Curriculum  /  Math  /  4th Grade  /  Unit 4: Fraction Equivalence and Ordering  /  Lesson 11

Fraction Equivalence and Ordering

Lesson 11

Math

Unit 4

4th Grade

Lesson 11 of 15

Objective

Compare two fractions where one numerator or denominator is a factor of the other by replacing one fraction with an equivalent one.

Common Core Standards

Core Standards

  • 4.NF.A.2 — Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Foundational Standards

  • 3.NF.A.3.D

Criteria for Success

  1. Compare two fractions with the same numerators or denominators using visual models (MP.3, MP.5).
  2. Understand that fractions are said to have a common numerator when they have the same number of units. Fractions are said to have a common denominator when they have the same sized units.
  3. Compare two fractions where one numerator is a factor of the other numerator by replacing one fraction with an equivalent one to compare them with like numerators (MP.3).
  4. Compare two fractions where one denominator is a factor of the other denominator by replacing one fraction with an equivalent one to compare them with like denominators (MP.3).
  5. Use the correct symbol (< , >, =) to record a comparison. 
  6. Understand that comparisons are valid only when the two fractions refer to the same whole.

Tips for Teachers

  • The supporting work of gaining familiarity with factors and multiples (4.OA.4) supports this major work of comparing fractions with related numerators or denominators by finding common units or number of units, since students must recognize that the fractions’ numerators or denominators share a common factor to be able to utilize this strategy.
  • As mentioned in Lesson 5, 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). 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, a list of potential resources can be found in the Tips for Teachers for Lesson 5. 
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Anchor Tasks

25-30 minutes

Problem 1

Below are measurements of ribbon in feet. For each pair of ribbons, determine which one is longer. Show or explain how you know.

a.   $${{3\over4}}$$ ft. and $${{1\over4}}$$ ft.

b.   $${{5\over12}}$$ ft. and $${{5\over6}}$$ ft.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grass Seedlings — Comparing Fractions

Grass Seedlings, accessed on Feb. 8, 2018, 12:51 p.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.
EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic C > Lesson 14 — Concept Development

Grade 4 Mathematics > Module 5 > Topic C > Lesson 14 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 2

Compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

a.   $${{2\over3}}$$ and $${{7\over9}}$$

b.   $${{7\over10}}$$ and $${{3\over5}}$$

Guiding Questions

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Student Response

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Problem 3

Compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

a.   $$\frac35$$ and $$\frac13$$

b.   $${{2\over3}}$$ and $${{4\over5}}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did the tape diagrams help you to determine which statements were true in #1? 
  • What values did you choose to support Phil’s claim? What about to show that it’s not always true? Was there more than one correct choice for either or both parts? 
  • #4a, 4d, and 4f can be compared using different types of reasoning. Explain the reasoning you used for each. 
  • How did you determine whether the first comparison in #5 was true or false? 
  • How can you determine whether you can make common numerators or common denominators when comparing fractions?

Target Task

5-10 minutes

Compare the following fractions by writing $${<}$$, $${>}$$, or $$=$$ in the blank.

a.   $${{4\over5}}$$  _____  $${{2\over3}}$$

b.   $${{3\over4}}$$  _____  $${{10\over12}}$$

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

Compare two fractions by replacing both fractions with equivalent ones.

Lesson 12
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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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