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在数轴上定位分数

在数轴上定位分数
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2020-11-03 09:09
数列几何作图函数图像
① 本范例演示了如何将分数拖动到数轴上的正确位置，并通过即时反馈检验理解。② 核心数学概念包括分数的意义、数轴上的点与有理数的对应关系，以及分数大小比较。③ 作图要点：使用GeoGebra的If、Vector、Sequence命令构建多个可拖动的分数点（如fracX41等）和对应的目标位置集合（Frac4PtSet1等），通过条件判断（If）和序列（Sequence）生成反馈机制，并利用向量（Vector）辅助定位。④ 适合小学高年级至初中阶段学习分数与数轴的学生，也可用于教师课堂演示或学生自主练习，帮助直观建立分数与数轴位置的对应关系。

GeoGebra 命令及参数

  1. If(set ≟ 1, Frac4PtSet1, If[set ≟ 2, Frac4PtSet2, If[set ≟ 3, Frac4PtSet3, If[set ≟ 4, Frac4PtSet4, If[set ≟ 5, Frac4PtSet5, Frac4PtSet6]]]]) → frac4MasterPt
  2. If(set ≟ 1 ∧ ckPlaceSet1, true, If[set ≟ 2 ∧ ckPlaceSet2, true, If[set ≟ 3 ∧ ckPlaceSet3, true, If[set ≟ 4 ∧ ckPlaceSet4, true, If[set ≟ 5 ∧ ckPlaceSet5, true, If[set ≟ 6 ∧ ckPlaceSet6, true, false]]]]]) → placeMasterYN
  3. If(x(frac4MasterPt) < x(dotA) + snapHorAmt ∧ x(frac4MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac4MasterPt) < x(dotB) + snapHorAmt ∧ x(frac4MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac4MasterPt) < x(dotC) + snapHorAmt ∧ x(frac4MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac4MasterPt) < x(dotD) + snapHorAmt ∧ x(frac4MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac4MasterPt) < x(dotE) + snapHorAmt ∧ x(frac4MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac4MasterPt) < x(dotF) + snapHorAmt ∧ x(frac4MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac4MasterPt) < x(dotG) + snapHorAmt ∧ x(frac4MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac4MasterPt)]]]]]]) → frac4X
  4. If(set ≟ 1, Frac3PtSet1, If[set ≟ 2, Frac3PtSet2, If[set ≟ 3, Frac3PtSet3, If[set ≟ 4, Frac3PtSet4, If[set ≟ 5, Frac3PtSet5, Frac3PtSet6]]]]) → frac3MasterPt
  5. If(x(frac3MasterPt) < x(dotA) + snapHorAmt ∧ x(frac3MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac3MasterPt) < x(dotB) + snapHorAmt ∧ x(frac3MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac3MasterPt) < x(dotC) + snapHorAmt ∧ x(frac3MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac3MasterPt) < x(dotD) + snapHorAmt ∧ x(frac3MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac3MasterPt) < x(dotE) + snapHorAmt ∧ x(frac3MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac3MasterPt) < x(dotF) + snapHorAmt ∧ x(frac3MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac3MasterPt) < x(dotG) + snapHorAmt ∧ x(frac3MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac3MasterPt)]]]]]]) → frac3X
  6. If(set ≟ 1, Frac2PtSet1, If[set ≟ 2, Frac2PtSet2, If[set ≟ 3, Frac2PtSet3, If[set ≟ 4, Frac2PtSet4, If[set ≟ 5, Frac2PtSet5, Frac2PtSet6]]]]) → frac2MasterPt
  7. If(x(frac2MasterPt) < x(dotA) + snapHorAmt ∧ x(frac2MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac2MasterPt) < x(dotB) + snapHorAmt ∧ x(frac2MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac2MasterPt) < x(dotC) + snapHorAmt ∧ x(frac2MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac2MasterPt) < x(dotD) + snapHorAmt ∧ x(frac2MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac2MasterPt) < x(dotE) + snapHorAmt ∧ x(frac2MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac2MasterPt) < x(dotF) + snapHorAmt ∧ x(frac2MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac2MasterPt) < x(dotG) + snapHorAmt ∧ x(frac2MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac2MasterPt)]]]]]]) → frac2X
