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Fraction Strip Addition Demo

Fraction Strip Addition Demo
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2017-06-16 16:12
Geometric ConstructionSlider AnimationGraphing
This example demonstrates the addition of two fractions using horizontal rectangular area models (fraction strips). It involves core math concepts like fraction addition, fraction modeling, and geometric representation. The construction utilizes GeoGebra commands such as FractionText, Polygon, Sequence, Segment, and objects like a, b, c, d, FractionSimplified, FracStripAB1Whole, etc. It is suitable for middle school mathematics teaching to visually understand fraction addition operations.

GeoGebra Commands & Parameters

  1. FractionText((a * d + c * b) / (b * d)) → FractionSimplified
  2. Polygon((0, 8.1), (4, 8.1), (4, 8.9), (0, 8.9)) → FracStripAB1Whole, h, i, j, k
  3. Polygon((6, 8.1), (10, 8.1), (10, 8.9), (6, 8.9)) → FracStripAB2Whole, p, q, r, s
  4. Polygon((0, 8.1), (If[a / b < 1, 4 * a / b, 4], 8.1), (If[a / b < 1, 4 * a / b, 4], 8.9), (0, 8.9)) → FracStripAB1Part, e, l, m, n
  5. Polygon((0, 7.1), (4, 7.1), (4, 7.9), (0, 7.9)) → FracStripAB3Whole, c_1, d_1, e_1, f_1
  6. Polygon((6, 8.1), (If[a / b < 2, 6 + 4 * (a / b - 1), 10], 8.1), (If[a / b < 2, 6 + 4 * (a / b - 1), 10], 8.9), (6, 8.9)) → FracStripAB2Part, g, t, a_1, b_1
  7. Polygon((0, 7.1), (If[a / b < 3, 4 * (a / b - 2), 4], 7.1), (If[a / b < 3, 4 * (a / b - 2), 4], 7.9), (0, 7.9)) → FracStripAB3Part, g_1, h_1, i_1, j_1
  8. Polygon((6, 7.1), (10, 7.1), (10, 7.9), (6, 7.9)) → FracStripAB4Whole, k_1, l_1, m_1, n_1
  9. Polygon((6, 7.1), (If[a / b < 4, 6 + 4 * (a / b - 3), 10], 7.1), (If[a / b < 4, 6 + 4 * (a / b - 3), 10], 7.9), (6, 7.9)) → FracStripAB4Part, p_1, q_1, r_1, s_1
  10. Polygon((0, 6.1), (4, 6.1), (4, 6.9), (0, 6.9)) → FracStripAB5Whole, t_1, a_2, b_2, c_2
  11. Polygon((0, 6.1), (If[a / b < 5, 4 * (a / b - 4), 4], 6.1), (If[a / b < 5, 4 * (a / b - 4), 4], 6.9), (0, 6.9)) → FracStripAB5Part, d_2, e_2, f_2, g_2
  12. Polygon((6, 4.1), (10, 4.1), (10, 4.9), (6, 4.9)) → FracStripAB10Whole, l_2, m_2, n_2, p_2
  13. Polygon((0, 5.1), (4, 5.1), (4, 5.9), (0, 5.9)) → FracStripAB7Whole, h_2, i_2, j_2, k_2
  14. Polygon((6, 5.1), (10, 5.1), (10, 5.9), (6, 5.9)) → FracStripAB8Whole, q_2, r_2, s_2, t_2
  15. Polygon((6, 6.1), (10, 6.1), (10, 6.9), (6, 6.9)) → FracStripAB6Whole, a_3, b_3, c_3, d_3
  16. Polygon((0, 4.1), (4, 4.1), (4, 4.9), (0, 4.9)) → FracStripAB9Whole, e_3, f_3, g_3, h_3
  17. Polygon((0, 5.1), (If[a / b < 7, 4 * (a / b - 6), 4], 5.1), (If[a / b < 7, 4 * (a / b - 6), 4], 5.9), (0, 5.9)) → FracStripAB7Part, i_3, j_3, k_3, l_3
  18. Polygon((6, 6.1), (If[a / b < 6, 6 + 4 * (a / b - 5), 10], 6.1), (If[a / b < 6, 6 + 4 * (a / b - 5), 10], 6.9), (6, 6.9)) → FracStripAB6Part, m_3, n_3, p_3, q_3
  19. Polygon((6, 5.1), (10, 5.1), (10, 5.9), (6, 5.9)) → FracStripAB8Part, r_3, s_3, t_3, a_4
