# Addition and Subtraction of Fractions/Decimals

## Objective

Add fractions with unlike denominators whose sum is less than 1.

## Materials and Resources

• Square-sized paper  — 2 pieces per student

## Common Core Standards

### Core Standards

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• 5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

• 5.NF.A.2 — Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

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• 4.NF.A.1

• 4.NF.B.3

## Criteria for Success

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1. Understand that in order to add quantities, they must have the same unit (which in the case of fractions, are their denominators).
2. Find common units for fractions with unlike denominators by finding equivalent fractions using a number line and an area model (MP.5).
3. Understand that there is more than one possibility for the common unit used, and use that to optionally find the least common denominator.
4. Add two fractions with unlike denominators whose sum is less than 1 (and therefore does not require regrouping), simplifying the sum if applicable.
5. Simplify a fraction.
6. Solve one-step word problems involving the addition of two fractions with unlike denominators whose sum is less than 1 (MP.4).

## Tips for Teachers

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• The Progressions for the Common Core State Standards in Math state, “It is not necessary to find a least common denominator to calculate sums of fractions, and in fact the effort of finding a least common denominator is a distraction from understanding algorithms for adding fractions” (p. 11). Thus, throughout the unit, students are encouraged to find a common denominator but never forced to use the least common denominator.
• There are five Anchor Tasks in today’s lesson. However, because the first one just lays a conceptual foundation for adding like units and all the subsequent ones include just a single computation, it should be possible to fit it in a single lesson.
• The algorithm for adding fractions with unlike denominators is explicitly discussed in Lesson 6. However, students might uncover it before then, especially since students have used multiplication and division to find equivalent fractions in Grade 4 (4.NF.1) and in Lesson 1. If that does happen, you can discuss it as a class when it comes up naturally, and allow students to use it as a strategy before Lesson 6.
• For when students get to the generalized algorithm for adding fractions with unlike denominators in Lesson 6, it may be helpful for students to see multiple examples of previous problems they’ve completed. Thus, keep anchor charts from the Anchor Tasks in Lessons 4 and 5 up after their instruction.
• Before the Problem Set, you could have students play a game to practice adding fractions with unlike denominators, such as "Wacky Fractions" or "Fraction Addition War", from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

1. Solve.
1. 1 orange + 3 oranges = ___________
2. 1 child + 3 adults = ___________
2. What do you notice about #1 above? What do you wonder?

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 3Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 3 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 your work with an area model.

${{1\over2}+{1\over4}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 3Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 3 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 3

Solve. Show your work with an area model and a number line.

${{1\over3}+{1\over2}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 3Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 3 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 4

Solve. Show your work with an area model and a number line.

${{2\over3}+{1\over4}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 3Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 3 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 5

1. Solve. Show your work with an area model and a number line.

${{2\over9}+{2\over3}}$

1. Is there another common unit that can be used to solve?

## Discussion of Problem Set

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• Look at #1. What fractions are equivalent to $\frac{4}{9}$? What fractions are equivalent to $\frac{2}{6}$? What equivalent fractions did you use to add these fractions together?
• Look at #2. How did you use the number line to figure out the sum?
• Look at #6. How did you use an area model to find your answer?
• Look at #8. For part (a), what common denominators did you choose? Why do both of them work? For part (c), how did you solve? What did you get as the sum?
• Look at #9. What is the sum of the two fractions you came up with? Was anyone able to find a closer sum? Did anyone get an exact sum of $\frac{1}{2}$

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### Problem 1

Solve. Show or explain your work.

${{1\over2}+{1\over5}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 3Exit Ticket, Question #1

Grade 5 Mathematics > Module 3 > Topic B > Lesson 3 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.

Carpenters are laying down hardwood floors in a living room. On the first day, they laid down $\frac{2}{5}$ of the whole floor. On the second day, they laid down $\frac{1}{4}$ of the whole floor. The area model shown can be used to find how much of the whole floor they laid over the two days. • How much of the floor did they lay down over the two days?
• Explain how the area model can be used to answer the question.

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