any values together on paper? How?
• What strategies did you use for #6(d)–(f)? Did you use the same strategies as your classmates?
• What two values did you come up with in #7? How many possible answers are there? What do all of those answers have in common?
• How is adding 4 tens 7 ones and 6 tens 9 ones like adding 4 ones 7 twelfths and 6 ones 9 twelfths? How is it different?
• If you were unsure of any answer on this Problem Set, what could you do to see if your answer is reasonable? Would drawing a picture or estimating the sum be helpful?

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Solve. Show or explain your work.

1.   ${2{3\over8}+1{5\over8}}$

2.   ${3{4\over5}+2{3\over5}}$

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