Lesson 19 | Fraction Operations | 4th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

4.NF.B.3.D — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Number and Operations—Fractions

4.NF.B.3.D — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
4.NF.B.4.C — Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Number and Operations—Fractions

4.NF.B.4.C — Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

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).
Solve two- and multi-step word problems that involve the addition, subtraction, and multiplication of fractions (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Let students work on each problem in 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.

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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 slideshow of images listed under Act 1 in Cans of Paint.

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

b. How much paint is in the display? Make an estimate.

Guiding Questions

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References

kristenacosta.com Cans of Paint

Cans of Paint is made available on kristenacosta.com under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to solve.

There are 12 cans of red paint that are each $$3\frac{10}{16}$$ quarts.
There are 14 cans of green paint that are each $$3\frac{11}{16}$$ quarts.
There are 4 cans of blue paint that are each $$3\frac{10}{16}$$ quarts.

Guiding Questions

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References

kristenacosta.com Cans of Paint

Cans of Paint is made available on kristenacosta.com under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: There are $$109\frac{5}{8}$$ quarts, or $$27\frac{13}{32}$$ gallons, of paint.

Was your answer reasonable? Why or why not?

Guiding Questions

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References

kristenacosta.com Cans of Paint

Cans of Paint is made available on kristenacosta.com under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by Fishtank Learning, Inc.

Problem 4

Act 4 (the sequel): A customer takes four cans of green paint from the display. How much paint, in quarts, is in the display now?

Guiding Questions

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References

kristenacosta.com Cans of Paint

Cans of Paint is made available on kristenacosta.com under the CC BY-NC 4.0 license. Accessed July 18, 2018, 4:39 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

How much land would be left unused in #1? How did you subtract from a whole?
How did you determine what could be the amount Jake added to his bottle in #3(b)?
How many tubes of paint are used for each shirt in #4? 2 or 18? How do you know?
When you check for reasonableness, do you look at your equations and model? How do you figure out if your answer is reasonable?

Target Task

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

A grocery store sells coleslaw in containers of various sizes and weights, as shown in the table below.

Coleslaw

Size	Weight (pounds)
Small	$${{3\over8}}$$
Medium	$${{7\over8}}$$
Large	$$1{{1\over8}}$$

Teri bought 4 small containers of coleslaw and Olin bought 2 large containers of coleslaw. What is the difference, in pounds, of how much coleslaw Teri and Olin bought?

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 18

Lesson 20

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

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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