Guided Lessons

# Absolute Value

In this lesson, students explore absolute value with and without a number line, compare the absolute values of two numbers, and apply their understanding of absolute value to real-world contexts.

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In this sixth-grade lesson plan, teachers will help students understand what absolute value is and how to find it with and without a number line. Students will also learn how to compare the absolute values of two numbers, and apply their understanding of absolute value within real-world contexts, such as temperature, elevation, and price discounts. Students will complete absolute value word problems to demonstrate their understanding. This lesson plan builds off students' understanding of opposite numbers to define absolute value.

• Students will be able to find and order absolute values of rational numbers.
• Students will also be able to apply absolute values in real-world contexts.
(5 minutes)
• Prior to teaching this lesson, make sure you have introduced integers, opposites, and rational numbers to your students.
• Write a number line on the board with a few missing numbers. Make sure to include 0 at the center of the number line. Include at least one missing positive number and at least one missing negative number. Ask students to identify the missing numbers on the number line and write those numbers on a sheet of paper.
• Ask 1–2 students to come up to the board to write the missing numbers.
• Once all of the numbers are labeled on the number line, plot a point on the number line (e.g., 3). Ask a student to come up and show the opposite of that number on the number line (e.g., “Show the opposite of 3 on the number line. Put a point there.”).
(10 minutes)
• Show students that opposites are the same distance from zero, just going in different directions. Show this using the opposites that your class labeled on the number line in the introduction. Tell students that because opposites are the same distance from zero, they have the same absolute value.
• Define the absolute value of a number as its distance from zero. Also introduce absolute value notation with this definition. Have students find the absolute values of the two opposites from the introduction (e.g., |3| and |-3|). Show students that you can find the absolute value of a number by counting how far that number is from zero on a number line.
• Plot another point on the original number line (e.g., -5). Ask students to find the absolute value of that number. Have students answer the question with a partner, and then ask one partner-pair to explain their answer to the class.
• Write another number line on the board that uses a different scale (e.g., going up/down by 20s). Plot a point on that number line (e.g., 60). Ask students to find the absolute value of that number. Have students answer the question with a partner, and then ask one partner-pair to explain their answer to the class.
• Ask students if they notice a pattern about absolute value (students should notice that absolute value is always positive). Then ask students how they would find |-45|, |2.5|, and |½| without a number line. Have students answer these questions with a partner, and then ask a couple partner-pairs to share and explain their answers.
• Tell students that absolute value is also helpful for understanding real-world situations. Write these temperatures on the board: -8°F and -1°F. Ask students to decide which temperature is colder. Then ask students to determine which temperature is closer to zero, or has the smaller absolute value. Have students discuss and explain their answers with a partner. Let them know that they can draw a number line (or thermometer) to help. Then ask one partner-pair to explain their answer to the class.
(10 minutes)
• Hand out the Understanding Absolute Value worksheet to your students.
• Have students work with their partners to complete this worksheet. Monitor students’ progress as they work on the different sections. Prompt students to explain their thinking to you for the problems in the last section (comparing the absolute values of two numbers).
(20 minutes)
• Hand out the Absolute Value Word Problems worksheet to your students.
• Have students work independently on these word problems.
• After 15 minutes, ask students which problems were most challenging. Go over answers for those problems with the class.

Support:

• If students are struggling to solve the Absolute Value Word Problems independently, have them complete the problems with a partner.
• Cut the Absolute Value Word Problems out, and use them as task cards with smaller groups so that students are only looking at one problem at a time.

Enrichment:

• Have students walk around and support other students who are still working on the Absolute Value Word Problems. Encourage these students to explain their thinking and rationale when providing support.
• Give students the Opposites and Absolute Value worksheet to work on. Ask students to explain key differences between opposites and absolute value at the bottom of the worksheet.
(10 minutes)
• Ask students to find the absolute value of the following numbers on a sheet of paper: |8|, |-2|, |0.5|, and |-4 ½|.
• Write the temperatures -5°F, 1°F, and -2°F on the board. Ask students which is the coldest temperature and which is the closest to zero. Students should write their answers to this problem on the same sheet of paper.
• Collect this assessment to gauge student understanding from this lesson.
(5 minutes)
• After you have collected the assessments, have a student explain their answer to the temperature assessment problem.
• Ask students to turn to a partner and define absolute value.