# 2. Understand that scaling does not always make numbers larger (C)

teaches Common Core State Standards CCSS.Math.Content.5.NF.B.5 http://corestandards.org/Math/Content/5/NF/B/5
teaches Common Core State Standards CCSS.Math.Content.5.NF.B.5a http://corestandards.org/Math/Content/5/NF/B/5/a
teaches Common Core State Standards CCSS.Math.Content.5.NF.B.5b http://corestandards.org/Math/Content/5/NF/B/5/b
teaches Common Core State Standards CCSS.Math.Content.5.NF.B.6 http://corestandards.org/Math/Content/5/NF/B/6
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards CCSS.Math.Practice.MP6 http://corestandards.org/Math/Practice/MP6

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Lesson objective: Understand that scaling does not always make numbers larger and that if we multiply a number by a fraction less than one the number will scale down.

Students bring prior knowledge of scaling by whole numbers and multiplying fractions by whole numbers from 4.NF.B.4. This prior knowledge is extended to multiplying by fractions and mixed numbers as students practice scaling down to solve word problems. A conceptual challenge students may encounter is thinking that multiplication will always result in a product greater than both factors.

The concept is developed through work with number lines, which provide a visualization of a fraction of a length compared to the original length.

This work helps students deepen their understanding that scaling does not always make numbers larger and multiplying numbers by fractions less than one will result in a smaller number.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they use number lines to interpret situations that involve multiplying a number by a fraction less than one and finding a solution that is less than the given number. They also engage in Mathematical Practice 6 (attend to precision) by using a number line accurately, as well as vocabulary, to explain why multiplication can be used to scale either up or down.

Key vocabulary:

• factor
• multiply
• partition
• product
• scaling
• scale factor
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