Lesson plan

11. Understand that rational numbers have opposites with the same absolute value (C)

teaches Common Core State Standards CCSS.Math.Content.6.NS.C.7c http://corestandards.org/Math/Content/6/NS/C/7/c
teaches Common Core State Standards CCSS.Math.Content.6.NS.C.7d http://corestandards.org/Math/Content/6/NS/C/7/d
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2
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Lesson objective: Understand that rational numbers have opposites and that the absolute value of those rational numbers is equivalent.

Students bring prior knowledge that the set of integers includes whole numbers, their opposites, and zero, and live on the number line with the other types of numbers students know from 6.NS.C.5. This prior knowledge is extended to the idea that opposite rational numbers have equivalent absolute values. A conceptual challenge students may encounter is that absolute value is a distance and is therefore always positive, even when the rational number is negative.

The concept is developed through work with a number line, which helps students see the distances from 0 that absolute values represent.

This work helps students deepen their understanding of number because it establishes the understanding that numbers have relationships that are defined by their distances from 0 on a number line.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they seek to establish the relationship between rational numbers concerning opposites, absolute value, and where rational numbers live on a number line.

Key vocabulary:

  • absolute value
  • integers
  • number line
  • opposite
  • rational numbers