# 1. Complete the whole

teaches Common Core State Standards 5.3K http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 4.3E http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 4.C.5 http://www.doe.in.gov/standards/mathematics
teaches Common Core State Standards CCSS.Math.Content.4.NF.B.3b http://corestandards.org/Math/Content/4/NF/B/3/b
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards 4.3B http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html

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Lesson objective: Understand that we can construct a whole from any fraction a/b by knowing that fractions can be decomposed into unit fractions. This is based on the definition of the fraction a/b as determined by the number of 1/b sized pieces, and b pieces the size of 1/b is one whole.

Conceptual Lesson: This lesson helps build conceptual understanding that numbers, including fractions, can be composed and decomposed. Something different that students will encounter is instead of being given “1” and asked to equipartition it, students are given a fraction and asked to construct 1. This concept is developed through work with tape diagrams as student use their knowledge that fractions can be decomposed into unit fractions. Because we know the number of unit fractions that makes one whole, we can iterate that unit fraction to make one.

Students engage in Mathematical Practice 4 (Model with mathematics) as they model lengths using a tape diagram.  This supports students as they investigate decomposing fractions in preparation for using them to add and subtract.  Mathematical Practice 7 (Look for and make use of structure) is also featured in this lesson as students use the structure of fractions and unit fractions to construct wholes.

Key vocabulary:

• decompose

• unit fraction

• compose
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