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分数加法可视化：用几何图形演示分数相加过程

分数加法可视化：用几何图形演示分数相加过程
几何画板及绘图内容加载中，请稍等……
2018-12-29 01:14
多边形数列几何作图滑块动画
① 本范例通过动态几何图形直观演示两个分数相加的过程，将抽象的分数运算转化为可视化的面积或长度比较。② 核心数学概念包括分数的意义、通分、加法运算以及分数与几何图形（如矩形、线段）的对应关系，同时涉及数列与统计中的基础表示方法。③ 作图要点：使用GeoGebra的Point、Ray、Polygon、Sequence等命令构造分数对应的图形区域，通过Textfield和Slider（如b1、h、C等对象）控制分子分母数值，利用FractionText命令显示分数文本，并用Segment、Vector辅助标注，最终通过Position1、Position2等对象布局文本，实现分数加法的动态演示。④ 适合小学高年级至初中阶段的学生学习分数运算，也可用于教师课堂演示，帮助学生建立分数与几何直观的联系，提升数形结合能力。

GeoGebra 命令及参数

  1. Point(yAxis) → C
  2. Point(Segment[C + (0, h), C + (0, (1.85 * h))]) → B
  3. If(t ≤ 0.5, 0, (2 * (t - 0.5))) → t2
  4. If(t ≤ 0.5, (2 * t), 1) → t1
  5. Point(Segment[B + (0, h), B + (0, (1.85 * h))]) → A
  6. Ray((0, 1.9), (0, 2.9)) → f
  7. Polygon({A, A + (l, 0), A + (l, h), A + (0, h)}) → poly1
  8. Polygon({B, B + (l, 0), B + (l, h), B + (0, h)}) → poly2
  9. Sequence(Segment[A + ((i * l / a1), 0), A + ((i * l / a1), h)], i, 1, a1 - 1) → list1
  10. Sequence(Segment[B + ((i * l / a2), 0), B + ((i * l / a2), h)], i, 1, a2 - 1) → list2
  11. Polygon({A, A + ((b1 * l / a1), 0), A + ((b1 * l / a1), h), A + (0, h)}) → poly3
  12. Polygon({B, B + ((b2 * l / a2), 0), B + ((b2 * l / a2), h), B + (0, h)}) → poly4
  13. Sequence(Sequence[Segment[A + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, a1 - 1) → list3
  14. Sequence(Sequence[Segment[B + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, a2 - 1) → list4
  15. If(a1 ≟ a2, true, false) → equald
  16. If(equald ∧ ((Div[b1 + b2, a1] > 0) ∨ (GCD[b1 + b2, a1] > 1)), true, If[(Div[(b1 * c1) + (b2 * c2), (a1 * c1)] > 0) ∨ (GCD[(b1 * c1) + (b2 * c2), (a1 * c1)] > 1), true, false]) → simplify
  17. Textfield(a1) → InputBox1
  18. Textfield(b1) → InputBox2
  19. Textfield(a2) → InputBox3
  20. Textfield(b2) → InputBox4
  21. Polygon({A', A' + (l, 0), A' + (l, h), A' + (0, h)}) → poly5
  22. Polygon({B', B' + ((b2 / a2 * l), 0), B' + ((b2 / a2 * l), h), B' + (0, h)}) → poly6
  23. Polygon({A', A' + ((b1 * l / a1), 0), A' + ((b1 * l / a1), h), A' + (0, h)}) → poly7
  24. Polygon({B', B' + ((b2 * l / a2), 0), B' + ((b2 * l / a2), h), B' + (0, h)}) → poly8
  25. Sequence(Sequence[Segment[A' + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A' + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, b1 - 1) → list8
  26. Sequence(Sequence[Segment[B' + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B' + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, b2 - 1) → list9
  27. Segment(C - (0, 0.5), C - (0, 1)) → g
  28. Segment(C + ((b1 / a1 * l), -0.5), C + ((b1 / a1 * l), -1)) → i
  29. Segment(C + ((b1 / a1 * l) + (b2 / a2 * l), -0.5), C + ((b1 / a1 * l) + (b2 / a2 * l), -1)) → j
  30. Vector(Midpoint[g], Midpoint[i]) → u
  31. Vector(Midpoint[i], Midpoint[g]) → v
  32. Vector(Midpoint[i], Midpoint[j]) → w
  33. Vector(Midpoint[j], Midpoint[i]) → a
  34. Sequence(Segment[A' + ((i * l / a1), 0), A' + ((i * l / a1), h)], i, 0, b1) → list6
  35. Sequence(Segment[B' + ((i * l / a2), 0), B' + ((i * l / a2), h)], i, 0, b2) → list7
  36. Sequence(Polygon[{C + ((i * l), 0), C + ((i * l) + l, 0), C + ((i * l) + l, h), C + ((i * l), h)}], i, 1, floor(b1 / a1 + b2 / a2)) → list5
  37. Segment(B', B' + ((b2 / a2 * l), 0)) → k
  38. Segment(B' + ((b2 / a2 * l), h), B' + (0, h)) → m
  39. If(b1 / a1 + b2 / a2 ≥ 1, true, false) → improper
  40. FractionText(b1 / a1 + b2 / a2) → text19
  41. FractionText(b1 / a1 + b2 / a2 - 1) → text20
  42. Sequence(Sequence[Segment[C + ((i * l / ((a1 * c1))) + (j * l), 0), C + ((i * l / ((a1 * c1))) + (j * l), h)], i, 1, (a1 * c1) - 1], j, 0, If[b1 / a1 + b2 / a2 ≤ 1, 0, 1]) → list10