Lesson plan

Decompose a fraction into a sum of fractions using an area model

teaches Common Core State Standards CCSS.Math.Content.4.NF.B.3a http://corestandards.org/Math/Content/4/NF/B/3/a
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.MP7 http://corestandards.org/Math/Practice/MP7

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Big Ideas: Any whole number, mixed number, or fraction can be decomposed into the sum of unit fractions. Fractions can be composed or decomposed into unit fractions with like denominators. In this lesson students will use visual fraction models to represent equal parts of a whole. Students explore fraction equivalence through the decomposition of unit and non-unit fractions using the context of tiling a bathroom floor, which highlights composition and decomposition of fractions and number sentences. Using an area model, students decompose fractions in different ways to represent sums of fractions with the same denominator. By leaving the task open ended, students reason why there are different possibilities for the tile design. The mathematics in this lesson build toward students' future work creating visual models to show the addition and subtraction of fractions and mixed numbers with like denominators. Vocabulary: area, unit fraction, composing fractions, decomposing fractions, numerator, denominator, equal parts Special Materials: colored pencils graph paper colored square tiles (optional)