积极 AI Logo 积极 AI

可视化除法：分配与包含两种模型交互演示

可视化除法：分配与包含两种模型交互演示
几何画板及绘图内容加载中，请稍等……
2020-11-08 02:00
函数数列几何作图滑块动画函数图像
该范例通过动态条形图与点阵动画，直观展示除法的两种基本含义：等分除（partitive）与包含除（quotative）。核心数学概念是除法运算的语义理解，以及除法与乘法、比例、函数图像之间的联系。作图要点包括：使用GeoGebra的If、First、Sequence、Flatten等命令构建分组布局，通过Textfield和InputBox实现用户输入被除数与除数，利用滑块（slider）和计时器（timer）控制点阵的逐步移动，展示等分时每组点数相同、包含时按固定数量分组的过程。适合小学高年级至初中阶段的学生学习除法概念，也可用于教师课堂演示，帮助学生从直观操作过渡到抽象算式，理解除法与平均分、包含分的关系。

GeoGebra 命令及参数

  1. If(a1 / a2 < 6, 1, If[a1 / a2 < 11, 2, 3]) → groupLayoutSizes2
  2. First(Flatten[Sequence[Sequence[Point[{i, j}], i, (0.5 * a1 / quotativeGPR), a1, a1 / quotativeGPR], j, ((-0.5 * a1)) / quotativeGPR - 1, ((-0.5 * a1)) / quotativeGPR - 1 - (a1 / quotativeGPR * (groupLayoutSizes2 - 1)), ((-a1)) / quotativeGPR]], q) → quotativeGroupCenters
  3. If(a2 > 2 ∧ q > 2, 0.5, 0.4) → polySize
  4. Sequence(Point[{i, 0}], i, 0, a1 - 1) → arrayPoints
  5. If(a2 < 6, 1, If[a2 < 11, 2, 3]) → groupLayoutSizes1
  6. Flatten(Sequence[Sequence[Point[{i, j}], i, (0.5 * a1 / partitiveGPR), a1, a1 / partitiveGPR], j, ((-0.5 * a1)) / partitiveGPR - 1, ((-0.5 * a1)) / partitiveGPR - 1 - (a1 / partitiveGPR * (groupLayoutSizes1 - 1)), ((-a1)) / partitiveGPR]) → partitiveGroupCenters
  7. Textfield(a1text) → InputBox0
  8. Textfield(a2text) → InputBox1
  9. Max(a1, a2) → arraySize
  10. Flatten(Sequence[Sequence[Element[partitiveGroupCenters, i] - (polySize / 2, polySize / 2) + (((1 - q) / q * (0.4 * a1 / partitiveGPR)) * (cos(((2 * π / q) * j)), sin(((2 * π / q) * j)))), j, 0, q - 1], i, 1, Length[partitiveGroupCenters]]) → partitiveGroupDots
  11. Min((-0.1 * a1), -2) → left
  12. If(c, (((-a1)) / partitiveGPR * groupLayoutSizes1) - 1, If[a, (((-a1)) / quotativeGPR * groupLayoutSizes2) - 1, 0]) → bottom
  13. Flatten(Sequence[Sequence[Element[quotativeGroupCenters, i] - (polySize / 2, polySize / 2) + (quotativeDistance * (cos(((2 * π / a2) * j) + π), sin(((2 * π / a2) * j) + π))), j, 0, a2 - 1], i, 1, Length[quotativeGroupCenters]]) → quotativeGroupDots
  14. Max((1.1 * a1), 2) → right
  15. Sequence((Element[arrayPoints, i] * (1 - timer2)) + (Element[quotativeGroupDots, i] * timer2), i, ((test - 1) * a2) + 1, (test * a2)) → movingQuotativeDots
  16. Sequence(Polygon[Element[arrayPoints, i], Element[arrayPoints, i] + (polySize, 0), 4], i, 1, a1) → fixedArrayPolys
  17. Last(fixedArrayPolys, a1 - (test * a2)) → quotativeRemainingPolys
  18. Last(fixedArrayPolys, a1 - (ms * a2)) → partitiveRemainingPolys
  19. If(a, quotativeDistance + 1 / 2, (0.5 * a1 / partitiveGPR) - 1 / 5) → PCS
  20. If(ms > 0, Sequence[Polygon[Element[movingPartitiveDots, i], Element[movingPartitiveDots, i] + (polySize, 0), 4], i, 1, Length[movingPartitiveDots]], {}) → movingPartitiveArrays
  21. Sequence(Sequence[Polygon[Element[partitiveGroupDots, i], Element[partitiveGroupDots, i] + (polySize, 0), 4], i, k, a1, q], k, 1, ms - 1) → partitiveGroupedPolys
  22. First(Sequence[Circle[Element[partitiveGroupCenters, i], PCS], i, 1, Length[partitiveGroupCenters]], circleTimer) → partitiveGroupCircles
  23. First(Sequence[Polygon[Element[quotativeGroupDots, i], Element[quotativeGroupDots, i] + (polySize, 0), 4], i, 1, (a2 * q)], (a2 * circleTimer)) → quotativeGroupedPolys
  24. If(ms > 0, Sequence[Polygon[Element[movingQuotativeDots, i], Element[movingQuotativeDots, i] + (polySize, 0), 4], i, 1, Length[movingQuotativeDots]], {}) → movingQuotativeArrays
  25. First(Sequence[Circle[Element[quotativeGroupCenters, i], PCS], i, 1, Length[quotativeGroupCenters]], circleTimer) → quotativeGroupCircles

AI 绘图提示语参考

画一个动态展示除法的图形，包括两个部分：分享到相等的组（部分分配模型）和按固定大小分组（配额分配模型）。使用点阵和条形图动态展示被除数如何被除数分割。设置两个输入框输入被除数和除数，根据输入动态调整点阵和条形图的位置和大小。使用动画效果展示分组过程，包括剩余部分的展示。
以上提示语为根据原始绘图命令整理而来，仅供参考。