1. Integers (-5) + (-2)

2. Terminology Negative integer Positive integer Zero pair Opposite integer

3. Representing Integers Integers can be modeled by using colored tiles or signed tiles Can be used to represent a -1 Can be used to represent a +1 + - Represents +3 Represents -4

4. Representing Integers Ex. Use colored tiles to model +2 Each pair of 1 yellow and 1 red tile makes a zero pair. The pair models 0. There are two yellow(positive) tiles left so the integers represented is +2

5. Adding Integers With Tiles To add integers with tiles we model each integer in the addition equation with the correct type of tile Ex. Evaluate (-3) + (+2) -3 +2 These zero pairs disappear There is only one red tile remaining which represents the integer (-1) Therefore (-3) + (+2) = (-1)

6. Adding Integers With A Number Line A number line can also be used to model the addition of integers An arrow can be drawn above the number line to model each of the integers in the addition expression The second arrow is started at the finishing point of the first arrow Ex. The arrow above the number line represents (-6)

7. Adding Integers With A Number Line Ex. Evaluate (+1) + (-6) Two arrows need to be drawn, one to represent (+1) and the second one to represent (-6) (+1) + (-6) = (-5)Because the second arrow (red) drawn stops at (-5) Notice the red arrow (-6) starts where the yellow arrow (+1) stops

8. Subtracting Integers With Tiles This is done by adding zero pairs to the first integer in the subtraction expression Recall that zero pairs do not change the value of an integer Both diagrams represent the integer (+2) Add two zero pairs (+2)

9. Subtracting Integers With Tiles Ex. Evaluate (-2) – (+3) Proceed by changing the subtraction expression into addition (-2) + (-3) (-2) Now add three zero pairs Cont. on next slide

10. Subtracting Integers With Tiles Ex. Evaluate (-2) – (+3) The original subtraction expression indicated that we had to take away (+3) which we can know do as there are 3 yellow tiles which leaves us with 5 red for an answer of (-5) These disappear

11. Rule for Subtracting Integers The rule when we subtract integers is to change the sign to addition and add the opposite integer: Example: -2 – (-5) -2 + 5 = 3 Change sign and add opposite! Find the difference and take sign of largest number!