1. Copyright © Ed2Net Learning, Inc.1 Integers Grade 5

2. Copyright © Ed2Net Learning, Inc.2 Integers An integer is any number from the set {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …} where … means continues without end. -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 Zero is neither negative nor positive. Positive numbers can be written with or without + sign. Negative numbers are written with a - sign. Integers less than zero are negative numbers. Integers greater than zero are positive numbers.

3. Copyright © Ed2Net Learning, Inc.3 Integers for Real-Life Situations Football: a gain of 5 yards on the first down  The word gain represents an increase. The integer is +5 or 5 Weather: a temperature of 10 degrees below zero  Any number that is below zero is a negative number The integer is -10. Read as negative ten Read as positive five

4. Copyright © Ed2Net Learning, Inc.4 Try This! Write an integer to describe each situation.  Lost 6 points  12 feet above sea level

5. Copyright © Ed2Net Learning, Inc.5 Graph an integer on a number line To graph an integer on a number line, draw a dot at the location on the number line that corresponds to the integer. -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 Draw a number line. Then draw a dot at the location that represents -3.

6. Copyright © Ed2Net Learning, Inc.6 Compare Integers A number line can also be used to compare and order integers. On a number line, the number to the left is always less than the number to the right.

7. Copyright © Ed2Net Learning, Inc.7 Compare Integers Graph -6 and -4 on a number line. Then compare. -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 Since -6 is to the left of -4, -6 < -4.

8. Copyright © Ed2Net Learning, Inc.8 Your Turn! Write, or = to make a true sentence.  -3 __ -5  -5 __ 0

9. Copyright © Ed2Net Learning, Inc.9 Ordering Integers When ordering integers from greatest to least, write the integers as they appear from right to left.

10. Copyright © Ed2Net Learning, Inc.10 Your Turn! The average daily temperatures in four northern towns are 6, -14, 10, and -8 degrees Fahrenheit. Order the temperatures from least to greatest.

11. Copyright © Ed2Net Learning, Inc.11 Opposite of an integer Opposites are numbers that are the same distance from zero in opposite directions on the number line. -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 The opposite of +6 is -6. 6 units left 6 units right

12. Copyright © Ed2Net Learning, Inc.12 Your Turn! Write the opposite of each integer.  -4  +8

13. Copyright © Ed2Net Learning, Inc.13 Absolute Value Absolute Value is the distance a number is from zero on the number line. The number line below shows that -3 and 3 have the same absolute value, 3. The symbol for absolute value is n -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 3 units 3 = 3 The absolute value of 3 is 3. -3 = 3 The absolute value of -3 is 3.

14. Copyright © Ed2Net Learning, Inc.14 Your Turn! 5 -2

15. Copyright © Ed2Net Learning, Inc.15 Zero Pairs Counters can be used to understand integers. A yellow counter represents the integer +1. A red counter represents the integer -1. When one yellow counter is paired with one red counter, the result is zero. The pair of counters is called a zero pair. + -

16. Copyright © Ed2Net Learning, Inc.16 Zero Pairs Use counters to model +4 and -4. then form as many zero pairs as possible to find the sum +4 + (-4). + -+ + + - - - Place four yellow counters on the mat to represent +4. Then place four red counters on the mat to represent -4. Step 1

17. Copyright © Ed2Net Learning, Inc.17 Zero Pairs + -+ + + - - - Pair the positive and negative counters. Then remove all zero pairs. Step 2 There are no counters on the mat. So, +4 + (-4) = 0.

18. Copyright © Ed2Net Learning, Inc.18 Your Turn! Use counters to model the pair of integers. Then form zero pairs to find the sum of the integers.  +3, -3

19. Copyright © Ed2Net Learning, Inc.19 Adding Integers To add integers, use counters or a number line.  Adding integers with the same sign: Find +3 + (+2) + + + + + Method 1: Use Counters Add 3 positive counters and 2 positive counters on the mat. So, +3 + (+2) = +5 or 5. Method 2: Use a number line Start at 0. Move 3 units to the right to show +3. From there, move 2 units right to show +2. -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +3+2

20. Copyright © Ed2Net Learning, Inc.20 Your Turn! Find -2 + (-4). Remember: To move right on a number line to add positive integers and left to add negative integers.

