New Discoveries, New Student Works!
Don's Calculus materials

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111. Barbara ~35 years ago, learned postman stories, now in 2011-12 teaches her 2 daughters how to multiply signed numbers

110. See Sara, 7th grader, solve a word problem with ratios

109. See Maya, 7th grader, make up identities for Logs

108.See Marina (a 7th grader), change an infinite repeating decimal to a fraction, using infinite series!

107.See Ratan (finished 7th gr.) gets the equation of the inverse of the peg game rule

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

105. See Julia's work when asked to make up an equation with NO answer +..

104. See these Guess My Rules made for Don- by Sara, Maya and Jack

103. Theo, age 9, makes up a guess my rule for Don-Watch this!

102. Don, Shaleen, & Lori rotate a sine wave 60o ccw.

101. Zachary's math summer of 2012.

100 Don and Shouri and Grant work on Rumanujan's infinite nesting of square roots.

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

98. Brenda finds lots about the regular pentagon.

97. Ashley, Cody, and Noah find the infinite repeating decimal equal to a fraction and display 3 cycles of it with needlepoint.

96.Don and his students study Ramanujan's Nest of Square Roots Given a number

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

94.Sara finds the area of a triangle

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

90. Jonty (autistic) and George work with Don

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

87. Anna L., a 4th grader, does some fine mathematics

86. Van, 4th grader, graphs in 3D

85. Jack invents new ways of looking at mathematics

84. While iterating a function, Laura, a 4th grader, divides 7.75 by 2- WOW!

83.  And Anushka, age 6, knew neither division nor graphs !

82.  Shaleen moves a parabola and gets something different.

81.  A conversation between Maya, 8 years old, Don, a TI-84 plus calculator, and WolframAlpha, to find the sum of  2 1/2 + 4 1/4,

80. Don and his students Jay, Chris, and Elizabeth find a new number-the Dottie Number

79. Ann-Emily, 2nd grader, adds fractions using complex fractions and multiplies mixed numbers-WOW!

78. Erin's diagrams of the 15-3x3x3 cubes she made with the 7 Soma pieces

77. Sara, and Maya, 7 yo twins, find Patterns in division

76. Alex, a 2nd grader, sees an infinite series!!

75. Margaret asks a great question!

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

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

72. Nanako changes a graph but keeps the equation the same, HOW?!

71. Jamie solves a quadratic equation by iteration

70. Geometric sequences and the 88 keys on a piano by Don

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

68. Shelby and Katy find the equation for mailing a letter.

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

63. Number names for today's date/number

62. Michael, a 5th grader, finds a pattern in infinite series

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

60. Don compares the spirals in the Natilus shell, the Fibonacci numbers, and The Equal Tempered Chromatic Music Scale

59.  Katy's discoveries about INFINITE SERIES

59. Maha's new method for dividing decimals

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

55. Tessa, 6 years old, solves equations and subtracts with negative numbers

54. Chris, an 8th grader, uses negative numbers in his work on iterating a function

53. Daly, a 3rd grader, works on percent, to fractions to decimals

52.  Geoffrey works on polypowers

51. Don's work on polypowers

50. Justin, a 10 grader, studies reflections with matrices

49. Lizzie and Don find the sum of the exterior angles of a concave polygon

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!

43.  Sheri, Math Girl, going into 5th grade, always doing new things!

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 Sara P. and Chris Y. +

38. Emily writes 642/3 , 25 ways

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?

16. Abe finds a theory to explain tessellations

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 ...

10. Maggie builds a box..and does some algebra

9. Mr. Matsumoto's method of using iteration to find square roots

8. Michael & Christie's finding the angle formed by 2 chords intersecting inside a circle, not at the center.

7. Andy's (a 9th grader) routine to find any polynomial equation given the roots!

6. Thomas, an 8th grader, wrote this program on the TI82 which gives the derivative of a monomial.

5. Don's new discovery about infinite series

4. Abe, a 12 year old, finds a pattern in an infinite sequence. He was iterating -16/x + 8, obtained in the process of solving the equation x^2-8x+16=0

3. Eva shares 5 cookies between 3 people- another new way! And Betty, a 5th grade teacher, asks a great question!!

2. Genny "doubles the size of the dog"

1. Paul, a 3rd grader, finds a pattern in finding the sum of the angles of a polygon.

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