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部分积乘法演示 by Duane Habecker

部分积乘法演示 by Duane Habecker
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2018-02-20 13:45
立体几何
①本范例演示了如何通过条形图和面积模型直观展示乘法运算中的部分积概念；②涉及的核心数学概念包括乘法、条形图/柱状图、面积计算、比率、立方体及几何变换；③作图要点——使用了Textfield, Segment, Point, Flatten, Sequence, Polygon, Line, Centroid, Midpoint等GeoGebra命令与对象来构建图形元素和交互界面；④适合初中数学教学，用于帮助学生理解乘法运算的分解过程和几何意义。

GeoGebra 命令及参数

  1. Textfield(factor1number) → Factor1
  2. Textfield(factor2number) → Factor2
  3. Segment((x(A) - a, y(A)), (x(A) - a, y(A) - factor1number)) → f
  4. Segment((x(A), y(A) + a), (x(A) + factor2number, y(A) + a)) → g
  5. Point(f) → B
  6. Point(g) → C
  7. Flatten(Sequence[Sequence[(x(A) + j, y(A) - i), j, 0, factor2number], i, 0, factor1number]) → DotsArray
  8. Sequence(Segment[Element[DotsArray, i], Element[DotsArray, ((factor2number + 1) * factor1number) + i]], i, 0, factor2number + 1, 1) → GridVertical
  9. Sequence(Segment[Element[DotsArray, ((factor2number + 1) * i) + 1], Element[DotsArray, ((factor2number + 1) * i) + factor2number + 1]], i, 0, factor1number, 1) → GridHorizontal
  10. Polygon(A, D, F, E) → q1, a_1, d, f_1, e
  11. Line(E, F) → h
  12. Line(D, F) → i
  13. Polygon(D, G, H, F) → q2, d_1, g_1, h_1, f_2
  14. Polygon(F, H, I, K) → q3, f_3, h_2, i_1, k
  15. Polygon(E, F, K, J) → q4, e_1, f_4, k_1, j
  16. Centroid(q1) → M
  17. Centroid(q4) → N
  18. Centroid(q2) → O
  19. Centroid(q3) → P
  20. Midpoint(g) → Q
  21. Midpoint(f) → R