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假分数的面积模型可视化

假分数的面积模型可视化
几何画板及绘图内容加载中，请稍等……
2020-04-02 01:45
函数几何作图滑块动画
该范例通过面积模型直观展示假分数（如分子大于分母的分数）的几何意义。核心数学概念是分数、假分数与带分数的转换，以及面积等分与部分占整体的关系。作图要点包括：使用Point、Rotate、CircleSector、Polygon等命令构造圆和扇形区域，通过Sequence和If生成动态的等分与填充，利用FractionText显示分数表达式，并借助滑块（如num1、denom1）调节分子分母，实时更新图形。适合小学高年级至初中阶段学习分数概念，也可用于教师课堂演示，帮助学生理解假分数为何大于1以及如何用带分数表示。

GeoGebra 命令及参数

  1. Point(Circle[M, 1]) → Q
  2. Point(Circle[N, 1]) → R
  3. Point(Circle[L_1, 0.02]) → U_1
  4. Point(Circle[U_1, 0.5]) → V_1
  5. Rotate(C_2, angle, Center1) → D_2
  6. CircleSector(Center1, C_2, D_2) → circle1sector
  7. Rotate(C_2, (360 / denom1)°, Center1) → B_2
  8. Polygon((x(Center1) - 0.09, y(Center1) - 0.07), (x(Center1) - 0.09 + (0.18 * (val1 - floor(val1))), y(Center1) - 0.07), (x(Center1) - 0.09 + (0.18 * (val1 - floor(val1))), y(Center1) + 0.07), (x(Center1) - 0.09, y(Center1) + 0.07)) → rect1shadePartial, g, h, i, j
  9. Polygon((Element[Position, 1], 0) + (-0.09, yRow1 - 0.07), (Element[Position, 1], 0) + (0.09, yRow1 - 0.07), (Element[Position, 1], 0) + (0.09, yRow1 + 0.07), (Element[Position, 1], 0) + (-0.09, yRow1 + 0.07)) → rect1outline1, c, d, e, f
  10. Sequence(Sequence[Segment[Rotate[(k, 0.525), ((360 / denom1 * i))°, (k, 0.525)], Rotate[(k, 0.525) + (0, CircleDiameters), ((360 * i / denom1))°, (k, 0.525)]], i, 0, denom1], k, 0.1, If[val1 ≥ 5, 0.9, Element[Position, ceil(val1)]], 0.2) → circle1div1
  11. If(val1 ≤ 5, Sequence[Circle[(i, yRow1), CircleDiameters], i, 0.1, Element[Position, If[val1 ≠ round(val1), floor(val1), ceil(val1)]], 0.2], Sequence[Circle[(i, yRow1), CircleDiameters], i, 0.1, Element[Position, 5], 0.2]) → circle1fill1
  12. If(val1 ≤ 5, Sequence[Circle[(i, yRow1), CircleDiameters], i, 0.1, Element[Position, ceil(val1)], 0.2], Sequence[Circle[(i, yRow1), CircleDiameters], i, 0.1, Element[Position, 5], 0.2]) → circle1outline1
  13. If(val1 ≤ 10, Sequence[Circle[(i, yRow2), CircleDiameters], i, 0.1, Element[Position, floor(val1)], 0.2], Sequence[Circle[(i, yRow2), CircleDiameters], i, 0.1, Element[Position, 5], 0.2]) → circle1fill2
  14. Sequence(Sequence[Segment[Rotate[(k, yRow2), ((360 / denom1 * i))°, (k, yRow2)], Rotate[(k, yRow2) + (0, CircleDiameters), ((360 * i / denom1))°, (k, yRow2)]], i, 0, denom1], k, 0.1, Element[Position, ceil(val1)], 0.2) → circle1div2
  15. If(val1 ≤ 10, Sequence[Circle[(i, yRow2), CircleDiameters], i, 0.1, Element[Position, ceil(val1)], 0.2], Sequence[Circle[(i, yRow2), CircleDiameters], i, 0.1, Element[Position, 10], 0.2]) → circle1outline2
  16. If(val1 ≤ 15, Sequence[Circle[(i, yRow3), CircleDiameters], i, 0.1, Element[Position, If[val1 ≠ round(val1), floor(val1), ceil(val1)]], 0.2], Sequence[Circle[(i, yRow3), CircleDiameters], i, 0.1, Element[Position, 15], 0.2]) → circle1fill3
  17. If(val1 ≤ 15, Sequence[Circle[(i, yRow3), CircleDiameters], i, 0.1, Element[Position, ceil(val1)], 0.2], Sequence[Circle[(i, yRow3), CircleDiameters], i, 0.1, Element[Position, 15], 0.2]) → circle1outline3
  18. If(val1 ≤ 20, Sequence[Circle[(i, yRow4), CircleDiameters], i, 0.1, Element[Position, ceil(val1)], 0.2], Sequence[Circle[(i, yRow4), CircleDiameters], i, 0.1, Element[Position, 20], 0.2]) → circle1outline4
  19. If(val1 ≤ 20, Sequence[Circle[(i, yRow4), CircleDiameters], i, 0.1, Element[Position, If[val1 ≠ round(val1), floor(val1), ceil(val1)]], 0.2], Sequence[Circle[(i, yRow4), CircleDiameters], i, 0.1, Element[Position, 20], 0.2]) → circle1fill4
