# 3. Practice completing 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 because the fraction a/b is determined by the number of 1/b sized pieces, we can construct any other fraction with the same denominator using iterations of the unit fraction 1/b.

Fluency and Procedural Skill Lesson: This lesson helps to build fluency with reasoning about fractions. Students work toward this goal by applying their understanding that non-unit fractions are composed of unit fractions, and that it takes a pieces of size of 1/b to make any fraction a/b. Tape diagrams will support students’ identification and iteration of unit fractions. This work develops students' understanding that fractions are numbers that can be composed and decomposed which will be useful for addition and subtraction.

Students engage in Mathematical Practice 4 (Model with mathematics) as they model fractions using a tape diagram to identify a unit fraction and use it to construct fractions other than one. Mathematical Practice 7 (Look for and make use of structure) is also featured as students use the definition and structure of fractions to decompose non-unit fractions and construct other fractions with the same denominator. The prompt to construct other fractions from a non-unit fraction leads students to recognize the structure of non-unit fractions as composed of unit fractions. Using a tape diagram, students

Key vocabulary:

• unit fraction

• non-unit fraction

• decompose
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