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1. Licensing information • Users should treat this material as a working draft. This material can be used in its current form, customized, and/or printed or displayed by the user. • The author(s) request feedback on all materials so that they can be continually improved and updated. • This material is licensed under the Creative Commons Attribution-Share Alike license: (http://creativecommons.org/licenses/by-sa/3.0/). • Author: Kevin Hall Wording for the legal statement above is adapted from the legal statement for Trigonometry, published in 2009 by The CK-12 Foundation: http://about.ck12.org/

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 1). Integers:Not Integers: • “Integers” are whole numbers or negative whole numbers. -3 -3.5 2 7 3 7 -0.3249 -3,249 same as 5 5.0 List all the integers? 5.1 {…-3, -2, -1, 0, 1, 2, 3, …}

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

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

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

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

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

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

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

11. 8 11 – 3 = 11 – 3 = 8 Start with To take away 3 positives… 11 Pos. How can you get rid of 3 Pos without “taking away”? 10 10 What’s left is 8. What’s left is 8. 5 5 Take away 3 Pos. 0 0 we’ll add3 negatives Your ideas? - 5 -5 -10 -10

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

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

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

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

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

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

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

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

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

21. Drill Practice

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

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

24. The game of Attack & Defendwith subtraction

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

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

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

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

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

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