Explore the concept of absolute value in terms of distances traveled. This video focuses on a real world application of absolute value and visualizes the problem by graphing points on coordinate plane.
This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.
understand absolute value in terms of distance from 0
define absolute value
apply the concept of absolute value to finding the distance between two points on the coordinate plane
Common Core State Standards: 6.NS.C.8
Vocabulary: Absolute value, positive, negative
Materials: Absolute Value worksheet; for teachers only: Absolute Value Solutions answer key
1. Introduction (5 minutes, whole group) Begin the lesson by introducing absolute value as the distance of any number from 0. Work some quick examples with students (such as |3| = 3 and |–12| = 12) using a number line to convey the idea that the absolute value of a number will always be non-negative. Continue to use the number line to help students think about ways to simplify the following expressions:
|3 + 4|
|3 – 4|
|–5 + 5|
|–9 + 1|
2. Watch the Video (10 minutes, whole group) Show students the video. This video presents a brief story that helps students apply absolute value to the distance between two points on a coordinate plane. (The video moves quickly, so it may be advisable to watch it twice before students begin to work on the next activity.) After playing the video, ask students why the distance between the two points is thought of in terms of absolute value and not as a positive or negative number.
3. Activity (10–15 minutes, pairs) Divide students into pairs and hand out the worksheet. The worksheet contains questions related to the video as well as other questions relating to finding absolute value on a coordinate plane.
When finished with the worksheet, students should check their answers against the answers of another group.
4. Pair Discussion (5 minutes, pairs) Staying in pairs, students can discuss the following questions:
Explain the concept of absolute value to your partner. Is absolute value important? Why or why not?
Joe says that |x| is always equal to x. Do you agree or disagree? Why? Use a number line to illustrate and justify your reasoning.
5. Conclusion (5 minutes, whole group) Discuss the relationship between absolute value and finding distances. As a challenge problem, ask students to give an example of a negative distance.
Next, pose the following question: Evan is thinking of a number. He adds 5 and then takes the absolute value of that sum. The absolute value is 6. What number was he thinking of? Have students solve the problem. Most students will come up with an answer of 1, but they should also identify that –11 is a possibility. Use a number line to show them that both |1 + 5| and |–11 + 5| are equal to 6.