## Absolute Value

Materials: A number line that the entire class can see; colored press-on/peel-off dots large enough to be seen from the back of the classroom.

Preparation: If you don't have a commercially prepared number line, draw one either on the chalkboard or on adding-machine tape. Include at least 20 to 20.

Prerequisite Skills and Concepts: Students need to be familiar with the inequality symbols and with how to make and use a number line. They also need to be able to compute with negative numbers.

• Stand so that the door is to your right.

• Ask: About how far is it from where I'm standing to the door?
Students should respond with an estimated number of feet.

• Ask: If I were blind-folded, how would you tell me where the door is?
Students should respond with both the estimated number of feet and a direction.

• Now, stand so that the door is to your left.

• Ask: About how far is it from where I'm standing to the door?
Students should respond with an estimated number of feet.

• Ask: If I were blind-folded, how would you tell me where the door is?
Students should respond with both the estimated number of feet and a direction.

• Say: When I asked how far I was from the door, you gave me a number of feet, and it didn't matter which way I was facing. But, when I asked where the door was in relation to my position, you gave me a direction as well as a number, and then it did matter which way I was facing. Today, we'll talk about absolute value. Absolute value tells how far from zero a number is. It doesn't tell you which direction from zero.

• Point to 6 on the number line.

• Ask: What number is this? How far from zero is this number?
Continue this questioning with 6, 0, 14, and 14, and so forth, until you are sure that students can differentiate between a directed distance and an absolute distance. Reinforce the response to each distance question by saying The absolute value of __ is __ and writing |___| = ___.

• Divide the class into two teams. Team 1 is the signed number team and Team 2 is the absolute value team.

• Ask: Can someone on Team 1 ask a question that would require a signed number or a direction as its answer?

You are looking for questions such as:

What was the temperature on the coldest day at the North Pole last winter?
How do I get to Lake Erie from here?

• Ask: Can someone on Team 2 ask the same question so that it does not require a signed number or a direction as its answer?

You are looking for questions such as:

How far below zero was the temperature on the coldest day at the North Pole last winter?
How far north is Lake Erie from here?

Encourage students to be creative with their questions. Team 2 should go first as often as Team 1 does.

• Place colored dots at 6 and 3 on the number line.

• Ask: How would you compare these two numbers?
Ask students to both say and write the comparison. 6 < 3 or -6 < 3.

• Ask: How would you compare the absolute values of these two numbers?
Ask students to both say and write the comparison. |6| > |3| or |6| > |3|.

Discuss why the direction of the comparison symbol changed. Do several more examples until you are satisfied that students can compare both signed numbers and absolute values.