# 6. Playing Speed: Using Area Model to Multiply Non-Unit Fractions by Whole Numbers (FP)

teaches Common Core State Standards CCSS.Math.Content.4.NF.B.4b http://corestandards.org/Math/Content/4/NF/B/4/b
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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Lesson objective: Multiply a non-unit fraction by a whole number.

This lesson helps to build fluency with multiplying a non-unit fraction by a whole number. The previous lesson used number lines to model this same skill. In this lesson area models are used to model this skill. This work develops students' understanding that a multiple of $$\frac ab$$ is a multiple of $$\frac1b$$: n x $$\frac ab$$ = $$\frac {n\ \times\ a}b$$.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they come to recognize that multiplying the numerator by the whole number is a more efficient way to calculate repeated addition of a non-unit fraction.

Key vocabulary:

• multiple
• non-unit fraction
• unit fraction
• whole number

Special materials needed:

• access to a way to keep track of time (e.g. stop watch or easily visible wall clock with a second hand)
• game cards for "Speed" (see "Additional materials")
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