Fraction Equivalence and Ordering

Lesson 12

Math

Unit 4

4th Grade

Lesson 12 of 15

Objective


Compare two fractions by replacing both fractions with equivalent ones.

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 where both fractions need to be replaced with an equivalent one to be able to compare common units (denominators) or common number of units (numerator) (MP.3).
  2. Understand that there are a variety of common units or number of units that can be compared, including the possibility to find the largest possible unit to compare (i.e., the lowest common denominator). 
  3. Use the correct symbol (<, >, =) to record a comparison. 

Tips for Teachers


As the Fractions Progressions states, “it is not necessary to find a least common denominator to calculate sums of fractions, and in fact the effort of finding a least common denominator is a distraction from understanding algorithms for adding fractions” (NF Progressions, p. 11). One can extend this rationale to finding a least common denominator to compare fractions. Because finding a least common denominator connects the supporting work of gaining familiarity with factors and multiples (4.OA.4) with fraction equivalence and comparison (4.NF.A), the idea is discussed briefly, particularly in Anchor Task #3; just be sure not to overemphasize the need to do so for all problems.

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Anchor Tasks


Problem 1

Would you rather have the leftover brownies in Scenario A or Scenario B? The pans in which the brownies were cooked are the same size.

Scenario A

Scenario B

Guiding Questions

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Problem 2

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

a.   $${{2\over3}}$$ and $${{5\over8}}$$

b.   $${{7\over4}}$$ and $${{9\over5}}$$

Guiding Questions

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Problem 3

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

a.   $${{7\over12}}$$ and $${{5\over8}}$$

b.   $${{13\over10}}$$ and $${{5\over4}}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • In #1, were some comparisons easier than others? Why? 
  • In #3, did you need to use multiplication for every part? Why or why not? When is multiplication not needed, even with different denominators? 
  • In #3(b), did everyone use forty-eighths? Did anyone use twenty-fourths? 
  • In #5, how did you compare the fractions? Why? 
  • Do we always need to multiply the denominators to make like units?

Target Task


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

a.   $${{5\over8}}$$  _____  $${{3\over5}}$$

b.   $${{2\over3}}$$  _____  $${{3\over4}}$$

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

Answer Keys

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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.

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Lesson 11

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Lesson 13

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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