Fraction Equivalence and Ordering

Lesson 7

Math

Unit 4

4th Grade

Lesson 7 of 15

Objective


Recognize and generate equivalent fractions with smaller units using area 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.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 area models (MP.5).
  3. Generate equivalent fractions with smaller units when given either the number of units (the numerator) or the size of the unit (the denominator) in the equivalent fraction.
  4. 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 garden is divided into rows of various vegetables. Three out of four rows are tomatoes.

a.   Partition and shade the square below to show how much of the garden is tomatoes. Then write a fraction to represent how much of the garden is tomatoes.

b.   The garden is going to be shared with family and friends so that each person’s share of the harvest is three-fourths tomatoes. How would you partition the garden if it’s shared by two people? Show on the model above. 

c.   What fraction of the newly divided garden is tomatoes? How is this fraction related to the one you wrote in Part (a)? 

d.   Go through the same process for the garden but now splitting it evenly for three and five people on the models below. What fraction of each newly divided garden is tomatoes? 

Guiding Questions

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References

John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II)Activity 12.16

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Modified by Fishtank Learning, Inc.

Problem 2

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

a.   $${{1\over8}}$$

b.   $${{10\over12}}$$

c.   $${{4\over3}}$$

Guiding Questions

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Problem 3

Solve for the missing value.

a.   $${{2\over5}={10\over \square}}$$

b.   $${{7\over6}={\square\over24}}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • How is the model in #2 different from the ones we’ve already seen? How is it similar? 
  • How did you determine how many pieces of cake were left in #3? How did the model help you? 
  • Look at #5. How many slices of pizza did he have left? How did you find that? If each friend ate $${{1\over4}}$$ of the pizza, how many slices did they eat? 
  • How did you decide how many squares to shade in #6? What fraction is represented in the model? What about #7? 

Target Task


The model below is made up of equal-sized pieces.

Explain how you can use the model to show $${{{{9\over12}}}}$$. Then write a fraction that is equivalent to $${{{{9\over12}}}}$$.

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.

Extra Practice Problems

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 6

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Lesson 8

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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