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分数大小比较与中点问题

分数大小比较与中点问题
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2023-11-29 21:38
数列解析几何几何作图滑块动画
所属专题 Ordnen und Vergleichen von Bruchzahlen
①本范例演示如何在 GeoGebra 中比较两个分数的大小，并找出它们之间的中点分数；②涉及的核心数学概念包括分数比较、中点计算、有理数概念；③作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Sequence（数列生成）、Circle（圆）、Textfield（文本框）、SpeechBubbleLeft（左侧文本气泡）、Midpoint（中点）、Point（点）、Segment（线段）、Join（连接）、Polygon（多边形）、IsInRegion（区域判断）、If（条件判断）、Text（文本显示）；④适合的学段或用途：小学高年级（5-6年级），用于教授和练习分数大小比较和有理数概念。

GeoGebra 命令及参数

  1. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 10), i, 0, 1) → U2Rechts
  2. Sequence(Zentrum + ((Vector[ZSR, ZSL] * 7) * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 10), i, 0, 6) → U2Links
  3. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 5), i, 0, 1) → U1Rechts
  4. Sequence(Zentrum + ((Vector[ZSR, ZSL] * 15) * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 5), i, 0, 3) → U1Links
  5. Circle(U1Rechts(1), 0.3) → B2Goal
  6. Circle(U1Links(2), 0.3) → B1Goal
  7. Textfield(input1) → InputBox1
  8. Textfield(input2) → InputBox2
  9. Textfield(input3) → InputBox3
  10. Textfield(input4) → InputBox4
  11. SpeechBubbleLeft(SpeechA1, 9, 3) → Step1Speech
  12. SpeechBubbleLeft(SpeechSpecial, 10.5, 2.4) → Step2Speech
  13. SpeechBubbleLeft(SpeechA2, 12, 1.5) → Step3Speech
  14. Midpoint(U1Links(1), U1Rechts(1)) → MPetrol1
  15. Circle(MPetrol1, 2.8) → Petrol1
  16. SpeechBubbleLeft(SpeechA4, 12, 2.5) → Step4Speech
  17. Point(StaengelPunkte) → ZoomPunkt
  18. Segment(StaengelStart, StaengelEnd) → Staengel
  19. SpeechBubbleLeft(SpeechA5, 11, 3) → Step5Speech
  20. Midpoint(U2Links(1), U2Rechts(1)) → MPetrol2
  21. Circle(MPetrol2, 2.8) → Petrol2
  22. SpeechBubbleLeft(SpeechA7, 11, 3) → Step7Speech
  23. Textfield(input5) → InputBox5
  24. Textfield(input6) → InputBox6
  25. SpeechBubbleLeft(SpeechA8, 11, 3) → Step8Speech
  26. SpeechBubbleLeft(SpeechA9, 11.5, 2.2) → Step9Speech
  27. Segment(ZSL, ZSR) → h
  28. Sequence(Zentrum + ((Vector[ZSR, ZSL] * 3) * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 20), i, 0, 14) → U3Links
  29. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 20), i, 0, 3) → U3Rechts
  30. Sequence(Zentrum + (Vector[ZSR, ZSL] * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 40), i, 0, 30) → U4Links
  31. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 40), i, 0, 7) → U4Rechts
  32. Sequence(Zentrum + ((Vector[ZSR, ZSL] * i) * masterzoom / 80), i, 0, 10) → U5Links
  33. Sequence(Zentrum - ((Vector[ZSR, ZSL] * i) * masterzoom / 80), i, 0, 7) → U5Rechts
  34. Join({Sequence[Segment[U1Links(i) + (0, 0.15), U1Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U1Rechts(i) + (0, 0.15), U1Rechts(i) + (0, -0.15)], i, 1, 5]}) → U1Strecken
  35. Join({Sequence[Segment[U2Links(i) + (0, 0.15), U2Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U2Rechts(i) + (0, 0.15), U2Rechts(i) + (0, -0.15)], i, 1, 5]}) → U2Strecken
