Fraction Equivalence and Ordering

Lesson 8

Math

Unit 4

4th Grade

Lesson 8 of 15

Objective


Recognize and generate equivalent fractions with smaller units using multiples.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 3.NF.A.3
  • 4.OA.A.1
  • 4.OA.B.4

Criteria for Success


  1. Develop a general method for finding equivalent fractions by multiplying both the numerator and the denominator by the same non-zero value. 
  2. Understand how the numbers and sizes of parts differ even though the two fractions are the same size, and connect this idea to the general method of using multiplication to find an equivalent fraction (MP.7).
  3. Generate equivalent fractions with smaller units using the general method. 
  4. Determine whether two fractions are equivalent using multiplication, and support that work with a visual model (MP.3, MP.5).

Tips for Teachers


As a supplement to the Problem Set, students can play a game to practice finding equivalent fractions with smaller units with increasing efficiency, such as “Fraction Scattergories” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

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Anchor Tasks


Problem 1

Allen drew an area model to represent $${{7\over8}}$$, as shown to the bottom left. He partitioned it to find an equivalent fraction, then covered the model to the bottom right.

a.   What equivalent fraction did Allen come up with? How do you know?

b.   Chin says she can represent this relationship with an equation: $$\frac78=\frac{7\times4}{8\times4}=\frac{28}{32}$$. How is this equation related to Allen’s images above?

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)Figure 12.19 (p. 225)

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 2

Find a fraction that is equivalent to each of the following using Chin's method from Anchor Task 1:

a.   $$\frac{1}{9}$$

b.   $${{4\over7}}$$

c.   $${{14\over11}}$$

Guiding Questions

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Problem 3

Determine whether each of the following equations are true. Correct those that are false by changing either the numerator or denominator in the fraction on the right-hand side of the equation. â€‹â€‹â€‹â€‹â€‹

a.   $${{9\over5}={27\over15}}$$

b.   $${{3\over4}={15\over16}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic B > Lesson 8Problem Set, Question #5

Grade 4 Mathematics > Module 5 > Topic B > Lesson 8 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


Answer Keys

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Discussion of Problem Set

  • Look at #2. How are the total number of fractional pieces and the total number of shaded fractional pieces related to the equation $${{2\times2}\over{3\times2}}$$?
  • Which equations were true in #6? How did you alter the false ones to make them true? 
  • What was Matilde’s error in #7? 
  • What were the missing values in #8?

Target Task


Problem 1

Find two fractions that are equivalent to $${{7\over12}}$$ whose numerators are greater than $$7$$.

Problem 2

Determine if the following fractions are equivalent. Then explain how you know. 

$${{5\over3}={15\over9}}$$

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

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 7

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Lesson 9

Lesson Map

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

Topic A: Factors and Multiples

Topic B: Equivalent Fractions

Topic C: Comparing and Ordering Fractions

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