Lesson 10 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Number and Operations—Fractions

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.

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

Estimate sums and differences.
Assess whether the actual solution of an addition or subtraction problem will be greater or less than a benchmark number.
Assess whether the actual solution to an addition or subtraction word problem will be greater or less than a benchmark number.
Assess the reasonableness and/or correctness of an answer based on number sense (MP.1).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Note that on the Problem Set, #8b is a two-step word problem, which is why it is near the end of the Problem Set. This provides a nice preview for the work students will do in Lesson 12.

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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

Estimate whether the following sums and differences are greater than or less than 1. For any estimate that is less than 1, estimate whether the sum or difference will be greater than or less than $$\frac{1}{2}$$. Be prepared to explain your reasoning.

a. $$\frac{1}{2} + \frac{3}{4}$$

b. $$1 \frac{2}{3} - \frac{2}{5}$$

c. $$\frac{3}{7} + \frac{12}{25}$$

d. $$1 \frac{42}{83} - \frac{99}{100}$$

Guiding Questions

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References

John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II) — Activity 13.1

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Modified by Fishtank Learning, Inc.

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 13 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 13 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 Fishtank Learning, Inc.

Problem 2

Joe is baking cookies. He needs a total of $$2$$ cups of sugar for the recipe. Joe bought a $$4{1\over2}$$ cup bag of sugar and has used $$2{3\over4}$$ cups already.

Without solving the problem, does Joe have enough sugar? Explain your thinking.

Guiding Questions

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References

North Carolina Department of Public Instruction Is Tim Incorrect?

Is Tim Incorrect? from the 3-5 Formative Instructional and Assessment Tasks for the Standards in Mathematics, made available by the North Carolina Department of Public Instruction (NCDPI) Elementary Mathematics Consultants and their public school partners under the CC BY-NC-SA 3.0 license. Accessed Feb. 9, 2018, 1:53 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Kevin and Tiana are making soup. The recipe calls for a pound of onions. They have one onion that weighs $${{1\over2}}$$ pound and another that weighs $${{2\over5}}$$ pound. Kevin says they only have $${{3\over7}}$$ pound of onion, so they definitely don't have enough. Do you think Kevin's answer is reasonable? Why or why not?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How can estimating help us assess whether our answers are reasonable?
Look at #3. What error did Sandra make? How could you use estimation to see that Sandra’s answer was incorrect before calculating the actual difference?
Look at #4. How did you decide whether the fractions were reasonable estimates or not?
Look at #6. What error did Toby make? How could you use estimation to see that Toby’s answer was incorrect before calculating the actual difference?
Look at #9. Why is Mark correct? How does this problem show that it’s possible to reason about sums and differences without actually having to compute them?

Target Task

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

Moises has $$7\over12$$ yard of fabric. He uses $$1\over3$$ yard of fabric to make a headband.

Moises says he now has $$2\over3$$ yard of fabric leftover because when you subtract the numerators and denominators, the difference is $$6\over9 $$, and $$6\over9 $$ is equivalent to $$2\over3$$ when you divide both the numerator and denominator by 3.

a. Explain why the student’s answer is not reasonable.

b. Find how much fabric, in yards, was left over after Moises made the headband. Show or explain your work.

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

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 9

Lesson 11

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

References

Problem 2

Guiding Questions

References

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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