Fraction Equivalence and Ordering

Lesson 6

Math

Unit 4

4th Grade

Lesson 6 of 15

Objective


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

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 number lines (MP.5).
  3. Determine whether two fractions are equivalent using visual models and explain why the models demonstrate their equivalence (MP.3).
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Anchor Tasks


Problem 1

a.   What fraction represents the point shown on the number line below?

b.   What fraction represents the point shown on the number line below?

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

Guiding Questions

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References

Illustrative Mathematics Explaining Fraction Equivalence with Pictures

Explaining Fraction Equivalence with Pictures, accessed on March 23, 2018, 8:50 a.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.

Problem 2

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

a.   $${{1\over2}}$$

b.   $${{2\over5}}$$

c.   $${{5\over2}}$$

Guiding Questions

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Problem 3

Determine whether the following are equivalent. Show or explain how you know.

a.   $${{2\over3}}$$ and $${{8\over12}}$$

b.   $${{3\over4}}$$ and $${{8\over10}}$$

c.   $${{5\over3}}$$ and $${{10\over6}}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Even if you were not given the number lines in #1, how could you determine which answers were incorrect?
  • What did you notice about the number lines in #2? What do you wonder?
  • Which fractions were equivalent in #3? Which ones weren’t? How do you know? 
  • How did you decompose $${{2\over5}}$$ into $$4$$ parts in #4b? What equivalent fraction did this produce? 

Target Task


The fraction $${{4\over5}}$$ is represented on the number line below.

Use the number line to find two more equivalent fractions.

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

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Lesson 5

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Lesson 7

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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