Fraction Operations

Lesson 3

Math

Unit 5

4th Grade

Lesson 3 of 21

Objective


Add and subtract fractions within 1 with the same units.

Common Core Standards


Core Standards

  • 4.NF.B.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • 4.NF.B.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Criteria for Success


  1. Understand that when adding or subtracting quantities with like units, one adds or subtracts the values and the unit stays the same, which in the case of fraction addition and subtraction means adding or subtracting the numerators while the denominator does not change. 
  2. Estimate solutions when adding or subtracting fractions less than 1 with the same units. 
  3. Add and subtract fractions with like units where the total is less than 1 using a number line. 
  4. Add and subtract fractions with like units where the total is 1, requiring regrouping. 
  5. (Optional) Simplify solutions by rewriting them using the largest possible unit.
  6. Assess the reasonableness of answers based on estimates (MP.1).

Tips for Teachers


Since it is possible to overemphasize the importance of simplifying fractions, the corresponding criteria for success and questions in the Anchor Tasks are optional. If you want the focus for today to solely be on adding and subtracting fractions within 1, you may decide to cut this aspect of the lesson, but be sure to touch on the idea at some point in the unit.

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Anchor Tasks

25-30 minutes


Problem 1

a.   Solve. 

  1. 5 ones + 2 ones = ___________
  2. 5 dogs + 2 dogs = ___________
  3. 5 meters + 2 meters = ___________
  4. 5 tenths + 2 tenths = ___________

b.   What do you notice about the problems in Part (a)? What do you wonder?

c.   Use what you observed in Part (a) to think about what the solution to 5 tenths – 2 tenths would be. 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 16Concept Development

Grade 4 Mathematics > Module 5 > Topic D > Lesson 16 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

Use a number line to represent each addition expression and to find its value.

a.   â€‹â€‹â€‹â€‹$${{2\over8}+{3\over8}}$$

b.   â€‹â€‹â€‹$${{1\over6}+{3\over6}}$$

Guiding Questions

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Student Response

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Problem 3

Solve each of the following.

a.   $${{4\over5}-{1\over5}}$$

b.   $${{7\over12}-{3\over12}}$$

Guiding Questions

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Student Response

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Problem 4

Solve. Show or explain your work. 

a.   $${{3\over4}+{1\over4}}$$

b.   $$1 - \frac{3}{10}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • How do #1 and #7 help you understand how to subtract or add fractions? 
  • What was difficult about #3? 
  • What error(s) did the student make in #6? How could you know, just by looking at the sum they came up with, that it’s incorrect? 
  • How did you solve #9? 
  • How did you subtract from 1 in #11? 
  • What made #12 different from previous problems? How did you solve? 
  • How is the number line helpful in showing how we can subtract and add fractions with like units?

Target Task

5-10 minutes


Solve.

a.   $${{7\over8}-{4\over8}}$$

b.   $${{5\over10}+{3\over10}}$$

c.   $${1-{2\over5}}$$

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

Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one.

Lesson 4
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Lesson Map

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

Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1

Topic B: Building, Adding, and Subtracting Fractions Less Than 2

Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2

Topic D: Multiplication of Fractions

Topic E: Line Plots

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