Lesson 4

Absolute Value of Numbers

4.1: Number Talk: Closer to Zero (5 minutes)

Warm-up

The purpose of this Number Talk is to elicit strategies and understandings students have about the distance from 0 on the number line. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to think about distance from 0 for various rational numbers. While four problems are given, it may not be possible to share every strategy. Consider gathering only two or three different strategies per problem.

Launch

Reveal one problem at a time. Give students 30 seconds of quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all previous problems displayed throughout the talk. Follow with a whole-class discussion.

Representation: Internalize Comprehension. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization

Student Facing

For each pair of expressions, decide mentally which one has a value that is closer to 0.

$$\frac{9}{11}$$ or $$\frac{15}{11}$$

$$\frac15$$ or $$\frac19$$

$$1.25$$ or $$\frac54$$

$$0.01$$ or $$0.001$$

Activity Synthesis

Ask students to share their reasoning for each problem. Record and display their explanations for all to see. To involve more students in the conversation, consider asking:

• “Who can restate ___’s reasoning in a different way?”
• “Did anyone have the same answer but would explain it differently?”
• “Did anyone reason about the problem in a different way?”
• “Does anyone want to add on to _____’s reasoning?”
• “Do you agree or disagree? Why?
Speaking: MLR8 Discussion Supports.: Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because . . ." or "I noticed _____ so I . . . ." Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)

4.2: Jumping Flea (15 minutes)

Activity

The purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, but helps students visualize relationships on the number line in a more concrete way. Students have used the concept of absolute value informally in previous lessons, but this is where the term is formally introduced and used precisely (MP6).

Launch

Allow students 10 minutes quiet work time followed by whole-class discussion.

Students using the digital materials, will use an applet to visualize the bug jumping. Students can pick a starting point for the bug, choose the direction it jumps, and then check where it lands.

Student Facing

Move the bug to a starting point, choose a jump distance, and press the jump button. You may need to zoom in or out if your bug jumps off the screen.