# Addition and Subtraction of Fractions/Decimals

## Common Core Standards

### Core Standards

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• 5.NF.A — Use equivalent fractions as a strategy to add and subtract fractions.

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• 4.NF.A.2

• 4.NF.B.3

## Criteria for Success

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1. Add two fractions with like denominators that does not require regrouping.
2. Add two fractions with like denominators that requires regrouping.
3. Rewrite a fraction as an equivalent mixed number.
4. Simplify a fraction.
5. Assess the reasonableness of an answer using number sense and estimation (MP.1).

## Tips for Teachers

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• Lessons 2 and 3 are intended to address the cluster heading “use equivalent fractions as a strategy to add and subtract fractions” (5.NF.A), which presumably includes adding fractions with like denominators. But, this lesson is arguably more directly aligned to the work of 4.NF.3 where students added and subtracted fractions with like denominators. It is up to your discretion about whether this lesson is needed or not.
• “The term ‘improper’ can be a source of confusion because it implies that this representation is not acceptable, which is false. Instead it is often the preferred representation in algebra. Avoid using this term and instead use ‘fraction’ or ‘fraction greater than one’” (Van de Walle, Teaching Student-Centered Mathematics, 3-5, vol. 2, p. 217). Further, fractions do not always need to be converted from ‘improper’ fractions to mixed numbers, since the need to do so often depends on the context (e.g., in the case of fractional coefficients in algebra, they are often written as fractions greater than one, which are generally easier to manipulate). Thus, while every anchor task below includes the question of whether the sum can be written as a mixed number, you may choose to skip that question for certain tasks so that students don’t get the wrong impression that fractions must always be written as mixed numbers whenever possible.
• “It is possible to over-emphasize the importance of simplifying fractions... There is no mathematical reason why fractions must be written in simplified form, although it may be convenient to do so in some cases” (NF Progression, p. 11). Thus, while each anchor task includes the question of whether the sum can be simplified, you may choose to skip that question for certain tasks so that students get the wrong impression that fractions must always be simplified whenever possible.
• As a supplement to the Problem Set, students can play "Kakooma" from 5.NF.1 - About the Math, Learning Targets, and Rigor by the Howard County Public School System (You can give students varying levels of difficulty. Note that there are a few examples in all versions where students will be working with fractions with unlike denominators. But, because students have done similar work in Grade 4, and this will be a challenge problem, it is appropriate and will preview work in coming lessons.)

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Solve.

1. Ms. Needham made a lasagna for dinner with her family. She cut the lasagna into 12 pieces. Her family ate 4 pieces of lasagna the night that she made it. The next day, they ate 3 more pieces. What fraction of the lasagna did Ms. Needham’s family eat altogether?
2. Ms. Roll is stringing beads to make a 16-inch necklace. At the end of the first night of working on it, she has 5 inches of beads strung. At the end of the second night of working on it, she has another 7 inches of beads strung. What fraction of the necklace has Ms. Roll completed?

### Problem 2

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

a.      $\frac{7}{8}+\frac{6}{8}$

b.     $\frac{13}{12}+\frac{5}{12}$

### Problem 3

Solve. Show or explain your work.

a.     ${5{1\over8}+{5\over8}}$

b.     ${9{11\over12}+{11\over12}}$

c.     ${3{4\over17}+4{8\over17}}$

d.     ${2{11\over15}+2{13\over15}}$

## Discussion of Problem Set

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• Look at #2. What strategies did you use to solve? How can you tell, before actually adding, whether you’ll need to regroup?
• Look at #8. What mistake did the student make? How can you use estimation to show the student that their answer is unreasonable?

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Solve. Show or explain your work.

1.     ${1{2\over5}+2{1\over5}}$

2.     ${4{5\over8}+3{7\over8}}$

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