积极 AI Logo 积极 AI

分数减法可视化模型

分数减法可视化模型
几何画板及绘图内容加载中，请稍等……
2020-01-22 23:14
几何作图
①本范例通过可视化模型演示分数减法，特别是通过将整数部分转化为分数部分进行减法运算的过程；②涉及的核心数学概念包括分数减法、通分、整数与分数的转换；③作图要点——使用了 GeoGebra 命令 If, Sequence, Point, Textfield, Polygon, Text, Segment 等，构建了分数减法模型；④适合初中数学教学，帮助学生直观理解分数减法运算。

GeoGebra 命令及参数

  1. If(Defined[minWhole], minWhole, 0) → realMinWhole
  2. If(Defined[minNum] ∧ Defined[minDen], If[Defined[subDen] ∧ Defined[subNum] ∧ b, (minNum * LCM[minDen, subDen] / minDen), minNum], 0) → realMinNum
  3. If(Defined[subDen], If[Defined[minDen] ∧ b, LCM[minDen, subDen], subDen], 1) → realSubDen
  4. If(((¬Defined[minDen]) ∨ minDen ≟ 1) ∧ Defined[realSubDen], realSubDen, If[Defined[minDen], If[Defined[subDen] ∧ b, LCM[minDen, subDen], minDen], 1]) → realMinDen
  5. If(Defined[subWhole], subWhole, 0) → realSubWhole
  6. If(Defined[subNum] ∧ Defined[subDen], If[Defined[minDen] ∧ Defined[minNum] ∧ b, (subNum * LCM[minDen, subDen] / subDen), subNum], 0) → realSubNum
  7. Sequence(Point[{i, -1 / 2}], i, 0, floor(minuend) - floor(subtrahend)) → subPoints
  8. Point(subPoints) → SubStartingPoint
  9. Sequence(Point[{i, 1 / 2}], i, 0, floor(minuend)) → minWholesPoints
  10. Textfield(minWhole) → InputBox1
  11. Textfield(minNum) → InputBox2
  12. Textfield(minDen) → InputBox3
  13. Textfield(subWhole) → InputBox4
  14. Textfield(subNum) → InputBox5
  15. Textfield(subDen) → InputBox6
  16. Polygon((0, 0), (realMinWhole + realMinNum / realMinDen, 0), (realMinWhole + realMinNum / realMinDen, 1), (0, 1)) → minPoly, f, g, h, i
  17. Point(minWholesPoints) → MinStartingPoint
  18. Polygon(SubStartingPoint + (0, -1 / 2), SubStartingPoint + (realSubWhole + realSubNum / realSubDen, -1 / 2), SubStartingPoint + (realSubWhole + realSubNum / realSubDen, 1 / 2), SubStartingPoint + (0, 1 / 2)) → subPoly, j, k, l, m
  19. Text(x(MinStartingPoint), (x(MinStartingPoint) / 2, 1.2)) → minWholeText
  20. Text(realSubWhole, SubStartingPoint + (realSubWhole / 2, -1)) → subWholeText
  21. Sequence(Segment[SubStartingPoint + (i, -1 / 2), SubStartingPoint + (i, 1 / 2)], i, 0, ceil(subtrahend)) → subWholeLines
  22. Sequence(Segment[SubStartingPoint + (i, -1 / 2), SubStartingPoint + (i, 1 / 2)], i, realSubWhole, ceil(subtrahend), 1 / realSubDen) → subDenLines
  23. Sequence(Segment[(i, 0), (i, 1)], i, x(MinStartingPoint), ceil(minuend), 1 / realMinDen) → minDenLines
  24. Sequence(Segment[(i, 0), (i, 1)], i, 0, ceil(minuend)) → minWholeLines
  25. Segment((0, 1), (ceil(minuend), 1)) → topMin
  26. Segment((0, 0), (ceil(minuend), 0)) → bottomMin
  27. Segment(SubStartingPoint + (0, -0.5), SubStartingPoint + (ceil(subtrahend), -0.5)) → bottomSub
  28. Segment(SubStartingPoint + (0, 0.5), SubStartingPoint + (ceil(subtrahend), 0.5)) → topSub

AI 绘图提示语参考

画一个图形表示分数减法，包括两个矩形分别表示被减数和减数，被减数矩形分为若干个单位分数部分，减数矩形也分为单位分数部分。在被减数矩形下方画出减数矩形，用线段表示单位分数部分，用文字标注整数部分和分数部分。
以上提示语为根据原始绘图命令整理而来，仅供参考。