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Lesson Plan

5. Alexa's Sand Designs: Understand that fractions can be decomposed in multiple ways

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.MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards CCSS.Math.Practice.MP5 http://corestandards.org/Math/Practice/MP5
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Lesson objective: Understand that a fraction can be composed from a combination of unit and non-unit fractions, or just from unit fractions, and that we can decompose a fraction into a sum of unit fractions or non-unit fractions.

The concept is developed through work with number lines and is connected to the structure of whole numbers. Students bring prior knowledge of fractions as numbers on the number line from grade 3. This knowledge helps students as they come to understand that fractions can be decomposed into unit fractions just as whole numbers can be decomposed into units of ones, tens, and hundreds, etc.

Students engage in Mathematical Practice 4 (Model with mathematics) as they model lengths on a number line. 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 connect the structure of the base ten number system to the structure of fractions.

Key vocabulary:

  • decompose
  • equation
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Decomposing and composing fractions for addition and subtraction

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