# 1. Represent multiplication with rational numbers on the number line (C)

teaches Common Core State Standards CCSS.Math.Content.7.NS.A.2 http://corestandards.org/Math/Content/7/NS/A/2
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

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Lesson objective: Multiply negative and positive numbers by representing problems on the number line.

From 6.NS.6, students bring prior knowledge of representing opposites on the number line, and from 7.NS.1, students bring prior knowledge of representing addition and subtraction of negative numbers on the number line. This prior knowledge is extended to multiplying with negative numbers. A conceptual challenge students may encounter is understanding that the "rules" for multiplying with negatives are not simply arbitrary facts to memorize but they follow naturally from their understanding of the number line.

Work with the number line helps students deepen their understanding of operations because they will be able to discover the patterns or "rules" for multiplying with negative numbers (i.e., the product of a positive number times a negative number is negative, the product of a negative number times a positive number is negative, and a the product of a negative number times a negative number is positive).

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they extend their knowledge of the number line to include multiplying with negative numbers and notice patterns in their work.

Key vocabulary:

• opposite

Special materials needed:

• number lines
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