8. Understand how multiplication and division by 10 relate to place value (C)

teaches Common Core State Standards CCSS.Math.Content.5.NBT.A.2 http://corestandards.org/Math/Content/5/NBT/A/2
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

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Lesson objective: Understand that multiplying a number by 10 shifts the position of its digits one place to the left, and dividing a number by 10 shifts the position of its digits one place to the right.

Students bring prior knowledge of relationship between the digits within a number from 5.NBT.A.1. This prior knowledge is extended to the new topic as students learn that there is a pattern in the way the digits of a number shift when you multiply or divide the number by the powers of 10. A conceptual challenge students may encounter is that the digits of a number shift place values while the decimal point remains in the same position.

The concept is developed through work with base ten blocks and place value chart, which serves as a visual model and supports the idea of the consistency of numerical system.

This work helps students deepen their understanding of operations because they will multiply a number by 10 shifting the position of its digits one place to the left, and divide a number by 10 shifting the position of its digits one place to the right.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they discern the patterns in multiplication and division of a number by the powers of 10.

Key vocabulary:

• digit
• power of 10
• product
• quotient
• value of a digit

Special materials needed:

• base ten blocks
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