Curriculum  /  Math  /  4th Grade  /  Unit 4: Fraction Equivalence and Ordering  /  Lesson 5

Fraction Equivalence and Ordering

Lesson 5

Math

Unit 4

4th Grade

Lesson 5 of 15

Objective

Recognize and generate equivalent fractions with smaller units using tape diagrams.

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

Criteria for Success

  1. Understand that equivalent fractions are fractions that refer to the same whole and are the same size. 
  2. Generate equivalent fractions with smaller units using visual models, namely tape diagrams (MP.5).
  3. Show that two fractions are equivalent using visual models, and explain why the models demonstrate their equivalence (MP.3). 
  4. Understand that equivalence is valid only when two fractions refer to the same whole.

Tips for Teachers

  • Students are familiar with equivalent fractions and how to recognize and generate simple ones from Grade 3 (3.NF.3). 
  • Depending on students’ comfort level with fraction representations from Grade 3, particularly tape diagrams/fraction strips and number lines, Lessons 5 and 6 can be combined. 
  • The standards state that work with fractions in Grade 4 is limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100, but in this lesson and throughout the unit, students are exposed to and asked to work with fractions whose denominators may not be included in that list. Bill McCallum notes that “The restrictions in the standards are intended to both restrict what can be put on an assessment, and to put the brakes on over-enthusiastic focus on one part of the standards; they aren’t intended to forbid the use of examples that time and common sense allow” (General questions about the Mathematics standards, Mathematical Musings); thus more denominators are used in order to not limit students’ understanding.
  • As a supplement to the Problem Set, students can play a game to practice finding equivalent fractions with smaller units using tape diagrams, such as “Show Me 2” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.
  • There are no problems in this Problem Set, or any hereafter, that are related to the idea that “comparisons are valid only when the two fractions refer to the same whole” (4.NF.2). (Note that the idea of equivalence is a type of comparison.) This is because this is also part of the third-grade expectations regarding fraction equivalence and comparison, so students should understand this idea already. However, if they would benefit from some additional practice, here are some sources of good problems aligned to this aspect of the standard:

Lesson Materials

  • Strips of paper (2 per student) — These should be identical in size, perhaps 4.25" by 11"
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Anchor Tasks

25-30 minutes

Problem 1

Would you rather have the leftover king-sized candy bar in Scenario A or Scenario B? The original candy bars were the same size.

Scenario A

Scenario B

Guiding Questions

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Student Response

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Problem 2

Find two fractions that are equivalent to each of the following:

a.   $$\frac{1}{3}$$

b.   $$\frac{3}{4}$$

c.   $$\frac{3}{2}$$

Guiding Questions

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Student Response

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Problem 3

Use pictures to explain why the following fractions are equivalent.

a.   $${{1\over2}={3\over6}}$$

b.   $${{2\over3}={8\over12}}$$

c.   $${{4\over3}={8\over6}}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How many pieces did you shade in #3? Why?
  • What answer did you choose in #4? What made these equivalent fractions different from the others we’ve looked at today?
  • Look at #5c. What did your picture look like for $${{5\over2}}$$? What about $${{15\over6}}$$? What made these fractions different from the others?

Target Task

5-10 minutes

Problem 1

The model below is shaded to represent a fraction. 

Which model below represents an equivalent fraction? 

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Student Response

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Problem 2

Use the pictures to explain why the two fractions represented above are equivalent.

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

Recognize and generate equivalent fractions with smaller units using number lines.

Lesson 6
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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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