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Decimal Multiplication and Geometric Construction Example

Decimal Multiplication and Geometric Construction Example
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2019-03-13 16:53
Coordinate GeometryGeometric ConstructionGraphing
This example demonstrates how to understand decimal multiplication through geometric figures. Key mathematical concepts include geometric construction, coordinate geometry, and graphing functions. Construction involves using GeoGebra commands like Segment, Polygon, Sequence, and If. Suitable for middle school students learning the integration of geometry and algebra.

GeoGebra Commands & Parameters

  1. Segment(A, D) → f
  2. Segment(D, C) → g
  3. Segment(C, B) → h
  4. Segment(B, A) → i
  5. Segment(E, F) → j
  6. Segment(F, G) → k
  7. Segment(G, H) → l
  8. Segment(H, E) → m
  9. Segment(I, J) → n
  10. Segment(J, K) → p
  11. Segment(K, L) → q
  12. Segment(I, L) → r
  13. Polygon((0, 20), (10, 20), (10, 21), (0, 21)) → q1, s, t, a, b
  14. Polygon((0, 22), (10, 22), (10, 23), (0, 23)) → q2, c, d, e, f_1
  15. Sequence((k, 24), k, 0, 7) → l1
  16. Sequence((k, 25), k, 0, 7) → l2
  17. Sequence(Polygon[Element[l1, k], Element[l1, k + 1], Element[l2, k + 1], Element[l2, k]], k, 1, 8, 2) → l3
  18. Sequence(Vector[Element[l4, k], Element[l5, k]], k, 1, 6) → l6
  19. If(0 < o < 1, Vector[Dilate[Element[l6, 1], o]], Vector[If[o ≥ 1, Vector[Element[l6, 1]]]]) → u
  20. If(1 ≤ o < 2, Vector[Dilate[Element[l6, 2], o - 1]], Vector[If[o ≥ 2, Vector[Element[l6, 2]]]]) → v
  21. If(2 ≤ o < 3, Vector[Dilate[Element[l6, 3], o - 2]], Vector[If[o ≥ 3, Vector[Element[l6, 3]]]]) → w
  22. If(3 ≤ o < 4, Vector[Dilate[Element[l6, 4], o - 3]], Vector[If[o ≥ 4, Vector[Element[l6, 4]]]]) → u_1
  23. If(4 ≤ o < 5, Vector[Dilate[Element[l6, 5], o - 4]], Vector[If[o ≥ 5, Vector[Element[l6, 5]]]]) → v_1
  24. If(5 ≤ o < 6, Vector[Dilate[Element[l6, 6], o - 5]], Vector[If[o ≥ 6, Vector[Element[l6, 6]]]]) → w_1
  25. Join({l8, l3}) → l9
  26. Sequence((0, k), k, 0, 9) → l11
  27. Sequence((10, k), k, 0, 9) → l12
  28. Sequence((12, k), k, 0, 9) → l13
  29. Sequence((22, k), k, 0, 9) → l14
  30. Sequence((24, k), k, 0, 9) → l15
  31. Sequence((25, k), k, 0, 9) → l16
  32. Sequence((26, k), k, 0, 9) → l17
  33. Sequence((27, k), k, 0, 9) → l18
  34. Sequence((28, k), k, 0, 9) → l19
  35. Sequence(Polygon[Element[l11, 11 - k], Element[l11, 10 - k], Element[l12, 10 - k], Element[l12, 11 - k]], k, 1, o - 5) → l20
  36. Sequence(Polygon[Element[l13, 11 - k], Element[l13, 10 - k], Element[l14, 10 - k], Element[l14, 11 - k]], k, 1, o - 5) → l21
  37. Sequence(Polygon[Element[l15, 11 - k], Element[l15, 10 - k], Element[l16, 10 - k], Element[l16, 11 - k]], k, 1, o - 5) → l22
  38. Sequence(Polygon[Element[l16, 11 - k], Element[l16, 10 - k], Element[l17, 10 - k], Element[l17, 11 - k]], k, 1, o - 5) → l23
  39. Sequence(Polygon[Element[l17, 11 - k], Element[l17, 10 - k], Element[l18, 10 - k], Element[l18, 11 - k]], k, 1, o - 5) → l24
  40. Sequence(Polygon[Element[l18, 11 - k], Element[l18, 10 - k], Element[l19, 10 - k], Element[l19, 11 - k]], k, 1, o - 5) → l25
  41. Sequence(Translate[Element[l9, k], Vector[Element[l7, k]]], k, 1, 2) → l10
  42. Sequence(Translate[Element[l9, k], Vector[Element[l7, k]]], k, 3, 6) → l26