In this task, students are introduced to the absolute value of a number as its distance from zero on the number line. The context is not realistic, but helps students visualize relationships on the number line in a more concrete way.

In the digital version of the activity, students use an applet to visualize a bug jumping on a number line. The applet allows students to pick a starting point for the bug, choose the direction it jumps, and then check where it lands. 

If students don't have individual access, displaying the applet for all to see would be helpful during the Launch and Activity Synthesis.

The purpose of this discussion is to formally introduce the term absolute value. The absolute value of a number is its distance from zero. Begin by asking students to contrast and . (They are both finding the distance from a number to zero. They both have the same value, but represent the distance between two different points and zero.) If needed, draw a number line, and demonstrate how -8 and 8 are both 8 units away from 0.

Here are some additional questions for discussion:

• “Does finding a number’s absolute value always mean changing the sign?” (No, absolute value represents a number’s distance from zero. Distances are always positive, so absolute value will always be positive.)
• “What is the absolute value of 12? Why?” (The absolute value of 12 is 12 because 12 is 12 units away from 0 on the number line.)
• “Are there any other numbers that have an absolute value of 12?” (Yes, the absolute value of -12 is also 12 because it is also 12 units away from 0, just on the opposite side of the number line.)
• “Can the absolute value of a number ever be negative?” (No, it can't be negative because absolute value represents a distance, and we can’t have a negative distance.)

Conclude the discussion by asking students to think of situations that use the concept of absolute value. (A car’s odometer tracks the miles driven regardless of the direction. A swimmer swimming laps in a pool will end up in the same location, but absolute value can be used to measure the total distance swam. People can get on or off a city bus. Absolute value measures the total number of riders.)

In this activity, students continue to develop their understanding that represents the distance from zero to and that and are equal.

The goal of this discussion is for students to explain how absolute value relates to distance and elevation in a situation. Arrange students in groups of 2, and display the image and expressions for all to see.

• -4 feet
• feet
• feet
• 15 feet

Give students 1 minute to study the image and match each letter with one of the expressions. (A: 15 feet, B: feet, C: feet, D: -4 feet) Have students discuss their matches with a partner before inviting students to share their responses and reasoning. Record and display student responses on the image for all to see.