# 10. Three Jars: Decompose mixed numbers

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: Decompose mixed numbers.

Conceptual Lesson: This lesson helps build conceptual understanding of a form of number students were introduced to in grade 3: mixed numbers. Earlier in the unit, students worked with fractions greater than 1, with the emphasis on decomposing the fractions into non-unit fractions. Here, mixed numbers are presented as a sum of a whole number and a fraction, and as another way to write and use fractions greater than 1. The concept is developed through the use of sums of lengths on a number line. Students decompose familiar numbers, and are asked to notice the correspondence between parts of the decomposition and whole numbers. The common procedures for rewriting mixed numbers as fractions and rewriting fractions greater than 1 as mixed numbers is not presented. Rather, the emphasis is on seeing "1s" in the fraction or rewriting the whole number part of the mixed number as a fraction. Students bring prior knowledge of decomposing whole numbers and fractions, including the relationship between the knowledge from grade 3 that whole numbers can be written as fractions. Students engage in Mathematical Practice 4 (Modeling with mathematics) as they use lengths on the number line. This supports students as they incorporate mixed numbers as a form of fractions into their understanding of "number". Mathematical Practice 7 (Look for and make use of structure) is also featured in this lesson as students connect the sums of lengths to the sum of a whole number and fraction shown by the mixed number form.

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