  36. Join({Sequence[Segment[U3Links(i) + (0, 0.15), U3Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U3Rechts(i) + (0, 0.15), U3Rechts(i) + (0, -0.15)], i, 1, 5]}) → U3Strecken
  37. Join({Sequence[Segment[U4Links(i) + (0, 0.15), U4Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U4Rechts(i) + (0, 0.15), U4Rechts(i) + (0, -0.15)], i, 1, 5]}) → U4Strecken
  38. Join({Sequence[Segment[U5Links(i) + (0, 0.15), U5Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U5Rechts(i) + (0, 0.15), U5Rechts(i) + (0, -0.15)], i, 1, 5]}) → U5Strecken
  39. Segment(C, ZSL) → i
  40. Segment(ZSR, D) → j
  41. Segment(U1Links(4) + (0, 0.3), U1Links(4) + (0, -0.3)) → f
  42. Segment(U1Rechts(2) + (0, 0.3), U1Rechts(2) + (0, -0.3)) → g
  43. Polygon({WhiteCheese1E1, WhiteCheese1E2, WhiteCheese2E2, WhiteCheese2E1}) → validatebox
  44. IsInRegion(B1Pos, validatebox) → b1inbox
  45. IsInRegion(B2Pos, validatebox) → b2inbox
  46. IsInRegion(B1Pos, B1Goal) → b1correct
  47. IsInRegion(B2Pos, B2Goal) → b2correct
  48. Midpoint(U, Q) → PlusZoom1
  49. Midpoint(R, Q) → PlusZoom2
  50. Midpoint(S, R) → PlusZoom3
  51. Midpoint(T, S) → PlusZoom4
  52. Join({Sequence[Segment[PlusZoomPunkte(i) + (0, 0.15), PlusZoomPunkte(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[PlusZoomPunkte(i) + (0, 0.15), PlusZoomPunkte(i) + (0, -0.15)], i, 1, 4]}) → PlusZoomStrecken
  53. If(step ≟ 3, 2 / 5, step ≟ 5, 3 / 5, 7 / 10) → grenzelinks
  54. If(step ≟ 3, input1 / input2 ≠ grenzesol ∧ grenzelinks < input1 / input2 < grenzerechts, step ≟ 5, input3 / input4 ≠ grenzesol ∧ grenzelinks < input3 / input4 < grenzerechts, input5 / input6 ≠ grenzesol ∧ grenzelinks < input5 / input6 < grenzerechts) → showhint
  55. If(masterzoom < 1.5, 5, 160, 1.5 ≤ masterzoom < 3, 10, 3 ≤ masterzoom < 6, 20, 6 ≤ masterzoom < 12, 40, 12 ≤ masterzoom < 22, 80) → maxnenner
  56. If(maxnenner ≟ 160, 1, maxnenner ≟ 5, 32, maxnenner ≟ 80, 2, maxnenner ≟ 40, 4, maxnenner ≟ 20, 8, maxnenner ≟ 10, 16) → helperdiv
  57. Text(Dyn35, U1Links(1) + (0, 0.9), false, true, 0, 0) → Text35
  58. Text(Dyn1320, U3Links(3) + (0, 0.9), false, true, 0, 0) → Text37
  59. Text(Dyn710, U2Links(1) + (0, 0.9), false, true, 0, 0) → Text38
  60. Text(Dyn1520, U3Links(1) + (0, 0.9), false, true, 0, 0) → Text39
  61. Text(Dyn45, U1Rechts(1) + (0, 0.9), false, true, 0, 0) → Text40
  62. Text(Dyn2940, U4Links(3) + (0, 0.9), false, true, 0, 0) → Text41
  63. Text(Dyn3140, U4Links(1) + (0, 0.9), false, true, 0, 0) → Text42
  64. Text(Dyn6180, U5Links(3) + (0, 0.9), false, true, 0, 0) → Text43
  65. Text(Dyn6380, U5Links(1) + (0, 0.9), false, true, 0, 0) → Text44

AI 绘图提示语参考

在坐标平面上画出若干竖直的标尺刻度区：用一条基准线与方向向量生成多列等距的点序列，并在两侧分别放置左右刻度点。以中间两端的点为界绘制多段短线条并形成网格状的标识。再标出两圆形目标区域：分别以两处中点为圆心画半径相同的圆，用于表示“目标答案”。同时准备若干可输入框用于比较与取中点，并放置引导文字气泡说明步骤。最后再取对应的中点并画出另一圆形目标区域，连同用于校验的区域边界多边形与包含判断区域一起呈现。
以上提示语为根据原始绘图命令整理而来，仅供参考。