# Lesson 6

Absolute Value of Numbers

## 6.1: 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 \(0.001\)

### Student Response

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### 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)*

## 6.2: 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.