Curriculum  /  Math  /  4th Grade  /  Unit 4: Fraction Equivalence and Ordering  /  Lesson 14

Fraction Equivalence and Ordering

Lesson 14

Math

Unit 4

4th Grade

Lesson 14 of 15

Objective

Compare two fractions using one half as a benchmark.

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 fractions to $${{{{{{{{{{{{1\over2}}}}}}}}}}}}$$. 
  2. Compare two fractions, one of which is less than $${{{{{{{{{{{{1\over2}}}}}}}}}}}}$$ and the other of which is greater than $${{{{{{{{{{{{1\over2}}}}}}}}}}}}$$, using $${{{{{{{{{{{{1\over2}}}}}}}}}}}}$$ as a benchmark (MP.3).
  3. Compare two fractions which are both either greater than or less than $${{{{{{{{{{{{1\over2}}}}}}}}}}}}$$ by reasoning about their proximity to $${{{{{{{{{{{{1\over2}}}}}}}}}}}}$$ (MP.3).
  4. Use the correct symbol (<, >, =) to record a comparison.
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Anchor Tasks

25-30 minutes

Problem 1

Look at the title and image of the Newsweek article, More Than Half of Medical Advice on 'Dr. Oz' Lacks Proof or Contradicts Best Available Science: Study.

According to this article, a research team looked at 80 pieces of medical advice from The Dr. Oz Show and found no evidence to support 43 of these recommendations.

a.   Do you agree or disagree with the claim in the headline based on this information? Why or why not?

b.   Determine whether the following fractions are greater or less than $$\frac12$$.

  1. $$\frac{5}{12}$$
  2. $$\frac35$$

Guiding Questions

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Student Response

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References

Problem 2

a.   Ishmael says that he knows $$\frac{5}{12}$$ is less than $$\frac35$$ because $$\frac{5}{12}$$ is less than $$\frac12 $$ and $$\frac35$$ is more than $$\frac12$$, so $$\frac{5}{12}$$ must be less than $$\frac35$$. Explain why Ishmael’s reasoning is correct using words or pictures. 

b.   Use Ishmael’s strategy to compare the following pairs of fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

  1. $${{4\over10}}$$ and $${{5\over8}}$$

  2. $${{7\over12}}$$ and $${{4\over9}}$$

  3. $${{1\over3}}$$ and $${{4\over7}}$$

Guiding Questions

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Student Response

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Problem 3

a.   Now Joslyn is comparing $$\frac46$$ and $$\frac58$$. She says that she knows $$\frac46$$ is more than $$\frac58$$ because $$\frac46$$ is $$\frac16$$ more than $$\frac12$$ and $$\frac58$$ is $$\frac18$$ more than $$\frac12$$ and $$\frac16$$ is more than $$\frac18$$. Explain why Jocelyn’s reasoning is correct using words or pictures. 

b.   Use any strategy to compare the following pairs of fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

  1. $$\frac{5}{12}$$ and $${{4\over10}}$$
  2. $${{3\over5}}$$ and $${{5\over9}}$$

  3. $${{1\over3}}$$ and $${{3\over7}}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • What did all of the problems in #1 have in common? How did that help with each comparison? 
  • Which fractions in #2 were greater than $${{{1\over2}}}$$? How did you know? Are any of them greater than $$1$$?
  • How did you solve in #3? Which ones were more difficult than others? Why?
  • Look at #4. Why do you think this problem was included in today’s lesson? 
  • What fractions did you find for #5? Was there more than one correct answer?
  • How did you solve in #6? Which ones were more difficult than others? Why? 
  • How did the number line help you to compare in #7c? Which fraction was closer to $${{{1\over2}}}$$? How do you know? 

Target Task

5-10 minutes

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

a.   $${{3\over8}}$$  _____  $${{4\over5}}$$

b.   $${{5\over8}}$$  _____  $${{7\over12}}$$

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 and order fractions using various strategies.

Lesson 15
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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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