Lesson plan

# 6. Understand the relationship between multiplication and division with fractions (C)

teaches Common Core State Standards CCSS.Math.Content.5.NF.B.7a http://corestandards.org/Math/Content/5/NF/B/7/a
teaches Common Core State Standards CCSS.Math.Content.5.NF.B.7b http://corestandards.org/Math/Content/5/NF/B/7/b
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

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Lesson objective: Understand that the relationship between multiplication and division does not change when unit fractions are included.

Students bring prior knowledge of the relationship between multiplication and division of whole numbers from 3.OA.A.2 and 3.OA.A.3. This prior knowledge is extended to fractions as students model the ways in which this relationship remains true when solving missing factor problems that involve fractions. A conceptual challenge students may encounter is explaining how the relationship between multiplication and division can be used to solve problems involving division of unit fractions and whole numbers in the context of comparison and scaling.

The concept is developed through work with scale models, number lines, and tape diagrams, which visually represent this relationship.

This work helps students deepen their understanding of operations because the relationships they already know hold when working with fractions.

Students engage in Mathematical Practice 4 (model with mathematics) as they notice and model situations that show how the relationship between multiplication and division remain, even with fractions included in problems about scaling and comparison.

Key vocabulary:

• dividend
• divisor
• quotient
• scaling