Lesson 7 | Fraction Operations | 4th Grade Mathematics

Objective

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Common Core Standards

Core Standards

The core standards covered in this lesson

4.NF.B.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Number and Operations—Fractions

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.

Number and Operations—Fractions

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.

Foundational Standards

The foundational standards covered in this lesson

4.NF.A.1

Number and Operations—Fractions

4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Make sense of a three-act task and persevere in solving it (MP.1).
Add fractions where one denominator is a multiple of the other and where the sum is between 1 and 2, by replacing one fraction with an equivalent fraction in such a way as to produce an equivalent sum of fractions with like denominators.
(Optional) Simplify solutions by rewriting them using the largest possible unit.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson goes beyond the explicit expectations of 4.NF.3. However, students will add fractions with denominators of 10 and 100 in Unit 6 (4.NF.5). Thus, today’s lesson is intended to prepare students for that work in Unit 6. The Progressions note that “students might encounter [such] situations, for example using a strip of paper or a tape diagram to reason that $$\frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$$” (NF Progression, p. 16).
In place of the Problem Set, you might decide to play the following NCTM Illuminations game, Fraction Game. This game can also be converted to a paper version if you don’t want to use the computer version.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Act 1: Watch the following video: Black box - Act 1.

a. What do you notice? What do you wonder?

b. What will the sum of $$\frac{1}{2} + \frac{1}{4}$$ be?

Guiding Questions

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References

101Questions Black Box 2

Black Box 2 by is made available on 101Questions under the CC BY 3.0 license. Accessed July 17, 2018, 1:45 p.m..

Modified by Fishtank Learning, Inc.

YouTube Video: “Black box - Act 1” by msbritton215

“Black box - Act 1” by msbritton215 by msbritton215 is made available by YouTube under the Standard YouTube License. Accessed Oct. 23, 2019, 5:27 p.m..

Problem 2

Act 2: Use the following information to solve.

Guiding Questions

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References

101Questions Black Box 2

Black Box 2 by is made available on 101Questions under the CC BY 3.0 license. Accessed July 17, 2018, 1:45 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Reveal the answer: Black box - Act 3. Was your answer reasonable? Why or why not?

Guiding Questions

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References

101Questions Black Box 2

Black Box 2 by is made available on 101Questions under the CC BY 3.0 license. Accessed July 17, 2018, 1:45 p.m..

Modified by Fishtank Learning, Inc.

YouTube Video: “Black box - Act 3” by msbritton215

“Black box - Act 3” by msbritton215 by msbritton215 is made available by YouTube under the Standard YouTube License. Accessed Oct. 23, 2019, 5:27 p.m..

Problem 4

Solve. Show or explain your work.

a. $${{1\over2}+{1\over8}}$$

b. $${{1\over5}+{3\over10}}$$

c. $${{2\over3}+{1\over6}}$$

d. $${{3\over4}+{5\over12}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 21 — Concept Development

Grade 4 Mathematics > Module 5 > Topic D > Lesson 21 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.

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 20 — Concept Development

Grade 4 Mathematics > Module 5 > Topic D > Lesson 20 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 Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How did you determine which amounts could have been what Jake added to the jug in #1?
In #2c, did you use sixths as the common denominator? Explain how thirds could be used as the common denominator.
For #5, what strategies did you use to estimate if the sum would be between 0 and 1 or 1 and 2?
Why is it important to have common denominators when adding fractions?
How can you find the sum of two fractions without using a model?
What benefit can you see in expressing a fraction as a mixed number or a mixed number as a fraction?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. Show or explain your work.

a. $${{3\over10}+{2\over5}=}$$ _____

b. $${{1\over2}+{5\over6}=}$$ _____

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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 6

Lesson 8

Lesson Map

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

Decompose fractions as a sum of unit fractions and as a multiple of a unit fraction.

4.NF.B.3.B 4.NF.B.4.A

Decompose fractions as a sum of fractions with the same denominator in more than one way.

4.NF.B.3.B 4.NF.B.4.A

Add and subtract fractions within 1 with the same units.

4.NF.B.3.A 4.NF.B.3.C

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

4.NF.B.3.D

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

Decompose non-unit fractions less than 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

4.NF.B.3.B 4.NF.B.4.A

Add and subtract fractions that require regrouping where the total is less than 2.

4.NF.B.3.A 4.NF.B.3.C

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

4.NF.B.3.A 4.NF.B.3.C

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

Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

4.NF.B.3.B

Convert fractions greater than 1 to mixed numbers.

4.NF.B.3.B 4.NF.B.3.C

Convert mixed numbers to fractions greater than 1.

4.NF.B.3.B 4.NF.B.3.C

Compare and order fractions greater than 1 using various methods.

4.NF.B.3.C

Add fractions and mixed numbers where the total is greater than or equal to 2.

4.NF.B.3.C

Subtract fractions and mixed numbers where the total is greater than or equal to 2.

4.NF.B.3.C

Add and subtract mixed numbers using a variety of mental strategies.

4.NF.B.3.C

Solve word problems involving addition and subtraction of fractions.

4.NF.B.3.D

Topic D: Multiplication of Fractions

Multiply a whole number by a fraction.

4.NF.B.4.B

Multiply a whole number by a mixed number.

4.NF.B.4.B

Solve word problems involving multiplication of fractions.

4.NF.B.4.C

Solve word problems involving addition, subtraction, and multiplication of fractions.

4.NF.B.3.D 4.NF.B.4.C

Topic E: Line Plots

Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit.

4.MD.B.4

Solve problems using information presented in line plots.

4.MD.B.4

Fraction Operations

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem 4

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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