Student Probe Absolute Value Give the written notation form to student. What is the value of: |-­‐6| |7| Solution: 6, 7 Students frequently have the misconception that absolute value means “opposite”, rather than “the distance from 0.” Lesson Description This lesson develops the understanding that the absolute value of a real number as its distance from 0 on the number line. Absolute value is interpreted as the magnitude of a positive or negative quantity in a real-­‐world situation. Rationale The distance between two points, either on a number line or in the plane, is an important concept in applications of mathematics. Distance can also refer to a mathematical distance such as the possible error between a measurement and the true value. Frequently students simply ignore or remove any negative signs without understanding the meaning of absolute value. This may cause difficulty when students encounter algebraic expressions. Preparation Prepare a visual display for number lines. Have number lines available for students to use. At a Glance What: The absolute value of a rational number is its distance from 0 on the number line. Common Core State Standard: CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-­‐world situation. Matched Arkansas Standard: AR.7.NO.3.5 (NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology. Mathematical Practices: Reason abstractly and quantitatively. Look for and make use of structure. Who: Students who do not understand absolute value as a distance from zero. Grade Level: 6 Prerequisite Vocabulary: magnitude Prerequisite Skills: locate numbers on a number line, determine the distance by counting on a number line Delivery Format: Individual, small group Lesson Length: 15 to 30 minutes Materials, Resources, Technology: Number lines for visual display and student use Student Worksheets: none Lesson The teacher says or does… 1. How far is 10 from 0? 2. How far is -­‐10 from 0? Expect students to say or do… If students do not, then the teacher says or does… 10 Let’s count the units from zero on the number line. Count the spaces together. 10 Let’s count the units from zero on the number line. Count the spaces together. 3. The distance of a number from zero is called the absolute value of the number. Sometimes we also call it the magnitude. We use this symbol: | |. 4. What is |-­‐8|? 8 How do you know? -­‐8 is 8 units from 0 on the number line. 5. What is |5|? 5 How do you know? 5 is 5 units from 0 on the number line. 6. What is |-­‐5|? How do you know? 5 -­‐5 is 5 units from 0 on the number line. 7. On the board, write |6| 6 and |-­‐6|. Ask students to 6 write the answers to each. 8. What two numbers have an absolute value of 3? Explain how you know. 3 and -­‐3 Both 3 and -­‐3 are three units from 0 on the number line. Let’s count the units from -­‐8 to 0 on the number line. Count the spaces together. Refer students to a number line to count the units from 5 to 0. Count the spaces together. Refer students to a number line to count the units from -­‐5 to 0. Count the spaces together. Repeat with additional numbers, having students count on the number line if necessary. Let’s start at 0. What number is 3 units to the right of 0? (Count with the students, if necessary.) What number is 3 units to the left of 0? (Count with the students, if necessary.) Teacher Notes 1. The absolute value of a number a is represented as |a|. 2. The absolute value of a number is geometrically defined as the distance between that number and zero. The algebraic definition is . 3. Students should understand that absolute value is the distance of a number from zero rather than simply thinking that it is always positive. This will avoid misconceptions such as when the student enters algebra courses. Variations Additional numbers may be used for added practice. Formative Assessment What is |-­‐4|? Explain how you know. What two numbers have an absolute value of 2? Explain how you know. References Mathematics Preparation for Algebra. (n.d.). Retrieved 12 10, 2010, from Doing What Works: http://dww.ed.gov/practice/?T_ID=20&P_ID=48 Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide -­‐ Response to Intervention in Mathematics. Retrieved 2 25, 2011, from rti4sucess: http://www.rti4success.org/images/stories/webinar/rti_and_mathematics_webinar_presentati
on.pdf Walle, J. A. (2007). Elementary and Middle School Mathematics Teaching Developmentally. Boston: Pearson Education, Inc.