  20. Polygon((0, 4.1), (4, 4.1), (4, 4.9), (0, 4.9)) → FracStripAB9Part, b_4, c_4, d_4, e_4
  21. Polygon((6, 4.1), (10, 4.1), (10, 4.9), (6, 4.9)) → FracStripAB10Part, f_4, g_4, h_4, i_4
  22. Polygon((0, 3.1), (If[c / d < 1, 4 * c / d, 4], 3.1), (If[c / d < 1, 4 * c / d, 4], 3.9), (0, 3.9)) → FracStripCD1Part, j_4, k_4, l_4, m_4
  23. Polygon((0, 3.1), (4, 3.1), (4, 3.9), (0, 3.9)) → FracStripCD1Whole, n_4, p_4, q_4, r_4
  24. Polygon((6, 3.1), (10, 3.1), (10, 3.9), (6, 3.9)) → FracStripCD2Whole, s_4, t_4, a_5, b_5
  25. Polygon((6, 3.1), (If[c / d < 2, 6 + 4 * (c / d - 1), 10], 3.1), (If[c / d < 2, 6 + 4 * (c / d - 1), 10], 3.9), (6, 3.9)) → FracStripCD2Part, c_5, d_5, e_5, f_5
  26. Polygon((0, 2.1), (4, 2.1), (4, 2.9), (0, 2.9)) → FracStripCD3Whole, g_5, h_5, i_5, j_5
  27. Polygon((6, 2.1), (10, 2.1), (10, 2.9), (6, 2.9)) → FracStripCD4Whole, k_5, l_5, m_5, n_5
  28. Polygon((0, 1.1), (4, 1.1), (4, 1.9), (0, 1.9)) → FracStripCD5Whole, p_5, q_5, r_5, s_5
  29. Polygon((6, 1.1), (10, 1.1), (10, 1.9), (6, 1.9)) → FracStripCD6Whole, t_5, a_6, b_6, c_6
  30. Polygon((0, 0.1), (4, 0.1), (4, 0.9), (0, 0.9)) → FracStripCD7Whole, d_6, e_6, f_6, g_6
  31. Polygon((6, -0.1), (10, -0.1), (10, -0.9), (6, -0.9)) → FracStripCD10Whole, h_6, i_6, j_6, k_6
  32. Polygon((6, 0.1), (10, 0.1), (10, 0.9), (6, 0.9)) → FracStripCD8Whole, l_6, m_6, n_6, p_6
  33. Polygon((0, -0.1), (4, -0.1), (4, -0.9), (0, -0.9)) → FracStripCD9Whole, q_6, r_6, s_6, t_6
  34. Polygon((0, 2.1), (If[c / d < 3, 4 * (c / d - 2), 4], 2.1), (If[c / d < 3, 4 * (c / d - 2), 4], 2.9), (0, 2.9)) → FracStripCD3Part, a_7, b_7, c_7, d_7
  35. Polygon((6, 2.1), (If[c / d < 4, 6 + 4 * (c / d - 3), 10], 2.1), (If[c / d < 4, 6 + 4 * (c / d - 3), 10], 2.9), (6, 2.9)) → FracStripCD4Part, e_7, f_7, g_7, h_7
  36. Polygon((6, 1.1), (10, 1.1), (10, 1.9), (6, 1.9)) → FracStripCD6Part, m_7, n_7, p_7, q_7
  37. Polygon((0, 1.1), (If[c / d < 5, 4 * (c / d - 4), 4], 1.1), (If[c / d < 5, 4 * (c / d - 4), 4], 1.9), (0, 1.9)) → FracStripCD5Part, i_7, j_7, k_7, l_7
  38. Polygon((0, 0.1), (4, 0.1), (4, 0.9), (0, 0.9)) → FracStripCD7Part, r_7, s_7, t_7, a_8
  39. Polygon((6, 0.1), (10, 0.1), (10, 0.9), (6, 0.9)) → FracStripCD8Part, b_8, c_8, d_8, e_8
  40. Polygon((0, -0.1), (4, -0.1), (4, -0.9), (0, -0.9)) → FracStripCD9Part, f_8, g_8, h_8, i_8
  41. Polygon((6, -0.1), (10, -0.1), (10, -0.9), (6, -0.9)) → FracStripCD10Part, j_8, k_8, l_8, m_8
  42. Sequence(Segment[(4 / If[cp, parts, b] * i, 8.1), (4 / If[cp, parts, b] * i, 8.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB1Partitions
  43. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 8.1), (6 + 4 / If[cp, parts, b] * i, 8.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB2Partitions
  44. Sequence(Segment[(4 / If[cp, parts, b] * i, 7.1), (4 / If[cp, parts, b] * i, 7.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB3Partitions
