Addition and Subtraction of Fractions/Decimals

Lesson 12

Objective

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

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.B.3

  • 4.OA.A.3

Criteria for Success

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  1. Solve two- and multi-step word problems that involve the addition and subtraction of decimals (MP.4).
  2. Assess the reasonableness of an answer to a word problem involving the addition and subtraction of decimals (MP.1).

Tips for Teachers

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Let students work on each problem on the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram; then allow them to try again on their own. Encourage students to use a strategy of their choice to assess the reasonableness of their answer.

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Anchor Tasks

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Mr. Manetta drove to Philadelphia to visit a friend. He was supposed to take Exit 345 shown in the image above but missed it and had to get off at Exit 344 and turn back around. How far did Mr. Manetta drive from where this picture is taken?

Guiding Questions

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References

Google Maps Map: I-76 Street View

Map data ©Google. Accessed Feb. 12, 2018, 11:35 a.m..

Discussion of Problem Set

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  • Look at #1. How did you figure out what fraction of the books were mysteries? What was the total you subtracted from? Why did you use that number as the total? 
  • Look at #2. What was similar about the three fractions in the problem? Did that change the way in which you approached solving the problem?
  • Look at #3. What made this problem much more difficult than some of the others? 
  • Look at #4. Was anyone able to answer the question without actually adding the values? Explain how you did it. 
  • Look at #6. How did you solve part (c)? Did anyone use multiplication? 
    • (Note: Students learned in Grade 4 how to multiply a whole number by a fraction, including mixed numbers (4.NF.4b). Thus, this question connects back to the work students did in Grade 4 and the work they’ll do in coming units on multiplication and division of fractions.) 

Target Task

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Each student in a class plays one of three sports: soccer, volleyball, or basketball. 

  • $${{3\over5}}$$ of the number of students play soccer.
  • $${{1\over4}}$$ of the number of students play volleyball.

What fraction of the number of students play basketball?

References

EngageNY New York State Testing Program Grade 5 Common Core Mathematics Test Released Questions June 2017Question Stem #21

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 5 Common Core Mathematics Test Released Questions June 2017. Internet. Available from https://www.engageny.org/resource/released-2017-3-8-ela-and-mathematics-state-test-questions/file/150271; accessed Dec. 5, 2017, 3:55 p.m..

Mastery Response

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