1. Warm-up Make the Connection Powerpoint Inverse Operations Guided Practice Directions Please! Models and Pictorials

2. Make the Connection (Warm Up) The chip board below shows a value of +5. There are two possible moves, one addition and one subtraction that would change the value on the board to +2 in one step. Complete the number sentences to represent each move? +5 + ___ = +2 and +5 – ___ = +2 -3 +3

3. Inverse Operations What is the opposite of addition? Subtraction How can we use addition and what we know about opposites to rename a subtraction problem. Give an example in your explanation. Possible answer: Because addition and subtraction are inverse operations and positive integers are the opposite of negative integers, I can rename an addition problem as a subtraction problem. +6 – (-5) is the same as +6 + (+5)

4. Inverse Operations Because addition and subtraction are Inverse operations you can view a subtraction problem as “adding the opposite”. Example: -10 – (+4) = Add the opposite: -10 + (-4) = -14 Is this example correct? Justify your answer. The example is correct. To justify, student might show a number line or chips.

5. Inverse Operations Write addition sentences that are equivalent to the following subtraction sentences and then solve. +18 – (-14) = -30 – (-30) = -54 – (+27)= +18 + (+14) = +32 -30 + (+30) = 0 -54 + -27 = -81

6. Inverse Operations We can use the concept of inverse operations and opposites to better help us understand subtraction of integers on the number line. Solve the following using a number line. Justify your answer. -3 – (-3) = Accept justification responses from several students. 0 1 2 3 4 5 -5 -4 -3 -2 -1 -3 – = 0 (-3)

7. Inverse Operations Let’s look at that again. 0 1 2 3 4 5 -5 -4 -3 -2 -1 -3 – = 0 (-3) Why did the arrow change directions? The minus sign makes the arrow go to the left. But when we subtract a negative number it is like adding the opposite so the arrow changes to the right. The same as -3 + (+3) = 0

8. Inverse Operations Let’s try another problem using the number line. 4 – (-1) = 0 1 2 3 4 5 -5 -4 -3 -2 -1 4 – = 5 (-1)

9. Inverse Operations Predict what the answer to this problem will be. 2 – 7 = (Allow students time to predict) Then solve using the number line. Was your prediction correct? 0 1 2 3 4 5 -5 -4 -3 -2 -1 2 – = -5 7 Why didn’t the arrow change in this problem? The direction of the arrow only changes when subtracting a negative. Accept student responses.

10. Inverse Operations Predict whether or not the arrow will change on this problem, then solve. 3 – 4 = Was your prediction correct? 0 1 2 3 4 5 -5 -4 -3 -2 -1 3 – = -1 4 Accept student responses.

11. Inverse Operations With your partner, construct an algorithm for subtracting integers. Be prepared to share with the class. Possible answer: To subtract integers add the opposite.

12. Direction Please! (Guided Practice) Solve the following using the number line. 1.-8 – 2 = 2.-6 – (-3) = 3.12 – 15 = Complete the number sentence. 4.+8 – (-5) = +8 + ___ 5.-4 – 6 = -4 + ___ 6.+396 – (-400) = +396 + ____ -10 -3 +5 -6 +400