Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 12

Addition and Subtraction of Fractions/Decimals

Lesson 12

Math

Unit 4

5th Grade

Lesson 12 of 17

Objective

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

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.B.3
  • 4.OA.A.3

Criteria for Success

  1. Understand when a problem calls for the use of addition or subtraction of fractions (MP.1, MP.4).
  2. Write a story context to match a given expression involving the addition or subtraction of fractions (MP.2).
  3. Write an expression to match a story context involving the multiplication of a fraction and a whole number (MP.2).
  4. Solve two- and multi-step word problems that involve the addition and subtraction of fractions (MP.4).
  5. Assess the reasonableness of an answer to a word problem involving the addition and subtraction of fractions (MP.1).

Tips for Teachers

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

25-30 minutes

Problem 1

For each of the following, determine whether or not $$\frac{2}{5}+\frac{3}{10}$$ represents the problem. Explain your decision.

a.   A farmer planted $$\frac{2}{5}$$ of his forty acres in corn and another $$\frac{3}{10}$$ of his land in wheat. Taken together, what fraction of the 40 acres had been planted in corn or wheat?

b.   Jim drank $$\frac{2}{5}$$ of his water bottle and Jon drank $$\frac{3}{10}$$ of his water bottle. How much water did both boys drink?

c.   Allison has a batch of eggs in the incubator. On Monday $$\frac{2}{5}$$ of the eggs hatched. By Wednesday, $$\frac{3}{10}$$ more of the original batch hatched. How many eggs hatched in all?

d.   Two fifths of the track team arrived at the weight room at 7 a.m. Ten minutes later, $$\frac{3}{10}$$ of the team showed up. The rest of the team stayed home. What fraction of the team made it to the weight room that day?

e.   Andy made 2 free throws out of 5 free throw attempts. Jose made 3 free throws out of 10 free throw attempts. What is the fraction of free throw attempts that the two boys made together?

f.   Two fifths of the students in the fifth grade want to be in the band. Three tenths of the students in the fifth grade want to play in the orchestra. What fraction of the students in the fifth grade want to be in one of the two musical groups? 

g.   Wesley ran $$\frac{2}{5}$$ of a mile on Monday and $$\frac{3}{10}$$ of a mile on Tuesday. How far did he run those two days? 

h.   The fifth grade at Lincoln School has two soccer teams, Team A and Team B. If $$\frac{2}{5}$$ of Team A are girls and $$\frac{3}{10}$$ of Team B are girls, what fraction of the players from the two teams are girls?

i.   Two fifths of the students at Washington Elementary School like soccer best and $$\frac{3}{10}$$ of them like basketball best. What fraction of students don’t like soccer or basketball best?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Do These Add Up?

Do These Add Up?, accessed on Feb. 3, 2022, 1:08 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

a.   Write a story context that can be solved by adding $$4\frac{2}{3}+1\frac{5}{8}$$.

b.   Write a story context that can be solved by subtracting $$1\frac{4}{9}-\frac{5}{6}$$.

Guiding Questions

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Student Response

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Problem 3

Mr. Manetta drove to Philadelphia to visit a friend. He was supposed to take Exit 345 shown in the image linked below 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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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • 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

5-10 minutes

Each student in a class lives in one of three neighborhoods: Roxbury, Dorchester, or Hyde Park.

  • $${{1\over3}}$$ of the number of students live in Roxbury.
  • $${{3\over5}}$$ of the number of students live in Dorchester.

What fraction of the number of students live in Hyde Park?

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 decimals where the total is less than or equal to 2.

Lesson 13
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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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