21. Copyright © Ed2Net Learning, Inc.21 Adding Integers with Different Signs To add two integers with different signs, it is necessary to remove any zero pairs.  Find 1 + (-5) + Method 1: Use Counters Add 1 positive counter and 5 negative counters on the mat. So, 1 + (-5) = -4. -- - -- + Next remove as many zero pairs as possible. -- - -- A number without a sign is assumed to be positive.

22. Copyright © Ed2Net Learning, Inc.22 Adding Integers with Different Signs So, 1 + (-5) = -4. Method 2: Use a number line Start at 0. Move 1 unit to the right to show +1. From there, move 5 units left to show -5. -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 -5 +1

23. Copyright © Ed2Net Learning, Inc.23 Your Turn! Add -6 + 3. Use counters or a number line if necessary.

24. Copyright © Ed2Net Learning, Inc.24 Add Integers The sum of two positive integers is always positive. 5 + 1 = 6 The sum of two negative integers is always negative. -5 + (-1) = -6. The sum of a positive integer and a negative integer is sometimes positive, sometimes negative, and sometimes zero.  5 + (-1) = 4;  -5 + 1 = -4;  -5 + 5 = 0

25. Copyright © Ed2Net Learning, Inc.25 Break!

26. Copyright © Ed2Net Learning, Inc.26

27. Copyright © Ed2Net Learning, Inc.27 Subtracting Integers Rule: To subtract an integer, add its opposite; or you can use counters. Find 3 - 1 + Method 1: Use Counters Place 3 positive counters on the mat to show +3. remove 1 positive counter. + + Method 2: Use the rule 3 -1 = 3 + (-1) = 2 The difference of 3 and 1 is 2. To subtract 1, add -1 Simplify So, 3 - 1 = 2

28. Copyright © Ed2Net Learning, Inc.28 Subtracting Integers Check: Use a number line to find 3 + (-1) -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +3

29. Copyright © Ed2Net Learning, Inc.29 Your Turn! Find -5 – (-3)

30. Copyright © Ed2Net Learning, Inc.30 Subtracting Integers Using Zero Pairs  Sometimes you need to add zero pairs before you can subtract  Find -2 -3. Method 1: Use Counters Place 2 negative counters on the mat to show -2. So, -2 - 3 = -5 - - Now, remove 3 positive counters. - - -- +++ - Since there are no positive counters, add 3 zero pairs. - - -- +++ -

31. Copyright © Ed2Net Learning, Inc.31 Subtracting Integers Method 2: Use the rule -2 - 3 = -2 + (-3) = -5 The difference of -2 and 3 is -5. To subtract 3, add -3 Simplify -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 -3 -2 Check: Use a number line to find -2 + (-3)

32. Copyright © Ed2Net Learning, Inc.32 Your Turn! Subtract – 8 – 3. Use counters if necessary.

33. Copyright © Ed2Net Learning, Inc.33 Assessment 1. Write the integer that describes 4 miles below sea level. 2. Draw a model to show 4 + (-3). 3. Explain how to subtract integers. 4. Write, or = to make a true sentence: -7 __ -3. 5. Order -5, -7, 4, -3, and -2 from greatest to least. 6. Add + 8 + (-3). Use counters or number line if necessary.

34. Copyright © Ed2Net Learning, Inc.34 Assessment 7. Subtract 9 – (+3). Use counters if necessary. 8. Find the value of d that makes d – (-5) = 17 a true sentence. 9. Explain why any negative integer is less than any positive integer. 10. A mole is trying to crawl out of its burrow that is 12 inches below ground. The mole crawls up 6 inches and then slides down 2 inches. What integer represents the mole’s location in relation to the surface?

35. Copyright © Ed2Net Learning, Inc.35 Great Job! Remember to do the practice worksheets!!!