1. Licensing information Users should treat this material as a working draft. This material can be redistributed, 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/).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/http://about.ck12.org/

2. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). Please fill in this column on your own. What did you notice?

3. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 Here are my answers. 8 16 10 5 5 + 3 = 8 2 = 16 – 6 = 10 2 =

4. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 This shows that the trick works when you start with 5. But how can we know if it will work for ANY number? 8 16 10 5 5 + 3 = 8 2 = 16 – 6 = 10 2 =

5. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 This represents x. x

6. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 It could be any length. x …because x is a variable.

7. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 It could be any length. 5

8. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 It could be any length. 7

9. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 It could be any length… 10

10. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 It could be any length… 11

11. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 x111 x

12. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5

13. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5

14. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5

15. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 Original number Final picture:

16. 2). Instructions Current Value Algebra Tiles Pick any number. a). Now add 3.b). Multiply that answer by 2. c). Subtract 6 from that answer. d). Divide that answer by 2. e). 5 8 16 10 5 We proved that it works when you start with ANY number. Final picture:

17. Do I need slides for the number trick with pictures shown in packet?

18. 4).Please write down these expressions and then draw each picture. a).b).c). 4 + 24 – 2 3 2 or

19. Just watch these examples to help you with the next questions on the sheet. Examples: Ex. 1Ex. 2Ex. 3 8x 3(x+1) 4 2 x 2 x1 8 4 = 2 3(x+1)

20. 4).Please write down these expressions and then draw each picture. d).e).f). 4x x + 4 6 2 g).h).i). 4x + 2 4(x+2) x 3 Why are these different?

21. What would be the difference between the pictures of 5(x + 3) and 5x + 3 ? Discuss this Example 5(x + 3)5x + 3 Your prediction?Why?

22. 4).Please write down these expressions and then draw each picture. j).k). 4x + 6 2 4x 2 + 6 Draw “4x + 6” first. Now divide by 2.

23. 4).Please write down these expressions and then draw each picture. j).k). 4x + 6 2 4x 2 + 6 Why keep all 6 squares here? Why NOT keep all 6 squares here?