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763270-133350Math Lesson: Absolute ValueGrade Level: 6Lesson Summary:Students compare positive and negative numbers on a number line with absolute value and engage in plotting and calculating absolute values, including rational numbers, on time lines and grids. Advanced students have the opportunity to develop their own time lines and calculate absolute values in their lives. Struggling students engage in solving a distance problem involving absolute value. Lesson Objectives:Understand ordering and absolute value of rational numbers.The students will know…that absolute value of a rational number is its distance from 0 on the number line.the difference between order in numbers on a number line and absolute value. The students will be able to…calculate absolute values in real world contexts.Learning Styles Targeted: FORMCHECKBOX Visual FORMCHECKBOX Auditory FORMCHECKBOX Kinesthetic/TactilePre-Assessment:Use this quick assessment to determine if students understand the difference between negative and positive numbers.Ask students to tell you where to plot 10 and -10 on the number line. Ask them to calculate the difference between 10 and -10. Record their answers and ask for reasoning, but do not present any information at this time.Leave the numbers on the board to reference at the end of the activity. Record their answers and note student responses.Whole-Class InstructionMaterials Needed: Show Your Stuff Independent Practice with Absolute Value*Procedure: PresentationDiscuss situations in which numbers less than 0 are useful (temperature, above and below sea level, bank balance) and times when they make no sense (you can’t have -8 ounces of water, you can’t travel -5 miles in distance, even if you travel backwards). Explain that negative numbers were nowhere to be found in mathematics until the 1600’s. Some mathematicians and philosophers were convinced that numbers less than zero could not exist and would lead to absurd conclusions.Create a time line on the board of US presidents. Mark the halfway point at 0 and label it 2000. Start in 2000, and make evenly spaced marks to represent every four years. Then plot the Presidents elected in each of those years. 2000 Bush, 2004 Bush, 2008 Obama. Then plot the presidents before 2000 (1996 Clinton, 1992 Clinton, 1988 Bush, 1984 Reagan, 1980 Reagan, and 1976 Carter). Confirm that the dates are in the right order.Have students calculate the difference between two dates on your timeline. For example, how many years between Carter’s election and Obama’s election [32 years]. Explain that in this case, you can add the distance from 1976 to 2000 to the distance from 2008 to 2000. Since 1976 is before 2000, and 2008 is after 2000, the distance between 1976 and 2008 can be represented by using absolute value.Demonstrate that when you calculate absolute value, all results are positive because you are calculating a number’s distance from 0 on the number line. So |8| = 8, and |24| = 24. Point out that you use vertical lines to indicate absolute value. Sometimes absolute values are represented by abs(8), for example, as a function in a graphing calculator or Excel. Guided PracticeExplain that students are going to play a type of football game. Have them draw a football field using the lines on a blank piece of notebook paper turned horizontally. Have them label the left end -50 and then label each line -45, -40, and so on until they reach +50. Discuss what the dividing line between positive and negative territory is . Have everyone start with a point at 0, and label that point A. Then have them follow your sequence of numbers to add and subtract by 5s, placing a point at each new number and labeling each new point sequentially B, C, and so on. Call out the number +15 and have them label the 15 line with a B. Then call out -2512 and have them count backwards from 15, so they should be at -1012 and label that with a C.Continue with -2012, +5012, -4012, +1012, +1012. See how many ended back at the zero line.Then have students add and subtract all the numbers and write the equation on the board 15-2512-2012+5012-4012+1012+1012=0 to prove that the numbers do add to 0.Next have them find the total distance traveled . This is the sum of the absolute values of each number given, since distance is always a positive number. Discuss the difference between the sum of all the numbers and the total distance and how the calculations differ depending on the question being asked.Independent PracticeDistribute Show Your Stuff Independent Practice with Absolute Value* and give students five minutes to complete it.Closing ActivityReview the Show Your Stuff solutions and have students defend their responses.Have students explain the difference between absolute value and positive and negative numbers on the number line. Advanced LearnerWhat Is a Rational Number?Materials Needed: NoneProcedure: Have students create timelines of their lives using the 0 point as their date of birth. Have them include events before and after they were born and include fractions of years with careful placement of values on the number line. Then have them calculate the absolute value between at least three events that occurred before they were born (such as a parent’s birth or the birth of an older sibling) and their own birth. Have them present their timelines and calculations to the class.Struggling LearnerOn the Number LineMaterials Needed: NoneProcedure:Have students draw this problem as you relate it: You are going on a trip of 50 miles. You drove 10 miles and then took a wrong turn and drove 12.5 miles the wrong way. You had to turn around to get back on track. How many miles did you drive altogether?Discuss the results and the difference between adding and subtracting positive and negative numbers and adding absolute value.*see supplemental resources ................
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