  20. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow1 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow1 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow1 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow1 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 ≤ 5, ceil(val1), 5]], 0.2) → rect1outline1Seq
  21. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow3 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow3 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow3 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow3 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 ≤ 15, ceil(val1), 15]], 0.2) → rect1outline3Seq
  22. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow4 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow4 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow4 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow4 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 ≤ 20, ceil(val1), 20]], 0.2) → rect1outline4Seq
  23. Sequence(Sequence[Segment[(k - 0.09 + (0.18 / denom1 * i), yRow1 - 0.07), (k - 0.09 + (0.18 / denom1 * i), yRow1 + 0.07)], i, 1, denom1 - 1], k, 0.1, If[val1 ≥ 5, 0.9, Element[Position, ceil(val1)]], 0.2) → rect1div1
  24. Sequence(Sequence[Segment[(k - 0.09 + (0.18 / denom1 * i), yRow2 - 0.07), (k - 0.09 + (0.18 / denom1 * i), yRow2 + 0.07)], i, 1, denom1 - 1], k, 0.1, If[val1 ≥ 10, 0.9, Element[Position, ceil(val1)]], 0.2) → rect1div2
  25. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow1 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow1 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow1 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow1 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 ≤ 5, floor(val1), 5]], 0.2) → rect1shade1Seq
  26. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow2 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow2 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow2 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow2 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 < 10, floor(val1), 10]], 0.2) → rect1shade2Seq
  27. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow2 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow2 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow2 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow2 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 < 10, ceil(val1), 10]], 0.2) → rect1outline2Seq
  28. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow3 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow3 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow3 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow3 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 ≤ 15, floor(val1), 15]], 0.2) → rect1shade3Seq
  29. Sequence(Polygon[Translate[(Element[Position, 1], 0) + (-0.09, yRow4 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow4 - 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (0.09, yRow4 + 0.07), Vector[(0, 0), (i, 0)]], Translate[(Element[Position, 1], 0) + (-0.09, yRow4 + 0.07), Vector[(0, 0), (i, 0)]]], i, 0, Element[Position, If[val1 ≤ 20, floor(val1), 20]], 0.2) → rect1shade4Seq
  30. FractionText(num1 / denom1 - floor(num1 / denom1)) → MixNumFrac
  31. FractionText(num1 / denom1) → FracSimplist

AI 绘图提示语参考

绘制一个用于演示假分数的面积模型。画一个圆形，将其按分母等分成若干扇形区域，并用滑块控制分子数值，动态填充相应数量的扇形以表示假分数。同时，在圆形下方绘制多行矩形条，每行被等分成与分母相同的份数，根据分子数值逐行填充矩形格子，并用不同颜色区分已填充和未填充部分。在图形上方显示假分数的分数形式及其带分数形式。整体布局清晰，便于观察假分数大于1的直观意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。