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分数除法问题与条形模型

分数除法问题与条形模型
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2016-12-29 02:27
函数解析几何几何作图滑块动画
本范例通过条形模型的可视化表示，帮助理解分数除法的概念以及余数的含义。在确定巨型……的份量时，该模型直观展示了分数除法的计算过程。涉及的核心数学概念包括分数除法、余数的意义以及条形图的应用。在GeoGebra构造中，使用了Element、Polygon、Segment、Point、If、Sequence、Textfield、Vector等命令和对象来绘制条形模型、计算结果并展示解题步骤。适合初中数学教学，帮助学生直观理解抽象的分数除法运算。

GeoGebra 命令及参数

  1. Element({1, 1.3, 1, 0.6, 1, 0.8, 0.8, 0.8, 1.4, 1.2}, prob) → scaleFactor
  2. Polygon(BoxPt + (((fullServ * divisor) * scaleFactor), remainShade2lower - boxHeight - 0.1), BoxPt + (((fullServ * divisor) * scaleFactor) + (divisor * scaleFactor), remainShade2lower - boxHeight - 0.1), BoxPt + (((fullServ * divisor) * scaleFactor) + (divisor * scaleFactor), remainShade2lower - 0.1), BoxPt + (((fullServ * divisor) * scaleFactor), remainShade2lower - 0.1)) → remainDivisor, remainDivisorSeg_1, remainDivisorSeg_2, remainDivisorSeg_3, remainDivisorSeg
  3. Segment(Midpoint[remainDivisorSeg_1] - (0.5, 0.5), Midpoint[remainDivisorSeg_1] + (0.5, -0.5)) → step2SplitSeg
  4. Point(step2SplitSeg) → Step2SplitSegPt7
  5. Point(step2SplitSeg) → Step2SplitSegPt10
  6. Point(step2SplitSeg) → Step2SplitSegPt9
  7. Point(step2SplitSeg) → Step2SplitSegPt8
  8. Point(step2SplitSeg) → Step2SplitSegPt6
  9. Point(step2SplitSeg) → Step2SplitSegPt5
  10. Point(step2SplitSeg) → Step2SplitSegPt4
  11. Point(step2SplitSeg) → Step2SplitSegPt3
  12. Point(step2SplitSeg) → Step2SplitSegPt2
  13. Point(step2SplitSeg) → Step2SplitSegPt1
  14. Polygon(BoxPt, BoxPt + ((dividend * scaleFactor), 0), BoxPt + ((dividend * scaleFactor), boxHeight), BoxPt + (0, boxHeight)) → dividendBoxPoly, dividendBox_2, dividendBox_3, dividendBox_4, dividendBox
  15. Polygon(BoxPt + (0, (-boxHeight) - 0.1), BoxPt + (((divisor * If[fullServ ≥ 0 ∧ showFullServ, fullServ, 1]) * scaleFactor), (-boxHeight) - 0.1), BoxPt + (((divisor * If[fullServ ≥ 0 ∧ showFullServ, fullServ, 1]) * scaleFactor), -0.1), BoxPt + (0, -0.1)) → servBox, servBoxSeg_1, servBoxSeg_2, servBoxSeg_3, servBoxSeg
  16. If(dividend - (fullServ * divisor) < 0, 1, If[dividend - (fullServ * divisor) > divisor, 2, 3]) → fullServFBSelect
  17. Polygon(BoxPt + (((fullServ * divisor) * scaleFactor), remainShade2lower), BoxPt + ((dividend * scaleFactor), remainShade2lower), BoxPt + ((dividend * scaleFactor), remainShade2lower + boxHeight), BoxPt + (((fullServ * divisor) * scaleFactor), remainShade2lower + boxHeight)) → remainShade2, remainShade2Seg_1, remainShade2Seg_2, remainShade2Seg_3, remainShade2Seg
