### New Discoveries, New Student Works!

Check out, and click on, Don's A Map to Calculus™ to see how all the student work and Don's books and videos fit into the scheme of things. He is preparing to make this file into an APP.

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 Don's Calculus materials Calculus For Young People (1 DVD- 3books,2videos,Map,poster) \$70.95 and electronically delivered Calculus By and For Young People (ages 7, yes 7 and up) (CD-ROM) \$23.95 Calculus By and For Young People-Worksheets (CD ROM) \$35.95

Choose one below:

107.See Ratan (7th gr.) & Don get the equation of the inverse of the tower puzzle rule using logs

99.  MarieK shares 8 cookies between 3 people to get a division problem 8 divided by 3 = 8/3 (a fraction) = 2 2/3 (a mixed number)= 2.666... (an infinite repeating decimal) = 2 + 6/10 + 6/100 + 6/1000 +   ... (an infinite series) and you could probably write it other ways! .  You can view the video of Don and Marie doing this on youtube at  https://www.youtube.com/watch?v=j4ZPKndDWs8&feature=plcp.

95. Don writes a program on a scientific calculator to find the area under a curve leading to the integral.

93. See Jonathan's way of finding the volume of a cylinder using calculus, on his blog at http://www.technicalmisery.  com/2011/02/cylinder-fun.html

[N.B. The student is much smarter than the teacher now!]

92. Jack draws a penguin & asks Don to help him make it with graphs of equations!

91. I found a formula to find the area of shapes on a geoboard, then graphed it in 2D and 3D by Irisa, a 6th grader

89. David's Rule Generator (in the process of being sent in to the NCTM for possible publication). It will get a rule for as many pairs of numbers you give him.

88. Don's new page about the hands-on materials, games and puzzles he uses with his students

74. Tara T creates an infinite series that Don hadn't thought of before!

73. See Erin K's work on infinite series +

69. Katy finds the area under a sine wave from 0 to Pi (after Archimedes)

67. Donna, a 4th grader,  graphs a circle, then changes the equation!!!

66. 2 ways to rotate a triangle 90° CW - by Alvaro, Ian & Don

65. Tim finds a new way to write the nth term of an infinite geometric series

64. Devin finds patterns in division

61. Tadeo & Don find the binomial expansion by flipping coins.

59.  Katy's discoveries about INFINITE SERIES

58. Laura and Robert make hard guess my rules, try them

57. Ian, a 4th grader, adds sine waves at right angles to make a bowtie (Lissajous figures)

56. Jesse, a 4th grader, finds a pattern to change a mixed number to an improper fraction

52.  Geoffrey works on polypowers

48. Geoffrey finds the ratios of Fibonacci numbers

47. Geoffrey finds the area under curves and the integral

46.Geoffrey generalizes the infinite series

45. Ross does arithmetic in Binary

44. Noah, age 13, does some things differently!

42. Tessa, at age 5: 1 tangent  x + 1 tangent  x =  2 tangent x  .. plus more!

41. IanM shares 6 cookies between 7 people, in 2 ways!

40. A Visualization of A2 - B2 = (A-B)(A+B)

39. Making a spiral ..by Sara P. and Chris Y. +

37. Geoffrey graphs x = y,  x2 = y,  x3 = y, and  x4 = y from x = -1 to 1 by 0.1's

36. Kevin finds identities for logarithms and graphs y = log10 x

35. Ryan adds .333...+ .999... to get .121212...  !

34. Ian finds Patterns in the ratios and differences of powers of powers, and gets e.

33. Emily, a 7th grader, finds the area and perimeter of the snowflake curve.

32. Mike, a 5th grader, makes The Sieve of Eratosthenes.

31. Kaitlin shares 3 cookies between 5 people- 3 ways.

30. Ana E., a 10th grader, finds patterns in the graphs of  (2 + i)n

29. Jay, a 2nd grader,  graphs x+y=6, x-y=6 and x* y=6

28. Kaitlin, a 4th grader, makes a new "Magic Number Cards" game with 6 cards instead of 5.

27. Jocelin, a 3rd grader,  find patterns in the infinite series

26. Jay, a 2nd grader, multiplies 2 1/2 x 2 1/2 three ways!

25. "A Quest For The Sacred Golden Pineapple, Pine Cone and Artichoke", by Tara Alan

24. Math from bubbles (Don figured out the equation for Joe's diagram!)

23. Olivia shows how she built the 3x3x3 cube with the 7 Soma pieces

22. Anna: " the sum of the angles of a triangle is not always equal to 180° "

21. Geoboard Magic by MaggieP, Patricia and Paul

20. Patterns in Iterating Functions- by Maura

19. Roxana uses a pantograph to enlarge Bugs Bunny (not ready yet)

18. Lizzy and Cheryl on infinite series

17. Can you find a pattern relating the denominator of a fraction with the number of repeated digits in its decimal?

15. Michael creates a snowflake curve in LOGO

14. KaitieR finds a pattern in the Peg Game

13. Paul, a 3rd grader, divides by zero.

12. Abe, a 6th grader, uses the TI 85 to find i1/2 WOW!

11. KatieR's pattern in the partial sums of the infinite series 1/2 + 1/4 + 1/8 + 1/16 ...

5. Don's new discovery about infinite series

2. Genny "doubles the size of the dog"

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