Addition and Subtraction of Fractions/Decimals

Lesson 10

Objective

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

Materials and Resources

Common Core Standards

Core Standards

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  • 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

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  • 4.NF.A.2

  • 4.NF.B.3

Criteria for Success

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  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

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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

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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 $$\frac{1}{2}$$.

a.     $${{1\over2}}+{3\over4}$$

b.     $$1{2\over3}-{2\over5}$$

c.     $${4\over10}+{2\over9}$$

d.     $$1{4\over7}-{9\over10}$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 13Concept 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 The Match Foundation, Inc.
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 The Match Foundation, 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 The Match Foundation, 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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Discussion of Problem Set

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  • 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

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After a class lunch, the class has $$\frac{9}{16}$$ gallon of soup left over. They give $$\frac{3}{8}$$ gallon of this soup to the school office. 

A student says they now have $$\frac{3}{4}$$ gallon of soup left over because when you subtract the numerators and denominators, the difference is $$\frac{6}{8}$$, and $$\frac{6}{8}$$ is equivalent to $$\frac{3}{4}$$ when you divide both the numerator and denominator by 2.

  • Explain why the student’s answer is not reasonable. 
  • Find how much soup, in gallons, was left over after giving soup to the school office. Show or explain your work. 

References

PARCC Released Items Math Spring Operational 2016 Grade 5 Released ItemsQuestion #22

Math Spring Operational 2016 Grade 5 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Dec. 5, 2017, 3:57 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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