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2. Today, some slides are just for discussion. On other slides, you should practice on your own (by writing on the handout). How can you tell which slides involve writing on the handout? − You will see a little number fly in, like this: − 1). That’s the question number on the handout.

3. We’ll Play “Attack & Defend” with Integer Subtraction “Integers” are whole numbers or negative whole numbers. Integers:Not Integers: -3-3 7 5.0 - 3,249 - 3.5 5.1 - 0.3249 same as 5 7 2 3 List all the integers? {…-3, -2, -1, 0, 1, 2, 3, …} 1).

4. 8 + - 5 =3 Now that we know how to ADD integers, we’re going to learn 10 5 - 5 0 What’s left is 3. Quick Review of Addition: New Topic: … how to SUBTRACT integers. Examples: 8 – 5 5 – 8 8 – - 5 - 8 – - 5 How do you tell them all apart? - 5 – - 8 - 5 – 8 5 – - 8 - 8 – 5 -10 2).

5. a). 4 – 2 = ? Please show how to subtract with your fingers b). 2 – 4 = ? Who can demonstrate? What’s wrong? Discussion 1

6. c). 3 – 9 = ? d). 9 – 3 = ? Please show how to subtract with your fingers

7. 10 5 -10 - 5 0 10 9 – 4 = What’s left is 5. 5 - 10 5 0 -5-5 Start: 9 Pos. Take away 4 Pos. - 9 – - 4 = -5-5 What’s left is - 5. Start: 9 Neg. Take away 4 Neg.

8. 10 5 -10 - 5 0 10 - 6 – - 2 = What’s left is - 4. -4-4 - 10 5 0 -5-5 Start: 6 Neg. 2 Neg. Please draw pictures for these, on your own: - 6 – = can’t do yet Uh-oh. What’s the problem? Start: 6 Neg. Take away 2 Pos. Take away 2 3).

9. Please do each problem, showing a picture: 10 5 - 5 0 2 – 7 = Take away: -10 Start: Oops, not enough to take away. can’t do 2 Pos. 7 Pos. 10 5 - 5 0 7 – 2 = Take away: -10 Start: 7 Pos. 2 Pos. 5 What’s left is 5. 10 5 - 5 0 7 – - 2 = Take away: -10 Start: Oops. We have no negatives to take. can’t do 7 Pos. 2 Neg. 4).

10. Discussion about “taking away” Discussion 2 What’s the problem we sometimes have with “taking away?

11. 10 5 -10 - 5 0 11 – 3 =8 To take away 3 positives… 10 11 – 3 = What’s left is 8. 8 - 10 5 0 -5-5 Start with 11 Pos. Take away 3 Pos. How can you get rid of 3 Pos without “taking away”? What’s left is 8. Your ideas? add 3 negatives we’ll add 3 negatives

12. 4 – 12 How do you take away 12 Pos? a). 3 – - 2 How do you take away 2 Neg? b). To “take away” something, we’ll cancel it out 3 + - 2 You are NOT supposed to take away 2 Neg here. What are you supposed to do? Why? c). You add 12 Neg. You add 2 Pos. You’re supposed to ADD 2 Neg, because it has a “+” sign. 5).

13. Please try on your own. To “take away” something, cancel it out. 10 5 - 5 0 8 – 6 =2 Take away 6 Pos. What’s left is 2. -10 Start 8 Pos. 10 5 - 5 0 - 4 – - 3 = -1 Take away 3 Neg. What’s left is - 1. -10 Start: 4 Neg. 6).

14. Let’s practice just drawing the picture for each problem: 10 5 - 5 0 3 – 8 = Take away: 8 Pos. -10 10 5 - 5 0 3 – - 8 = Take away: 8 Neg. -10 10 5 - 5 0 3 + - 8 = Add: 8 Neg. -10 Start: 3 Pos. Start: 3 Pos. Start: 3 Pos. by adding 8 Neg. by adding 8 Pos. 7).

15. The biggest mistake people make is… Forgetting the difference between ADDING and SUBTRACTING. Let’s practice that skill. 8).

16. What’s the difference between the two questions below? 5 - 5 0 - 5 – 2 = b). Can you explain this? 5 - 5 0 - 5 + 2 = a). Let’s try to solve the questions using pictures. Start: 5 Neg. Start: 5 Neg. - 7 - 3 Please explain the steps in this example.9). c). Why do this? d). Why do we do this?

17. 5 - 5 0 - 1 + - 4 = Add : 4 Neg. 5 - 5 0 - 1 – - 4 = Take away : 4 Neg. a). b). Please do these questions on your own. Start: 1 Neg. Start: 5 Neg. - 5 3 10).

18. Example: Study this to help with #11. 5 - 5 0 _______ = 10 - 10 5 - 5 0 _______ = b). 10 - 10 Start with 4 Neg Take away – - 4 -6-6 -5-5 - 9 Start with 4 Pos. Add + 4 Practice: Try this on your own. 11). What question goes with this picture? - 9

19. Is this picture shown correctly? 5 - 5 0 8 + - 5 = What do you think? 10 - 10 5 - 5 0 8 + - 5 = 10 - 10 Wrong Right: Add: 5 Neg. Example:

20. Practice: Is this picture correct? 5 - 5 0 - 2 – 10 = a). 10 - 10 Right Take away: 10 Pos. Example: Is this picture correct? 5 - 5 0 - 2 + 10 = a). 10 - 10 Right Add: 10 Pos. 12). What do you think?

21. Drill Practice

22. Practice: Draw each picture and find each answer. 10 5 - 5 0 - 1 – - 9 = Take away: 9 Neg. -10 10 5 - 5 0 3 + - 6 = Add: 6 Neg. -10 10 5 - 5 0 3 – - 6 = Take away: 6 Neg. -10 Start: 1 Neg. Start: 3 Pos. Start: 3 Pos. 8 - 3 9 13).

23. 10 5 - 5 0 5 – 7 = Take away: 7 Pos. -10 10 5 - 5 0 7 – 5 = Take away : 5 Pos. -10 10 5 - 5 0 - 4 + - 6 = Add: 6 Neg. -10 Start: 5 Pos. Start: 7 Pos. Start: 4 Neg. - 2 2 - 10 Practice: Draw each picture and find each answer. 14).

24. The game of Attack & Defend with subtraction

25. How to play Attack & Defend with subtraction t + - 2 Cards look like this: t = your total points right now. Shows how this card will add or take away chips. 5 - 5 0 How to Track Your Chips: Chips you already have New chips from this card

26. 5 - 5 0 Practice: You have 5 chips right now. You get this card: t + -2t + -2 Chips you already have New chips from this card 5 -2-2Add 15).

27. 5 - 5 0 This person started the round with ____ chips. The card said -3-3 Add 1 Pos. t + 1 Example:

28. 10 5 - 5 0 -10 t – - 3 Take away 3 Neg. By adding 3 Pos. BEFORE this card, you had ___ chip(s). The card you get is: -2-2 AFTER this card, you have ___ chip(s). 1 16).

29. 10 5 - 5 0 -10 t – 4 Cancel out 4 Pos. By adding 4 Neg. Before this card, you had ___ chip(s). The card you get is: 1 After this card, you have _____ chip(s). 1 -3-3 17).

30. 10 5 - 5 0 -10 t + - 4 Add 4 Neg. Before this card, you had _____ chip(s). The card you get is: -3-3 After this card, you have _____ chip(s). -3-3 -7-7 = 18).