Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 10

Addition and Subtraction of Fractions/Decimals

Lesson 10

Math

Unit 4

5th Grade

Lesson 10 of 17

Objective

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

Common Core Standards

Core Standards

  • 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

  • 4.NF.A.2
  • 4.NF.B.3

Criteria for Success

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

Tips for Teachers

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

25-30 minutes

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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Student Response

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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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Student Response

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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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Student Response

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Problem Set

15-20 minutes

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

5-10 minutes

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

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

Next

Add and subtract more than two fractions.

Lesson 11
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Addition and Subtraction of Fractions

Topic B: Addition and Subtraction of Decimals

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