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使用面积模型加法分数

使用面积模型加法分数
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2017-11-28 23:41
几何作图
这个范例通过面积模型演示了如何加法分数。它涉及的核心数学概念是分数加法和面积模型。作图要点包括使用Point, Circle, OrthogonalLine, Intersect, Segment, Mirror, Sequence, Polygon, GCD, Random等GeoGebra命令和对象。适合小学高年级或初中生学习分数加法。

GeoGebra 命令及参数

  1. Point(c) → A
  2. Circle(A, squaresize) → d
  3. OrthogonalLine(A, c) → e
  4. Intersect(d, e, 2) → B_1
  5. Intersect(d, c, 2) → C
  6. Segment(B_1, C) → f
  7. Mirror(A, f) → A'
  8. Sequence((x(A) + (i * squareside / denominator2), y(A)), i, 1, denominator2) → DotsBottom
  9. Sequence((x(B_1) + (i * squareside / denominator2), y(B_1)), i, 1, denominator2) → DotsTop
  10. Polygon(A, (x(A) + (numerator2 * squaresize / denominator2), y(A)), (x(B_1) + (numerator2 * squaresize / denominator2), y(B_1)), B_1) → poly1, a, h, i, j
  11. Sequence(Segment[(x(A) + (i * squaresize / denominator2), y(A)), (x(B_1) + (i * squaresize / denominator2), y(B_1))], i, 1, denominator2) → DashedLines1
  12. Polygon(A, C, A', B_1) → poly2, a_1, c_1, a', b_1
  13. Point(c) → B
  14. Circle(B, squaresize) → g
  15. OrthogonalLine(B, c) → b
  16. Intersect(g, b, 2) → E
  17. Intersect(g, c, 2) → F
  18. OrthogonalLine(E, b) → k
  19. OrthogonalLine(F, c) → l
  20. Intersect(k, l) → G
  21. Sequence((x(B), y(B) + (i * squaresize / denominator1)), i, 1, denominator1) → DotsLeft
  22. Sequence((x(F), y(F) + (i * squaresize / denominator1)), i, 1, denominator1) → DotsRight
  23. Sequence(Segment[(x(B), y(B) + (i * squaresize / denominator1)), (x(F), y(F) + (i * squaresize / denominator1))], i, 1, denominator1) → DashedLines2
  24. Polygon(B, F, (x(F), y(F) + (numerator1 * squaresize / denominator1)), (x(B), y(B) + (numerator1 * squaresize / denominator1))) → poly3, d_1, f_1, m, n
  25. Polygon(B, F, G, E) → poly4, d_2, f_2, g_1, e_1
  26. GCD(MixedNum, commondenom) → ReduceBy
  27. Random(2, 10) → seeddenominator1
  28. Random(2, 10) → seeddenominator2