  8. If(set ≟ 1, Frac1PtSet1, If[set ≟ 2, Frac1PtSet2, If[set ≟ 3, Frac1PtSet3, If[set ≟ 4, Frac1PtSet4, If[set ≟ 5, Frac1PtSet5, Frac1PtSet6]]]]) → frac1MasterPt
  9. If(x(frac1MasterPt) < x(dotA) + snapHorAmt ∧ x(frac1MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac1MasterPt) < x(dotB) + snapHorAmt ∧ x(frac1MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac1MasterPt) < x(dotC) + snapHorAmt ∧ x(frac1MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac1MasterPt) < x(dotD) + snapHorAmt ∧ x(frac1MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac1MasterPt) < x(dotE) + snapHorAmt ∧ x(frac1MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac1MasterPt) < x(dotF) + snapHorAmt ∧ x(frac1MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac1MasterPt) < x(dotG) + snapHorAmt ∧ x(frac1MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac1MasterPt)]]]]]]) → frac1X
  10. Vector((1, 0), (-0.2, 0)) → numLnL
  11. Vector((1, 0), (2.2, 0)) → numLnR
  12. Sequence((k - 0.037, -0.25), k, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → labelPtList
  13. If(x(Frac1PtLn) ≤ 2.2 ∧ x(Frac2PtLn) ≤ 2.2 ∧ x(Frac3PtLn) ≤ 2.2 ∧ x(Frac4PtLn) ≤ 2.2 ∧ x(Frac1PtLn) ≥ -0.2 ∧ x(Frac2PtLn) ≥ -0.2 ∧ x(Frac3PtLn) ≥ -0.2 ∧ x(Frac4PtLn) ≥ -0.2 ∧ y(Frac1PtLn) ≟ 0 ∧ y(Frac2PtLn) ≟ 0 ∧ y(Frac3PtLn) ≟ 0 ∧ y(Frac4PtLn) ≟ 0, true, false) → allOnLine
  14. If(x(Frac4PtLn) / Element[numLnMax, set] ≥ Element[frac4Num, set] / Element[frac4Denom, set] - 0.016 ∧ x(Frac4PtLn) / Element[numLnMax, set] ≤ Element[frac4Num, set] / Element[frac4Denom, set] + 0.016, true, false) → frac4PlaceYN
  15. If(x(Frac3PtLn) / Element[numLnMax, set] ≥ Element[frac3Num, set] / Element[frac3Denom, set] - 0.016 ∧ x(Frac3PtLn) / Element[numLnMax, set] ≤ Element[frac3Num, set] / Element[frac3Denom, set] + 0.016, true, false) → frac3PlaceYN
  16. If(x(Frac2PtLn) / Element[numLnMax, set] ≥ Element[frac2Num, set] / Element[frac2Denom, set] - 0.016 ∧ x(Frac2PtLn) / Element[numLnMax, set] ≤ Element[frac2Num, set] / Element[frac2Denom, set] + 0.016, true, false) → frac2PlaceYN
  17. If(x(Frac1PtLn) / Element[numLnMax, set] ≥ Element[frac1Num, set] / Element[frac1Denom, set] - 0.016 ∧ x(Frac1PtLn) / Element[numLnMax, set] ≤ Element[frac1Num, set] / Element[frac1Denom, set] + 0.016, true, false) → frac1PlaceYN
  18. If(set ≟ 1 ∧ ckHintSet1, true, If[set ≟ 2 ∧ ckHintSet2, true, If[set ≟ 3 ∧ ckHintSet3, true, If[set ≟ 4 ∧ ckHintSet4, true, If[set ≟ 5 ∧ ckHintSet5, true, If[set ≟ 6 ∧ ckHintSet6, true, false]]]]]) → hintMasterYN
  19. Vector(frac3MasterPt + (0.04, -1.5), Frac3PtLn + (0, 0.2)) → Frac3Seg
  20. Vector(frac1MasterPt + (0.04, -1.5), Frac1PtLn + (0, 0.2)) → Frac1Seg
  21. Vector(frac2MasterPt + (0.04, -1.5), Frac2PtLn + (0, 0.2)) → Frac2Seg
  22. Vector(frac4MasterPt + (0.04, -1.5), Frac4PtLn + (0, 0.2)) → Frac4Seg
  23. Sequence(Segment[(i, 0.28), (i, -0.28)], i, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → scaleHashZXaxis
  24. If(set ≟ 1 ∧ ckHintSet1b, true, If[set ≟ 2 ∧ ckHintSet2b, true, If[set ≟ 3 ∧ ckHintSet3b, true, If[set ≟ 4 ∧ ckHintSet4b, true, If[set ≟ 5 ∧ ckHintSet5b, true, If[set ≟ 6 ∧ ckHintSet6b, true, false]]]]]) → hintMasterYNb
  25. Sequence((0.26 + j, 3.7), j, 0, 1.5, 0.498) → fracAlignPts

AI 绘图提示语参考

在一条水平线上创建一个数轴，标出多个等距的点，每个点代表一个分数。设计可拖动的分数点，让它们能自动吸附到数轴上最接近的正确位置。根据分数大小和拖动位置，显示反馈信息，如分数是否放置正确。数轴上有标签，分数点旁边有对应的分数标签，整体用于教学演示分数与数轴位置的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。