  45. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 7.1), (6 + 4 / If[cp, parts, b] * i, 7.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB4Partitions
  46. Sequence(Segment[(4 / If[cp, parts, b] * i, 6.1), (4 / If[cp, parts, b] * i, 6.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB5Partitions
  47. Sequence(Segment[(4 / If[cp, parts, d] * i, 3.1), (4 / If[cp, parts, d] * i, 3.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD1Partitions
  48. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 3.1), (6 + 4 / If[cp, parts, d] * i, 3.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD2Partitions
  49. Sequence(Segment[(4 / If[cp, parts, d] * i, 2.1), (4 / If[cp, parts, d] * i, 2.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD3Partitions
  50. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 2.1), (6 + 4 / If[cp, parts, d] * i, 2.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD4Partitions
  51. Sequence(Segment[(4 / If[cp, parts, d] * i, 1.1), (4 / If[cp, parts, d] * i, 1.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD5Partitions
  52. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 6.1), (6 + 4 / If[cp, parts, b] * i, 6.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB6Partitions
  53. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 5.1), (6 + 4 / If[cp, parts, b] * i, 5.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB8Partitions
  54. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 4.1), (6 + 4 / If[cp, parts, b] * i, 4.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB10Partitions
  55. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 1.1), (6 + 4 / If[cp, parts, d] * i, 1.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD6Partitions
  56. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 0.1), (6 + 4 / If[cp, parts, d] * i, 0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD8Partitions
  57. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, -0.1), (6 + 4 / If[cp, parts, d] * i, -0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD10Partitions
  58. Sequence(Segment[(4 / If[cp, parts, d] * i, 0.1), (4 / If[cp, parts, d] * i, 0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD7Partitions
  59. Sequence(Segment[(4 / If[cp, parts, d] * i, -0.1), (4 / If[cp, parts, d] * i, -0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD9Partitions
  60. Sequence(Segment[(4 / If[cp, parts, b] * i, 5.1), (4 / If[cp, parts, b] * i, 5.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB7Partitions
  61. Sequence(Segment[(4 / If[cp, parts, b] * i, 4.1), (4 / If[cp, parts, b] * i, 4.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB9Partitions
  62. Segment((12.192632439999999, 0.47543172), (16.732632440000003, 0.47543172)) → SumLine
  63. Segment((12.665158779999999, 2.6284661199999997), (12.64515878, 1.46846612)) → AddSignVert
  64. Segment((12.116438780000001, 2.06389612), (13.23643878, 2.06389612)) → AddSignHoriz