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Fraction and Decimal Hundredths Grids

Fraction and Decimal Hundredths Grids
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2017-02-25 18:12
Coordinate GeometryGeometric ConstructionGraphing
This example demonstrates the visual representation of fractions and hundredths using grids. It involves core math concepts like fractions, decimals, percentage conversion, and grid visualization. Construction highlights include using GeoGebra commands such as Sequence, Point, If, Polygon, Text, and Segment. Suitable for middle school and above, it helps students understand the geometric meaning and conversion between decimals and fractions.

GeoGebra Commands & Parameters

  1. Sequence((i - 1 + floor((i - 1) / 11), -13), i, 1, 33) → Q10list
  2. Point(Q10list) → Q10
  3. Sequence((x(Q10) + 1, i), i, -13, -3) → Q100list
  4. Point(Q100list) → Q100
  5. If(y(Q100) ≟ -3, 1, 0) → carry2H
  6. If(y(Q100) ≟ -3 ∧ (x(Q10) ≟ 9 ∨ x(Q10) ≟ 21 ∨ x(Q10) ≟ 33), 1, 0) → carry2D
  7. If(x(Q10) < 10, 0, If[x(Q10) < 22, 1, If[x(Q10) < 34, 2, 3]]) → du2
  8. Sequence((i - 1 + floor((i - 1) / 11), 0), i, 1, 33) → P10list
  9. Point(P10list) → P10
  10. Sequence((x(P10) + 1, i), i, 0, 10) → P100list
  11. Point(P100list) → P100
  12. If(y(P100) ≟ 10 ∧ (x(P10) ≟ 9 ∨ x(P10) ≟ 21 ∨ x(P10) ≟ 33), 1, 0) → carry1D
  13. If(x(P10) < 10, 0, If[x(P10) < 22, 1, If[x(P10) < 34, 2, 3]]) → du1
  14. If(y(P100) ≟ 10, 1, 0) → carry1H
  15. Polygon((0, 0), (10, 0), 4) → Square1
  16. Polygon((12, 0), (22, 0), 4) → Square2
  17. Polygon((24, 0), (34, 0), 4) → Square3
  18. Sequence(Segment[(0, i), (10, i)], i, 1, 9) → h1
  19. Sequence(Segment[(i, 0), (i, 10)], i, 1, 9) → v1
  20. Sequence(Segment[(12, i), (22, i)], i, 1, 9) → h2
  21. Sequence(Segment[(24, i), (34, i)], i, 1, 9) → h3
  22. Sequence(Segment[(i + 12, 0), (i + 12, 10)], i, 1, 9) → v2
  23. Polygon(((12 * digitunit), 0), ((12 * digitunit), 10), ((12 * digitunit) + digit10th, 10), ((12 * digitunit) + digit10th, 0)) → poly10th, a, b, c, d
  24. Sequence(Segment[(i + 24, 0), (i + 24, 10)], i, 1, 9) → v3
  25. Polygon(P10, P10 + (1, 0), P100, P100 - (1, 0)) → poly100th, e, f, g, h
  26. Polygon((0, 0), (10, 0), 4) → ColorSquare1
  27. Polygon((12, 0), (22, 0), 4) → ColorSquare2
  28. Polygon((24, 0), (34, 0), 4) → ColorSquare3
  29. Text(Element[List1, digitunit + 1]) → text16
  30. Text(("點" * Element[List1, digit10th + 1])) → text17
  31. Text(Element[List1, digit100th + 1]) → text18
  32. Polygon((0, -13), (10, -13), 4) → Square4
  33. Polygon((12, -13), (22, -13), 4) → Square5
  34. Polygon((24, -13), (34, -13), 4) → Square6
  35. Polygon((0, -13), (10, -13), 4) → ColorSquare4
  36. Polygon(((12 * digitunit2), -3), ((12 * digitunit2), -13), ((12 * digitunit2) + digit10th2, -13), ((12 * digitunit2) + digit10th2, -3)) → poly10th2, i, j, k, l
  37. Polygon((12, -13), (22, -13), 4) → ColorSquare5
  38. Polygon((24, -13), (34, -13), 4) → ColorSquare6
  39. Polygon(Q10, Q10 + (1, 0), Q100, Q100 - (1, 0)) → poly100th2, q10, m, q100, n
  40. Text(Element[List1, digitunit2 + 1]) → text31
  41. Text(("點" * Element[List1, digit10th2 + 1])) → text32
  42. Text(Element[List1, digit100th2 + 1]) → text33
  43. Segment(M, M + (L, 0)) → q
  44. Segment(M + (L, 0), M + (L, H)) → r
  45. Segment(M + (L, H), M + (0, H)) → s
  46. Segment(M, M + (0, H)) → t
  47. Segment(N, N + (L, 0)) → a_1
  48. Segment(N + (L, 0), N + (L, H)) → b_1
  49. Segment(N + (L, H), N + (0, H)) → c_1
  50. Segment(N, N + (0, H)) → d_1
  51. Segment((0, -1.5), (34, -1.5)) → p
  52. Sequence(Segment[(i, -13), (i, -3)], i, 1, 9) → v4
  53. Sequence(Segment[(i + 12, -13), (i + 12, -3)], i, 1, 9) → v5
  54. Sequence(Segment[(i + 24, -13), (i + 24, -3)], i, 1, 9) → v6
  55. Sequence(Segment[(0, i), (10, i)], i, -12, -4) → h4
  56. Sequence(Segment[(12, i), (22, i)], i, -12, -4) → h5
  57. Sequence(Segment[(24, i), (34, i)], i, -12, -4) → h6
  58. Polygon(B, C, D, E) → poly1, b_2, c_2, d_2, e_1

AI Drawing Prompt Reference

Draw a hundredths grid with three 10x10 small grids and three 100x1 small grids. Each small grid is labeled with fractions and decimals using points and segments. In each small grid, points represent the positions of fractions and decimals, and lines connect these points. Draw grid lines at the top and bottom of each small grid, and use different colors to distinguish the grids.
The prompt above was compiled from the original drawing commands and is for reference only.