I will understand absolute value and use it to find magnitude of a positive or negative quantity.
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1 Today's Objective: I will understand absolute value and use it to find magnitude of a positive or negative quantity. 1
2 Lesson 11: Absolute Value Magnitude and Distance Opening Exercise: 2
3 Example 1: The Absolute Value of a Number The absolute value of ten is written as: 10. On the number line, count the number of units from 10 to 0. How many units is 10 from 0? 10 = What other number has an absolute value of 10? Why? 3
4 The absolute value of a number is the distance between the number and zero on the number line. 4
5 Exercises 1 3 Complete the following chart. Number Absolute Value Number Line Diagram Different Number with the same Absolute Value 5
6 Example 2: Using Absolute Value to Find Magnitude Mrs. Owens received a call from her bank because she had a checkbook balance of 45 dollars. What was the magnitude of the amount overdrawn? The magnitude of a quantity is found by taking the absolute value of its numerical part 6
7 Exercises 4 8 For each scenario below, use absolute value to determine the magnitude of each quantity. 4. Maria was sick with the flu and her weight change as a result of it is represented by 4 pounds. How much weight did Maria lose? 5. Jeffrey owes his friend $5. How much is Jeffrey s debt? 6. The elevation of Niagara Falls, which is located between sea Lake Erie and Lake Ontario, is 326 feet. How far is this above level? 7. How far below zero is 16 degrees Celsius? 8. Frank received a monthly statement for his college savings account. It listed a deposit of $100 as It listed a withdrawal of $25 as The statement showed an overall ending balance of $ How much money did Frank add to his account that month? How much did he take out? What is the total amount Frank has saved for college? 7
8 Exercises Meg is playing a card game with her friend Iona. The cards have positive and negative numbers printed on them. Meg exclaims: The absolute value of the number on my card equals 8! What is the number on Meg s card? 10. List a positive and negative number whose absolute value is greater than 3. Explain how to justify your answer using the number line. 11. Which of the following situations can be represented by the absolute value of 10? Check all that apply. The temperature is 10 degrees below zero. Express this as an integer. Determine the size of Harold s debt if he owes $10. Determine how far 10 is from zero on a number line. 10 degrees is how many degrees above zero? 12. Julia used absolute value to find the distance between 0 and 6 on a number line. She then wrote a similar statement to represent the distance between 0 and 6. Below is her work. Is it correct? Explain. 6 = 6 and 6 = 6 8
9 13. Use absolute value to represent the amount, in dollars, of a $ profit. 14. Judy lost 15 pounds. Use absolute value to represent the number of pounds Judy lost. 15. In math class, Carl and Angela are debating about integers and absolute value. Carl said two integers can have the same absolute value and Angela said one integer can have two absolute values. Who is right? Defend your answer. 16. Jamie told his math teacher: Give me any absolute value, and I can tell you two numbers that have that absolute value. Is Jamie correct? For any given absolute value, will there always be two numbers that have that absolute value? 17. Use a number line to show why a number and its opposite have the same absolute value. 18. A bank teller assisted two customers with transactions. One customer made a $25.00 withdrawal from a savings account. The other customer made a $15 deposit. Use absolute value to show the size of each transaction. Which transaction involved more money? Which is farther from zero: 7 or 7? Use absolute value 4 2 to defend your answer. 9
10 1. Jessie and his family drove up to a picnic area on a mountain. In the morning, they followed a trail that led to themountain summit, which was 2,000 feet above the picnic area. They then returned to the picnic area for lunch. After lunch, they hiked on a trail that led to the mountain overlook, which was 3,500 feet below the picnic area. Exit Ticket: a. Locate and label the elevation of the mountain summit and mountain overlook on a vertical number line. The picnic area represents zero. Write a rational number to represent each location. picnic area: 0 mountain summit: mountain overlook: b. Use absolute value to represent the distance on the number line of each location from the picnic area. Distance from the picnic area to the mountain summit: Distance from the picnic area to the mountain overlook: c. What is the distance between the elevations of the summit and overlook? Use absolute value and your number line from part (a) to explain your answer. 10
11 11
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