 # Decompose Unit Fractions using Area Models

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Lesson Plans and Worksheets for Grade 4
Lesson Plans and Worksheets for all Grades

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 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.

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.
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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