Lesson 3 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

Subtract fractions with like denominators.

Common Core Standards

Core Standards

The core standards covered in this lesson

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

Number and Operations—Fractions

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

Foundational Standards

The foundational standards covered in this lesson

4.NF.A.2

Number and Operations—Fractions

4.NF.A.2 — Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.B.3

Number and Operations—Fractions

4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Subtract two fractions with like denominators that does not require regrouping.
Subtract two fractions with like denominators that requires regrouping, including subtracting from a whole.
Rewrite a fraction greater than one as an equivalent mixed number.
Simplify a fraction.
Assess the reasonableness of an answer using number sense and estimation (MP.1).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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). 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.
While every Anchor Task below includes the question of whether the difference 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. "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).
While each Anchor Task includes the question of whether the difference 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. "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).
As a supplement to the Problem Set, students can play "The Fraction Splat!" by Steve Wyborney. All of lesson 11 and lesson 12 align to this lesson.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

a. Ms. White has $${{5\over8}}$$ of a cake. Throughout the week, she ate $${{2\over8}}$$ of it. How much of the cake does Ms. White have left?

b. Ms. Cole’s hair was $${{11\over12}}$$ of a foot long. She went to the hairdresser and cut off $${{2\over12}}$$ of a foot of her hair. How long is Ms. Cole’s hair now?

Guiding Questions

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Problem 2

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

a. $${1-{3\over8}}$$

b. $${1{3\over12}-{7\over12}}$$

Guiding Questions

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Problem 3

Solve. Show or explain your work.

a. $${4{7\over8}-{3\over8}}$$

b. $${8-{5\over6}}$$

c. $${9{1\over12}-{7\over12}}$$

d. $${5{6\over13}-4{4\over13}}$$

e. $${6-4{5\over16}}$$

f. $${14{7\over18}-12{13\over18}}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #2. What strategies did you use to solve? How can you tell, before actually subtracting, whether you’ll need to regroup?
Look at #4. How do you regroup a whole when there is no fractional part?
Look at #5. What strategies did you use to solve?
What are the simplified solutions to #5a and #5c? What does that make you think about how to add or subtract fractions with unlike denominators?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. Show or explain your work.

a. $${{1}-{1\over4}}$$

b. $$1\frac{7}{8}-\frac{3}{8}$$

d. $${7{1\over6}-2{5\over6}}$$

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 2

Lesson 4

Lesson Map

Topic A: Addition and Subtraction of Fractions

Recognize and generate equivalent fractions.

5.NF.A

Add fractions with like denominators.

5.NF.A

Subtract fractions with like denominators.

5.NF.A

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

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 1 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is less than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is greater than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions greater than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers.

5.NF.A.2

Add and subtract more than two fractions.

5.NF.A.1

Solve two- and multi-step word problems involving addition and subtraction of fractions.

5.NF.A.2

Topic B: Addition and Subtraction of Decimals

Add decimals.

5.NBT.B.7

Subtract decimals.

5.NBT.B.7

Solve two- and multi-step word problems involving addition and subtraction of decimals.

5.NBT.B.7

Addition and Subtraction of Fractions/Decimals

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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