  18. Polygon(BoxPt + (((fullServ * divisor) * scaleFactor), 0), BoxPt + ((dividend * scaleFactor), 0), BoxPt + ((dividend * scaleFactor), boxHeight), BoxPt + (((fullServ * divisor) * scaleFactor), boxHeight)) → remainShade1, remainShade1Seg_1, remainShade1Seg_2, remainShade1Seg_3, remainShade1Seg
  19. Polygon(Step1ArrowsPt + (0, 0.05), Step1ArrowsPt + (0.3, 0.05), Step1ArrowsPt + (0.15, 0.4)) → step1ArrowUp, step1ArrowSeg_2, step1ArrowSeg_3, step1ArrowSeg_4
  20. Polygon(Step1ArrowsPt + (0, -0.05), Step1ArrowsPt + (0.3, -0.05), Step1ArrowsPt + (0.15, -0.4)) → step1ArrowDown, step1ArrowSeg_1, step1ArrowSeg_5, step1ArrowSeg
  21. Sequence(Segment[BoxPt + (i, (-boxHeight) - 0.1), BoxPt + (i, -0.1)], i, (divisor * scaleFactor), ((divisor * scaleFactor) * (fullServ - 1)), (divisor * scaleFactor)) → servBoxDiv
  22. If(ansFrac ≟ remainNum / remainDenom, true, false) → step2Verify
  23. Element({"Ted", "Alex", "Jasmine", "Miguel", "Alessa", "Mohammad", "Georgia", "Jasper", "Frankie", "Doug"}, prob) → names
  24. Textfield(solutionWhole) → inputSolutionWhole
  25. Textfield(solutionNum) → inputSolutionNum
  26. If(step3Check ∧ ansFrac ≟ solutionNum / solutionDenom ∧ solutionWhole ≟ ansWhole, true, false) → step3Verify
  27. Textfield(solutionDenom) → inputSolutionDenom
  28. Polygon(ServKeyPt, ServKeyPt + (((-divisor) * scaleFactor), 0), ServKeyPt + (((-divisor) * scaleFactor), boxHeight), ServKeyPt + (0, boxHeight)) → servKey, servKeySeg_1, servKeySeg_2, servKeySeg_3, servKeySeg
  29. Vector(Midpoint[BoxPt + (((fullServ * divisor) * scaleFactor), -0.2), BoxPt + ((dividend * scaleFactor), -0.2)], Midpoint[BoxPt + (((fullServ * divisor) * scaleFactor), remainShade2lower + boxHeight + 0.1), BoxPt + ((dividend * scaleFactor), remainShade2lower + boxHeight + 0.1)]) → remainVector
  30. Sequence(Segment[BoxPt + (((fullServ * divisor) * scaleFactor) + i, remainShade2lower - boxHeight - 0.1), BoxPt + (((fullServ * divisor) * scaleFactor) + i, remainShade2lower - 0.1)], i, ((scaleFactor * divisor)) / step2DivisorSections, (((scaleFactor * divisor)) / step2DivisorSections * (step2DivisorSections - 1)), ((scaleFactor * divisor)) / step2DivisorSections) → divisorSectionsList
  31. Sequence(Segment[BoxPt + (i, -0.18), BoxPt + (i, boxHeight + 0.25)], i, (divisor * scaleFactor), ((divisor * scaleFactor) * fullServ), (divisor * scaleFactor)) → sandwichBoxSections
  32. Segment(BoxPt + ((dividend * scaleFactor), remainShade2lower + boxHeight + 0.2), BoxPt + ((dividend * scaleFactor), remainShade2lower - 1.08)) → step2AlignmentSeg
  33. Textfield(remainDenom) → inputRemainDenom
  34. Textfield(remainNum) → inputRemainNum

AI 绘图提示语参考

画一个分数除法的条形模型图，展示如何用条形分割来理解分数除法和余数的意义。包含多个条形，分别代表总数、除数、商和余数，用不同颜色或阴影区分。先画出代表总数的条形，再根据除数分割，标出商和余数部分，最后用箭头或文字说明计算过程和结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。