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Difference Numbers, Squares, Lines & Dots Number Model

Difference Numbers, Squares, Lines & Dots Number Model
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2017-05-23 02:53
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① This GeoGebra example presents an interactive number model that visualizes the relationship between difference numbers, squares, lines, and dots, allowing users to manipulate buttons and text fields to observe numerical changes. ② Core mathematical concepts include natural numbers, subtraction, square numbers, real numbers, and the geometric representation of arithmetic relations through points, segments, polygons, and ellipses, incorporating sequence and statistical interval ideas. ③ Construction highlights: Sequence generates lists, Point and Random create random points, RotateText rotates labels, Ellipse, Polygon, and Segment draw geometric shapes, while Textfield and button1 enable input; objects include list24, list25, points A, B, E, F, I, J, M, N, Q, R, and digit placeholders rhund, rten, rone for hundreds, tens, and ones, with text1–text6 providing explanations. ④ Suitable for upper elementary to middle school students learning number and algebra, and for teachers demonstrating numerical patterns and geometric modeling to make abstract arithmetic concepts visually intuitive.

GeoGebra Commands & Parameters

  1. Sequence((i, 23), i, 70, 88, 2) → list24
  2. Point(list24) → A
  3. Point(list24) → B
  4. Point(list24) → E
  5. Point(list24) → F
  6. Point(list24) → I
  7. Point(list24) → J
  8. Point(list24) → M
  9. Point(list24) → N
  10. Point(list24) → Q
  11. Point(list24) → R
  12. Sequence((i, 27), i, 70, 88, 2) → list25
  13. Point(list25) → U
  14. Point(list25) → V
  15. Point(list25) → A_1
  16. Point(list25) → B_1
  17. Point(list25) → E_1
  18. Point(list25) → F_1
  19. Point(list25) → I_1
  20. Point(list25) → J_1
  21. Point(list25) → M_1
  22. Point(list25) → N_1
  23. Point(list25) → Q_1
  24. Point(list25) → R_1
  25. Point(list24) → U_1
  26. Point(list24) → V_1
  27. Random(1, 9) → rhund
  28. Random(0, 9) → rten
  29. Random(0, 9) → rone
  30. RotateText(text4, 45°) → text10
  31. RotateText(text5, 45°) → text11
  32. RotateText(text6, 45°) → text12
  33. Ellipse(A_2, B_2, C_2) → c_2
  34. Polygon(D_2, E_2, F_2, G_2) → poly13, d_2, e_2, f_3, g_3
  35. Point(g_3) → H_2
  36. Point(e_2) → I_2
  37. Segment(H_2, I_2) → q_2
  38. Textfield(YourGuess) → InputBox1
  39. RotateText(text17, 45°) → text18
  40. Point(list25) → C
  41. Point(list25) → D
  42. Polygon(C, D, 4) → poly1, f, g, h, i, G, H
  43. Point(list25) → K
  44. Point(list25) → L
  45. Polygon(K, L, 4) → poly2, j, k, l, m, O, P
  46. Point(list25) → S
  47. Point(list25) → T
  48. Polygon(T, S, 4) → poly3, n, p, q, r, W, Z
  49. Point(list25) → C_1
  50. Point(list25) → D_1
  51. Polygon(D_1, C_1, 4) → poly4, s, t, a, b, G_1, H_1
  52. Point(list25) → K_1
  53. Point(list25) → L_1
  54. Polygon(K_1, L_1, 4) → poly5, c, d, e, f_1, O_1, P_1
  55. Point(list24) → S_1
  56. Point(list24) → T_1
  57. Polygon(T_1, S_1, 4) → poly6, g_1, h_1, i_1, j_1, W_1, Z_1
  58. Point(list24) → J_2
  59. Point(list24) → K_2
  60. Polygon(J_2, K_2, 4) → poly7, k_1, l_1, m_1, n_1, L_2, M_2
  61. Point(list24) → N_2
  62. Point(list24) → O_2
  63. Polygon(N_2, O_2, 4) → poly8, p_1, q_1, r_1, s_1, P_2, Q_2
  64. Point(list24) → R_2
  65. Point(list24) → S_2
  66. Polygon(R_2, S_2, 4) → poly9, t_1, a_1, b_1, c_1, T_2, U_2
  67. Point(list24) → V_2
  68. Point(list24) → W_2
  69. Polygon(V_2, W_2, 4) → poly10, d_1, e_1, f_2, g_2, Z_2, A_3
  70. Sequence(Polygon[(68, i), (68, i + 1), 4], i, 22, 31) → list15
  71. Sequence(Polygon[(68, i), (68, i + 1), 4], i, 11, 20) → list19
  72. Sequence(Polygon[(68, i), (68, i + 1), 4], i, 0, 9) → list14
  73. Sequence(Polygon[(66, i), (66, i + 1), 4], i, 0, 9) → list13
  74. Sequence(Polygon[(66, i), (66, i + 1), 4], i, 11, 20) → list20
  75. Sequence(Polygon[(66, i), (66, i + 1), 4], i, 22, 31) → list17
  76. Sequence(Polygon[(64, i), (64, i + 1), 4], i, 22, 31) → list18
  77. Sequence(Polygon[(64, i), (64, i + 1), 4], i, 11, 20) → list21
  78. Sequence(Polygon[(64, i), (64, i + 1), 4], i, 0, 9) → list12
  79. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 53, 62) → list11
  80. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 53, 62) → list8
  81. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 53, 62) → list6
  82. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 42, 51) → list10
  83. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 42, 51) → list4
  84. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 42, 51) → list5
  85. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 31, 40) → list1
  86. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 31, 40) → list2
  87. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 31, 40) → list3
  88. Sequence(Sequence[Polygon[(i, j), (i + 4, j), 4], i, 69, 87, 4], j, 22, 26, 4) → list23