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用图形解决整数除以分数的问题

用图形解决整数除以分数的问题
几何画板及绘图内容加载中，请稍等……
2022-11-15 04:55
几何作图
这个范例通过GeoGebra的图形模型，演示如何用盒子或弹珠的视觉化方式解决整数除以分数或混合数的数学问题。核心数学概念包括分数除法、混合数运算以及比例关系。作图要点涉及使用Shuffle、Element、Random、If、Max、Min、Sequence等GeoGebra命令，以及Polygon、Segment、Midpoint等对象来构建动态图形。适合小学四年级至五年级的学生，用于理解分数除法的实际应用和数学建模能力。

GeoGebra 命令及参数

  1. Shuffle({1, 2, 3, 1, 2, 3}) → randomList1, {2, 1, 3, 2, 1, 3}
  2. Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1
  3. Shuffle({2, 3, 4, 2, 3, 4}) → randomList3, {2, 4, 4, 3, 2, 3}
  4. Element(randomList3, Mod[countQuestion, Length[randomList3]] + 1) → randomNum3
  5. Shuffle({0, 0, 0, 0, 1, 1, 2, 2}) → randomList2, {0, 1, 2, 0, 2, 0, 1, 0}
  6. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2
  7. Random(1, den - 1) → num
  8. If(Defined[input1], Min[input1, totalSlots + 1] + 1, 1) → timeOrange
  9. Max(timeOrange, marblesTotal + 1) → timePurple
  10. Min(2, If[ratioPic > ratioReference, Distance[C1, C2] / widthReference, Distance[C1, C4] / heightReference]) → radius
  11. Sequence((x(Midpoint[C1, C3]) - widthBox / 2 + (0.7 * radius) + ((radius * 1.2) * (n - 1)), y(Midpoint[C1, C3]) - (radius * heightReference / 2) + (0.2 * radius) + radius / 2), n, 1, marblesBox) → centers
  12. Flatten(Sequence[Sequence[(x(Midpoint[C1, C3]) - widthBox / 2 + (0.7 * radius) + ((radius * 1.2) * (n - 1)), y(Midpoint[C1, C3]) - (radius * heightReference / 2) + (0.2 * radius) + radius / 2 + ((T * 1.8) * radius)), n, 1, marblesBox], T, whole, 1, -1]) → centersWhole
  13. Flatten({centersWhole, centers, {ExtraCenter}}) → centersTotal
  14. Sequence(Circle[FromTo[A, Element[centersTotal, k], step(k, time)], radius / 2], k, input1 + 1, marblesTotal) → marblesAnimTotal
  15. If(time ≤ 1, 0, time ≤ timeOrange, 1, time ≤ timePurple, 2, time ≤ timeFading, 3, 4) → animStep
  16. Sequence(Circle[FromTo[A, Element[centersTotal, k], step(k, time)], radius / 2], k, 1, Min[input1, (numBoxes * marblesBox) + 1]) → marblesAnimSt
  17. Textfield(input1) → InputBox1
  18. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  19. Sequence(Polygon[{(x(Midpoint[C1, C3]) - widthBox / 2, y(Midpoint[C1, C3]) + (((n * 1.8) - heightReference / 2) * radius)), (x(Midpoint[C1, C3]) + widthBox / 2, y(Midpoint[C1, C3]) + (((n * 1.8) - heightReference / 2) * radius)), (x(Midpoint[C1, C3]) + widthBox / 2, y(Midpoint[C1, C3]) + (radius * (1.4 + (1.8 * n) - heightReference / 2))), (x(Midpoint[C1, C3]) - widthBox / 2, y(Midpoint[C1, C3]) + (((1.8 * n) + 1.4 - heightReference / 2) * radius))}], n, 1, whole) → boxes
  20. Polygon({(x(Midpoint[C1, C3]) - widthBox / 2 + ((0.1 + ((num * factor) * 1.2)) * radius), y(Midpoint[C1, C3]) + (((-heightReference)) / 2 * radius)), (x(Midpoint[C1, C3]) + widthBox / 2, y(Midpoint[C1, C3]) + (((-heightReference)) / 2 * radius)), (x(Midpoint[C1, C3]) + widthBox / 2, y(Midpoint[C1, C3]) + (radius * (1.4 - heightReference / 2))), (x(Midpoint[C1, C3]) - widthBox / 2 + ((0.1 + ((num * factor) * 1.2)) * radius), y(Midpoint[C1, C3]) + ((1.4 - heightReference / 2) * radius))}) → boxUnused
  21. Segment((x(Midpoint[C1, C3]) - widthBox / 2 + ((0.1 + ((num * factor) * 1.2)) * radius), y(Midpoint[C1, C3]) + (((-heightReference)) / 2 * radius) - 0.5), (x(Midpoint[C1, C3]) - widthBox / 2, y(Midpoint[C1, C3]) + (((-heightReference)) / 2 * radius) - 0.5)) → brace
  22. Midpoint(brace) → labelBracePos
  23. Sequence(Circle[FromTo[A, Element[Join[{centers, Sequence[A, p, 1, input1 - marblesBox]}], k], step(k, timeStep)], radius / 2], k, 1, input1) → marblesAnim
  24. Take(boxes, 1, Length[boxes] - 1) → shadowedBoxes
  25. Zip(Circle[P, radius / 2], P, centersWhole) → marblesWhole
  26. Sequence(Circle[Element[Join[{centers, Sequence[A, p, 1, input1 - marblesBox]}], k], radius / 2], k, input1 + 1, marblesBox) → marblesMissing
  27. Polygon({(x(Midpoint[C1, C3]) - widthBox / 2, y(Midpoint[C1, C3]) + (((-heightReference)) / 2 * radius)), (x(Midpoint[C1, C3]) - widthBox / 2 + ((0.1 + ((num * factor) * 1.2)) * radius), y(Midpoint[C1, C3]) + (((-heightReference)) / 2 * radius)), (x(Midpoint[C1, C3]) - widthBox / 2 + ((0.1 + ((num * factor) * 1.2)) * radius), y(Midpoint[C1, C3]) + ((1.4 - heightReference / 2) * radius)), (x(Midpoint[C1, C3]) - widthBox / 2, y(Midpoint[C1, C3]) + ((1.4 - heightReference / 2) * radius))}) → boxUncomplete
  28. Take(centersTotal, marblesBox + 1, Length[centersTotal]) → centersNotTop
  29. Sequence(Circle[Element[centersTotal, k], radius / 2], k, input1 + 1, (marblesBox * numBoxes)) → marblesMissingTotal
  30. If(animStep < 3, 0, animStep > 3, goalOpac, ((time - timePurple) * goalOpac / (timeFading - timePurple))) → fadingOpac
  31. Zip(Circle[P, radius / 2], P, centersNotTop) → fading
  32. Corner(5) → Appsize

AI 绘图提示语参考

画一个包含若干个盒子和小球的图形。首先画一个边界框，然后在框内随机分布一些盒子，每个盒子内随机放置一些小球。接着，根据给定的数字，从盒子中移除一些小球，并用不同颜色标记这些小球。最后，根据剩余小球的数量，动态显示剩余小球的动画效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。