积极 AI Logo 积极 AI

在数轴上定位小数（2）

在数轴上定位小数（2）
几何画板及绘图内容加载中，请稍等……
2018-09-20 23:13
函数三角函数解析几何几何作图滑块动画
本范例演示如何在数轴上正确放置小数分数，并获取即时反馈。这是一个更具挑战性的版本，使用了不同的端点。涉及的核心数学概念包括数轴、小数、有理数和实数。作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Polygon（多边形）、PointIn（点在内部判断）、If（条件判断）、Vector（向量）、Sequence（序列）；对象：set（集合）、restrictPts（限制点）、f、h、i、j、Frac4PtSet1至Frac4PtSet6、Frac4PtSet1、frac4MasterPt、numLnMax、PtA至PtF、dotA至dotF、ckPlaceSet1至ckPlaceSet6、placeMasterYN、snapHorAmt、frac4X、snapHorHeight、snapVertAmt、Frac3PtSet1。适合初中及以上数学教学，用于帮助学生理解和掌握小数在数轴上的位置。

GeoGebra 命令及参数

  1. Polygon((-0.05, 0.4), (2.05, 0.4), (2.05, 3.3), (-0.05, 3.3)) → restrictPts, f, h, i, j
  2. PointIn(restrictPts) → Frac4PtSet1
  3. PointIn(restrictPts) → Frac4PtSet2
  4. PointIn(restrictPts) → Frac4PtSet3
  5. PointIn(restrictPts) → Frac4PtSet4
  6. PointIn(restrictPts) → Frac4PtSet5
  7. PointIn(restrictPts) → Frac4PtSet6
  8. If(set ≟ 1, Frac4PtSet1, If[set ≟ 2, Frac4PtSet2, If[set ≟ 3, Frac4PtSet3, If[set ≟ 4, Frac4PtSet4, If[set ≟ 5, Frac4PtSet5, Frac4PtSet6]]]]) → frac4MasterPt
  9. 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
  10. 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
  11. PointIn(restrictPts) → Frac3PtSet1
  12. PointIn(restrictPts) → Frac3PtSet2
  13. PointIn(restrictPts) → Frac3PtSet3
  14. PointIn(restrictPts) → Frac3PtSet4
  15. PointIn(restrictPts) → Frac3PtSet5
  16. PointIn(restrictPts) → Frac3PtSet6
  17. If(set ≟ 1, Frac3PtSet1, If[set ≟ 2, Frac3PtSet2, If[set ≟ 3, Frac3PtSet3, If[set ≟ 4, Frac3PtSet4, If[set ≟ 5, Frac3PtSet5, Frac3PtSet6]]]]) → frac3MasterPt
  18. 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
  19. PointIn(restrictPts) → Frac2PtSet1
  20. PointIn(restrictPts) → Frac2PtSet2
  21. PointIn(restrictPts) → Frac2PtSet3
  22. PointIn(restrictPts) → Frac2PtSet4
  23. PointIn(restrictPts) → Frac2PtSet5
  24. PointIn(restrictPts) → Frac2PtSet6
  25. If(set ≟ 1, Frac2PtSet1, If[set ≟ 2, Frac2PtSet2, If[set ≟ 3, Frac2PtSet3, If[set ≟ 4, Frac2PtSet4, If[set ≟ 5, Frac2PtSet5, Frac2PtSet6]]]]) → frac2MasterPt
  26. 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
  27. PointIn(restrictPts) → Frac1PtSet1
  28. PointIn(restrictPts) → Frac1PtSet6
  29. PointIn(restrictPts) → Frac1PtSet2
  30. PointIn(restrictPts) → Frac1PtSet3
  31. PointIn(restrictPts) → Frac1PtSet4
  32. PointIn(restrictPts) → Frac1PtSet5
  33. If(set ≟ 1, Frac1PtSet1, If[set ≟ 2, Frac1PtSet2, If[set ≟ 3, Frac1PtSet3, If[set ≟ 4, Frac1PtSet4, If[set ≟ 5, Frac1PtSet5, Frac1PtSet6]]]]) → frac1MasterPt
  34. 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
  35. Vector((1, 0), (-0.2, 0)) → numLnL
  36. Vector((1, 0), (2.2, 0)) → numLnR
  37. Sequence((k - 0.02, -0.75), k, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → labelPtList
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. 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
  44. Sequence(Segment[(i, 0.28), (i, -0.28)], i, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → scaleHashXaxis
  45. Sequence((0.26 + j, 3), j, 0, 1.5, 0.498) → fracAlignPts