Decompose Unit Fractions using Area Models

Videos, solutions, and examples to help Grade 4 students learn how to decompose unit fractions using area models to show equivalence.

Common Core Standards: 4.NF.3b, 4.NF.4a, 4.NF.3a

New York State common Core Grade 4 Module 5, Lesson 5

Worksheets for Grade 4

 

Lesson 5 Concept Development
Problem 1: Draw an area model to illustrate that 1/5 is equal to 2/10.
Problem 2: Decompose 1/3 as 4/12 represented in an area model and as the sum and product of unit fractions.
Problem 3: Model 1/2 = 5/10 and represent the decomposition as the sum and product of unit fractions.

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Lesson 5 Problem Set

1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence.
   a. 2 rows
   b. 2 rows
   c. 4 rows
2. Draw area models to show the decompositions represented by the number sentences below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence.
   a. 1/2 = 3/6
   b. 1/2 = 4/8
   c. 1/2 = 5/10
   d. 1/3 = 2/6
   e. 1/3 = 4/12
   f. 1/3 = 3/12
3. Explain why 1/12 + 1/12 + 1/12 is the same as 1/4.

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Lesson 5 Homework

1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence.
   a. 3 rows
   b. 2 rows
   c. 4 rows
2. Draw area models to show the decompositions represented by the number sentences below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence. a. 1/3 = 2/6
   b. 1/3 = 3/9
   c. 1/3 = 4/12
   d. 1/3 = 5/15
   e. 1/5 = 2/10
   f. 1/5 = 3/15
3. Explain why 1/12 + 1/12 + 1/12 + 1/12 is the same as 1/3.

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