张宝幼与您分享

2. 透過悅趣活動發展 數學解題能力 张宝幼与您分享

3. Prof. Vincent J. Matsko http://staff.imsa.edu/~vmatsko/

4. 分配蛋糕 (a) 如何把七个蛋糕公平地分配给十位同学？每位同学将获得两片蛋糕。

5. 分配蛋糕 提示: 如何把上图所显示的七个蛋糕公平地分配给十位同学？每位同学将获得两片不同的蛋糕。

6. 分配蛋糕

7. 分配蛋糕 (b) 如何把七个蛋糕公平地分配给十二位同学？每位同学将获得两片蛋糕。

8. 分配蛋糕 (b) Or ------------------------------------------------------------

9. 5 • - 1,4 • 2,3 • LCM for 1, 4, 2, 3 = 12 2 answers (c) How can you divide the 5 cakes among 12 students equally (fairly) where each student gets two pieces of cake?

10. (c) How can you divide the 5 cakes among 12 students equally (fairly) where each student gets two pieces of cake? Or ------------------------------------------------------------

11. 1 answer • 5 • 2,3 • LCM=6 • 5 cakes divide among 6 students each one gets 2 pieces • 2x3 • 3x2

12. No answer • 5 • 2,3 (LCM=6) • 1,4 (LCM=4) • 1,2,3,4 (LCM=12) • 5 cakes divide among 7 students each one gets 2 pieces

13. 跳出 思想框框

14. 跳出 思想框框 Prof. HartwigMeissner, Germany

15. 跳出 思想框框 A B Prof. Hartwig Meissner, Germany

16. Learning vs Unlearning Learning makes us smart and proud, Unlearning makes us wise and humble. Charlie “Tremendous” Jones

17. “The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.” - Alvin Toffler -

18. 学生的看法可能与我们不一样 Prof. HartwigMeissner, Germany

19. 48x63= 48 x 63 144 2 4 288 1 1 3024 Show Your Working

20. Dice Construction Top View Side View Front View The diagram above shows a model constructed using 4 dice with its top view, front view and side view.

21. L2b Dice Construction Diagrams below show the front view and side view of a model constructed using some dice. Based on these views, can you construct this model using the least number of dice? Draw the top view of your answer. Front view Side view Reference: Prof. Hartwig

22. L2b answer Dice Construction

23. L2b answer 2 2 2 2 2 2 2 2 Dice Construction Answers:

24. Important Mathematical Thinking Skills Reasoning from Evidence Jim Ridgway - organize unsorted data and draw conclusions

25. L9a The Last Special Card “Kruskal Count” Special cards 1 2 First secret number = 3 3 1 2 3 4 1 The Last Special card

26. How to Increase the Chances of Wining? 1-6 Average advance = (1+2+3+4+5+6)/6 = 21/6 = 3.5 Average Steps taken = 24/3.5 = 6.857, about 7 steps The density of the victim’s cards is 1/3.5 = 0.286, so there’s a 1 − 0.286 = 0.714 chance of a miss. But you have to miss all 7 times,and this will occur about (0.714)7 = 0.0945 so you’ll win about 0.905 of the time.

27. How to Increase the Chances of Wining? 1-5 Average advance = (1+2+3+4+5)/5 = 15/5 = 3 Average Steps taken = 24/3 = 8, 8 steps The density of the victim’s cards is 1/3 = 0.333, so there’s a 1 − 0.333 = 0.667 chance of a miss. But you have to miss all 8 times,and this will occur about (0.667)8 = 0.0392 so you’ll win about 0.961 of the time.

28. How to Increase the Chances of Wining? 1-3 Average advance = (1+2+3)/3 = 6/3 = 2 Average Steps taken = 24/2 = 12, 12 steps The density of the victim’s cards is 1/2 = 0.5, so there’s a 1 − 0.5 = 0.5 chance of a miss. But you have to miss all 12 times,and this will occur about (0.5)12 = 0.00024 so you’ll win about 0.9998 of the time.

29. L9a [P. 1-2] Twinkle, Twinkle, Little Star Twinkle, twinkle, little star, How I wonder what you are. Up above the world so high, Like a diamond in the sky. When the blazing sun is gone, When he nothing shines upon, Then you show your little light, Twinkle, twinkle, all the night. Then the traveller in the dark, Thanks you for your tiny spark, He could not see which way to go, If you did not twinkle so.

30. Weighing Cards This is a very impressive trick where the Magician can predict the number of cards selected by the spectator by just weighing the card in his palm.

31. L11a Weighing Cards … …

32. Weighing Cards • How does the trick work? • If the Magician sees a red card on top of the faced up stack, he takes the number (x) multiply by 2 and then plus 2. • Number of cards = 2x + 2 • If the Magician sees a blue card, he takes the number multiply by 2 and then subtract the result from 29. • Number of cards = 29 – 2x • Number of cards = 30 - (2x+2 – 1) • = 30 – (2x + 1) • = 29 – 2x

33. L11a [P1-2] Weighing Cards • Variation for P1-2: No need to add the yellow cards. • Calculation for P1-2: • If the Magician sees a red card on top of the faced stack, he doubles the number (x) • Number of cards = x + x • If the Magician sees a blue card, he slides the top card down a bit to take a look at the next red card. He doubles the number on the red card (y) then plus one. • Number of cards = y+y+1

34. Ann's Tower One of Ann’s Christmas presents was a box of building bricks. The bricks were all cubes with an edge of 5cm and completely filled the box which was also in the shape of a cube. Like many young children, Ann was fascinated with building towers. She started by building a large cube, then a smaller cube on top of that and a yet smaller cube on top of the latter. When the three cubes were complete she could still look over the top of her tower when standing, which disappointed her, but she had the satisfaction that she had used every single brick in her construction. How high was the tower? [Bolt, (1989) p. 14]

35. a3 + b3 + c3 = d3 27 + 64 + 125 = 216 33 + 43 + 53 = 63 The height of the tower = 5(3+4+5)cm = 60cm Make a table/list

36. 马来西亚新加坡 通过数学提升创意的方法 • 魔术 • 趣题 • 手工 • 历史 • 游戏 • 项目

37. pp. 58-60 魔法卡片

41. 如何解?

42. 0 1 0 1 4 2 1 8

43. 1 1 1 0 4 2 1 8

44. ?

45. ? 0 1 1 1 4 2 1 8

46. 20 要是有些卡片的号码更大呢？

47. 1 0 1 1 0 4 2 1 8 16

48. 1 2 0 Variation 2 1 x 9 2 x 1 0 x 3

49. 马来西亚新加坡 通过数学提升创意的方法 • 魔术 • 趣题 • 手工 • 历史 • 游戏 • 项目

50. L5a Calendar Game The table below shows a list of 12 months in a year and 31 days in a month. Two players take turns to circle either a month or a date in ascending order. The first person to arrive at December 31st is the winner.