Comparing & Ordering Integers

1. Comparing & Ordering Integers

2. Objective • Content Objective: We will compare and order integers. We will communicate mathematical ideas using graphical models. • Why learn this: We use positive and negative numbers to measure temperature, height (as in above and below sea level), money, and more. We use absolute value to determine the distance from a point, without regard to the direction we are moving from that point.

3. Vocabulary • integers: all positive whole numbers, their opposites, and zero. • opposites: two numbers that are the same distance from zero on the number line, but in opposite directions. Ex. 2, -2 • absolute value: a number’s distance from zero on the number line (always a positive value).

4. Finding Absolute Value Find the l3l and l-3l. l3l and l-3l = 3

5. WHERE DO WE SEE INTEGERS IN OUR DAILY LIVES Money! Temperature! Elevations (height or depth of places in the world) Years Time Recipes/Cooking Integers are EVERYWHERE!

6. Integers less than zero Integers greater than zero are negative integers are positive integers -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 negatives are zero is neither positives CAN written with negative nor be written a (-) sign positive with a (+) sign

8. 5 positives Integers greater than zero 4 are written are positive integers 3 with + sign 2 1 zero is neither 0 negative nor -1 positive -2 -3 negatives -4 written with Integers less than zero -5 a - sign are negative integers

9. Writing Integers in Real-Life Situations Write an integer to describe each situation Example 1: an increase of 6 inches + 6 Example 2:owe your parents $15 - 15 Example 3:a loss of 7 pounds - 7 Example 4:earned 5 dollars interest + 5 Example 5:a temperature of 9 degrees below zero - 9

11. Quick Practice Write the opposite of each number. • 2 b) 4 c) -3 d) -11 a) -2 b) -4 c) 3 d) 11

12. Quick Practice Find each absolute value. • l-21l b)l14l c) l-1l d)l21l a) 21 b)14 c) 1 d)21

13. Comparing Integers Compare -4 and 1 using <, =, or >. Remember, numbers increase going from left to right. -4 < 1

14. Quick Practice Which number in the pair is farther away from zero. a) 4, -5 b) 2, 5 c) -1, -3 d) -12, 11 a) -5 b) 5 c) -3 d) -12

15. Quick Check Compare using <, =, or >. a) -6 -3 b) -23 0 c) 17 -18 d) 5 -1 a) -6 < -3 b) -23 < 0 c) 17 > -18 d) 5 > -1 e) l-21l 21 f) -14 l14l c) l-1l -5 e) l-21l = 21 f) -14 < l14l c) l-1l > -5

16. Ordering Integers Order the numbers -8, 7, -4, and 3 from least to greatest. Use a number line to plot the points. Then put them in order from least to greatest. Remember, numbers increase going from left to right. -8, -4, 3, and 7

17. Extension The number shows the amounts of money Erica, Jerry, Bob, and Ray have in their wallets or owe one of their parents. Who has the most money? Who has the least money? Who owes four dollars? 10 Ray 8 6 4 Erica 2 0 - 2 Jerry - 4 - 6 - 8 Bob -10

18. Quick Practice In golf, the person with the lowest score is the winner. Rank the players below by ordering their scores from lowest to highest. • B. Hive • P. Tree • L. Emons • J. Umps • T. Ricks

19. l-4l l-3l >

20. l12l l-12l =

21. l-20l l10l >

22. l-14l l-15l <

23. l-7l 6 >

24. -5 l-4l <

25. -15 5 <

26. l-13l l12l >

27. 19 l-19l =

28. l-27l 28 <

30. Absolute Value Evaluate the expression. Example 1:| 3 | 3 Example 2:| - 68| 68 Example 3:| 6 | + | - 9| 6 + 9 = 15 Example 4:| - 8 | - | - 9| 8 – 9 = -1 Integers & Absolute Value

31. Extension Evaluate 6 + |n | if n = - 16. 6 + |n | = 6 + |- 16| = 6 + 16 = 22 Integers & Absolute Value

32. Integers & Absolute Value Absolute Value in real life! An eyeglass prescription is given as a positive or negative number. A prescription for a person who is farsighted is positive. A prescription for a person who is nearsighted is negative. The greater absolute value, the stronger the prescription. Which prescription is stronger, -3 or 2? Step 1: Think about the problem. What information was given and what am I trying to figure out?

33. Integers & Absolute Value Absolute Value in real life! An eyeglass prescription is given as a positive or negative number. A prescription for a person who is farsighted (can’t see near) is positive. A prescription for a person who is nearsighted is negative. The greater absolute value, the stronger the prescription. Which prescription is stronger, -3 or 2? Step 2: Determine the answer What is the absolute value of each prescription? | -3 | | 2 | 3 2 Which prescription is greater? -3!

34. Absolute Value in real life! A seagull is flying at an altitude of 107 feet and a shark is swimming at a depth of 112 feet relative to sea level. Which animal is farther from sea level? 107 feet Sea level (0 feet) -112 feet