Lesson 1 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

Recognize and generate equivalent fractions.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.NF.A — Use equivalent fractions as a strategy to add and subtract fractions.

Number and Operations—Fractions

5.NF.A — Use equivalent fractions as a strategy to add and subtract fractions.

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

Understand that equivalent fractions are fractions of the same size or at the same point on a number line.
Generate equivalent fractions using an area model, a number line, or multiplication/division (MP.5).
Determine whether two fractions are equivalent using an area model, a number line, or multiplication/division (MP.3).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lesson 1 is intended to address the cluster heading “use equivalent fractions as a strategy to add and subtract fractions” (5.NF.A) by ensuring that students are able to recognize and generate equivalent fractions. Recognizing and generating equivalent fractions is an expectation in Grade 4 (4.NF.1), so it is up to your discretion about whether this lesson is needed or not. But, since using equivalent fractions to add and subtract is mentioned in the cluster heading, and since this lesson also provides the opportunity for students to refamiliarize themselves with the models used to represent fractions, the area model and the number line, it is recommended to include it.
As a supplement to the Problem Set, we recommend:
- The applet “Equivalent Fractions” by NCTM to generate equivalent fractions.
- “Fraction Blackout”, which can be found 4.NF.1 - About the Math, Learning Targets, and Rigor by the Howard County Public School System. Note that this game relies on the use of tape diagrams as a model, which you can choose to change into area models and/or number lines.
- “Fraction Taboo” or “Fraction Scattergories" from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.
- “Double Trouble” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog to preview finding equivalent fractions with common denominators when given two fractions (which they’ll need for fraction addition with unlike denominators starting in Lesson 4).

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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

Ms. Kosowsky makes brownies in two pans of the same size. She cuts the pans in the following way:

Pan A	Pan B

Ms. Kosowsky gives one brownie from Pan A to Ms. Kohler and gives four brownies from Pan B to herself. Ms. Kohler thinks this isn’t fair since she only got one brownie and Ms. Kosowsky got four. Ms. Kosowsky thinks it’s fair.

Who do you agree with, Ms. Kosowsky or Ms. Kohler? Why?

Guiding Questions

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Problem 2

a. What fraction does the point on the number line below represent?

b. What fraction does the point on the number line below represent?

c. Use the number lines to explain why the two fractions represented above are equivalent.

Guiding Questions

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References

Illustrative Mathematics Explaining Fraction Equivalence with Pictures

Explaining Fraction Equivalence with Pictures, accessed on March 23, 2018, 8:50 a.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 3

Find two more fractions that are equivalent to each of the following. Use pictures and an equation to explain why the fractions are equivalent.

a. $$\frac{1}{3}$$

b. $$\frac{2}{5}$$

c. $$\frac{4}{6}$$

d. $$\frac{36}{24}$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic A > Lesson 1 — Concept Development

Grade 5 Mathematics > Module 3 > Topic A > Lesson 1 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 4

Solve for the missing value.

a. $${{2\over5}={10\over\square}}$$

b. $${{5\over4}={\square\over16}}$$

c. $${{18\over24}={\square\over4}}$$

d. $${{18\over15}={6\over\square}}$$

Guiding Questions

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References

John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II) — Activity 12.15

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #3. How did you come up with your list of equivalent fractions?
Look at #5. Since the number line was not partitioned into fourths, how did you decide where to plot $$\frac{5}{4}$$? How could you use this number line to write a fraction that is equivalent to $$\frac{5}{4}$$?
Look at #6. How can you use the model to show $$\frac{1}{3}$$?

Target Task

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

Find three fractions that are equivalent to each of the following fractions. Use pictures and an equation to explain why the fractions are equivalent.

a. $${{5\over8}}$$

b. $${{6\over4}}$$

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 2

Lesson Map

Topic A: Addition and Subtraction of Fractions

Recognize and generate equivalent fractions.

5.NF.A

Add fractions with like denominators.

5.NF.A

Subtract fractions with like denominators.

5.NF.A

Add fractions with unlike denominators whose sum is less than 1.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 1 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is less than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is greater than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions greater than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers.

5.NF.A.2

Add and subtract more than two fractions.

5.NF.A.1

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

5.NF.A.2

Topic B: Addition and Subtraction of Decimals

Add decimals.

5.NBT.B.7

Subtract decimals.

5.NBT.B.7

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

5.NBT.B.7

Addition and Subtraction of Fractions/Decimals

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

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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