1. Copyright © Ed2Net Learning, Inc.1 Comparing and Ordering Integers

2. Copyright © Ed2Net Learning, Inc. 2 Warm Up Use > or < to compare the numbers. 1. 83 108 2. 2,376 2,367 3. Round 568 to the nearest hundreds place. 4. Round 5,986 to the nearest tens place.

3. Copyright © Ed2Net Learning, Inc. 3 Integers Integers are all of the positive whole numbers, their opposites, and zero.  Example:....., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,...... Integers consist of positive numbers, negative numbers and zero (which is neither positive nor negative)

4. Copyright © Ed2Net Learning, Inc. 4 INTEGERS can be shown as points on a number line. Zero is the Origin. Integers on this side of zero are POSITIVE. Integers on this side of zero are NEGATIVE. It is neither positive nor negative! Integers Negative Integers are integers that are less than 0. Positive Integers are integers that are greater than 0. The integer -5 is read “negative 5.” -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Positive Numbers Negative Numbers

5. Copyright © Ed2Net Learning, Inc. 5 Integers Integers are often used to represent real- world quantities. Words like profit, increase, and above indicate a positive integer. Words like loss, decrease, and below indicate a negative integer.

6. Copyright © Ed2Net Learning, Inc. 6 Example: Using Integers Write the integer that represents the situation. 1. The countdown for the space shuttle is at “T-10 seconds.” -10 seconds 2. A withdrawal of $25 -$25

7. Copyright © Ed2Net Learning, Inc. 7 Your turn now! Write the integer that represents the situation. 1. A $15 profit 2. A 9 point decrease 3. A loss of 5 yards

8. Copyright © Ed2Net Learning, Inc. 8 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 8 units Opposites Numbers increase as you move from left to right on a number line. Two numbers are opposites if they are the same distance from 0 on a number line, but are on opposite sides of 0. -8 and 8 are opposites. They are both 8 units away from zero!

9. Copyright © Ed2Net Learning, Inc. 9.....-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,...... These 2 numbers are opposites. Can you name another pair of opposites? INTEGERS Opposites

10. Copyright © Ed2Net Learning, Inc. 10 Can you find the opposite of -3? How many units are they away from zero? Are they both the same number of units away from zero? -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Identifying Opposites 3 units The opposite of -3 is 3.

11. Copyright © Ed2Net Learning, Inc. 11 Your turn now! Find the opposite of the integer. 1. 8 2. -7 3. -12 4. 0

12. Copyright © Ed2Net Learning, Inc. 12 Absolute Value The Absolute Value of a number is its distance from zero on the number line.  Example: The Absolute Value of 4 is written as 4

13. Copyright © Ed2Net Learning, Inc. 13 Let's find the Absolute Value of 4. Remember that we write the Absolute Value of 4 as 4 102 34567 89 10 -3-4-5-6-7-8-9 -10 The Absolute Value of 4 OR 4 is the distance of 4 from zero. Therefore.......... 4 = 4.. 4 is 4 units from zero. -2

14. Copyright © Ed2Net Learning, Inc. 14 Let's find the Absolute Value of -3. Remember that we write the Absolute Value of -3 as -3 102 34567 89 10 -3-4-5-6-7-8-9 -10 The Absolute Value of -3 OR -3 is the distance that -3 is from zero.. Therefore.......... -3 = 3 -3 is 3 units from zero. -2

15. Copyright © Ed2Net Learning, Inc. 15 Distance is Positive Since Absolute Value is the distance from zero, Absolute Value is always Positive. 9 = 9 -11 = 11

16. Copyright © Ed2Net Learning, Inc. 16 Let's find..... 10 = -17 = 1 = -8 =

17. Copyright © Ed2Net Learning, Inc. 17 We can compare and order integers using the number line. 102 34567 89 10 -3-4-5-6-7-8-9 -10.. -8 is 8 units to the left of zero. 3 is 3 units to the right of zero. -8 < 3 smaller numbers bigger numbers Therefore... -2 Compare & Order Integers If we compare 2 numbers on a number line, the number that is further to the left is the smaller number!

18. Copyright © Ed2Net Learning, Inc. 18 102 34567 89 10 -3-4-5-6-7-8-9 -10 Let's compare and order -5 and -9 First, let's plot the integers on the number line... Since -9 is to the left of -5 on the number line....... -2 -9 < -5 smaller numbers bigger numbers

19. Copyright © Ed2Net Learning, Inc. 19 You try this one! Order these integers on the number line. 102 34567 89 10 -3-4-5-6-7-8-9 -10 4 -7 -3 1 Which is the smallest integer? Which is the largest integer? -2

20. Copyright © Ed2Net Learning, Inc. 20 1) I am a number less than 100 and greater than 20. The digit in my tens place is one less than the digit in my ones place. When you add my digits together, you get a number between 10 and 12. WHAT NUMBER AM I?????

21. Copyright © Ed2Net Learning, Inc. 21 2.)How far away is -4 from 3? 102 34567 89 10 -3-4-5-6-7-8-9 -10 -2-2

22. Copyright © Ed2Net Learning, Inc. 22 3.) Write 2 numbers between 4 and 5. 0 -3-4 -5 12 34 5 Are they Integers???? -2

23. Copyright © Ed2Net Learning, Inc. 23 4.) Write 2 numbers between -3 and -4. 0 -3-4 -5 12 34 5 Are they Integers? -2

24. Copyright © Ed2Net Learning, Inc. 24 Let's see how well we understood the lesson today. 1) What are integers? 2) Is zero a positive or negative integer? 3) What is the opposite of 16? 4) 56 = 5) -19 = Assessment

25. Copyright © Ed2Net Learning, Inc. 25 6)Is 4.5 an integer? 7)True or False? Absolute Value is the distance a number is from zero. 8) Insert a. 5 b. -6 c. 0 -5 -10

26. Copyright © Ed2Net Learning, Inc. 26 Let's Review INTEGERS are all of the positive whole numbers, their opposites, and zero. Example:.....-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,...... INTEGERS consist of positive numbers, negative numbers and zero (which is neither positive nor negative).

27. Copyright © Ed2Net Learning, Inc. 27 Two numbers that are the same distance from zero on the number line are called OPPOSITES. Example: -6 and 6 The ABSOLUTE VALUE of a number is its distance from zero on the number line. ABSOLUTE VALUE is always positive! 18 = 18 -32 = 32

28. Copyright © Ed2Net Learning, Inc. 28 0 -3-4 -5 12 34 5.. If we compare 2 numbers on a number line, the number that is furthest to the left is the smaller number! -4 is smaller than < -2

29. Copyright © Ed2Net Learning, Inc.29 You had a GREAT lesson today!