Fraction Equivalence and Ordering

Lesson 9

Math

Unit 4

4th Grade

Lesson 9 of 15

Objective


Recognize and generate equivalent fractions with larger units using visual models.

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.2
  • 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 larger units using visual models (MP.5).
  3. Generate equivalent fractions with larger units when given either the number of units (the numerator) or the size of the unit (the denominator) in the equivalent fraction.
  4. Show that two fractions are equivalent using visual models and explain why the models demonstrate their equivalence (MP.3).

Tips for Teachers


  • After spending lots of time exploring various fraction models and how to use them to recognize and generate equivalent fractions with smaller units, students will work with all models in this lesson. Students should feel more comfortable with their use after going in-depth in Lessons 5–7 and are likely to be able to see the general method involving division much more readily. However, if students seem to need more work with any model in particular, you may choose to break this into two lessons and focus exclusively on that model in need of more work on the additional day.
  • As a supplement to the Problem Set, students can play a game to practice finding equivalent fractions with larger units using visual models, such as “Show Me 2” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.
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Anchor Tasks


Problem 1

a.   What fraction of the rectangle below is shaded?

b.   Laura says that $${{1\over4}}$$ of the model is shaded. Do you think she is correct? Explain why or why not by using the picture.

Guiding Questions

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References

Illustrative Mathematics Fractions and Rectangles

Fractions and Rectangles, accessed on March 23, 2018, 9:23 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.

Problem 2

A point is shown on the number line diagram below. 

Write three equivalent fractions that name this point. 

Guiding Questions

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References

Achieve the Core Fraction Concepts Mini-AssessmentQuestion #2

Fraction Concepts Mini-Assessment by Student Achievement Partners is made available by Achieve the Core under the CC0 1.0 license. Accessed March 23, 2018, 9:16 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

Solve for the missing value.

a.   $${{8\over24}={\square\over6}}$$

b.   $${{32\over10}={16\over\square}}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #2c. What denominator made this statement true? Is there another way to rename this fraction? (Discuss how this is equivalent to the whole number 2.) 
  • How did you shade the fraction strip in #3? What made this pair of equivalent fractions different from many of the others we’ve looked at so far? Because of that difference, how could you ensure that they were equivalent?
  • Look at #4. I think the correct answer is C. Do you agree or disagree? Why? What error did I make?

Target Task


Problem 1

The model below represents one whole. 

Which fraction is equivalent to the one represented by the shaded part of the model?

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Problem 2

A point is shown on the number line diagram below. 

Write three equivalent fractions for the location of this point.

Problem 3

Use the number line to explain how you know the fractions in #2 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.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 8

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Lesson 10

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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