Seeing Sums

Seventh Grade Poster Problem
The Number System

Unlike other poster problems, this problem is about mastering a mathematical model, the number line model for sums, rather than using the model to solve a “real life” problem. The model will spark a discussion in which your students will use language and reasoning highlighted in the CCSSM. In the launch, you will first set the stage by asking students to consider limitations of the familiar set model for sums and differences. Then, you can introduce the number line model using a short animation. Next, the students explore the model, first by hand, and then with a dynamic number line game. Finally, in the concluding discussion, you will use the model to elicit key ideas from your students.

Learning Objectives:

  • Represent addition and subtraction on a number line diagram.
  • Understand p + q as the number located a distance |q| from p. The direction depends on whether q is positive or negative.
  • Understand subtraction as adding the additive inverse. p − q = p + (-q)
  • Use the number line model to show that the sum of two opposites is zero.
  • Use terminology such as additive identity, opposite, additive inverse, and absolute value to reason about relationships among rational numbers.

Common Core State Standards for Mathematics:

The Lesson Plan:

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Strategic Education Research Partnership
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Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation

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