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Gegenzahl：分数输入与数轴表示

Gegenzahl：分数输入与数轴表示
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2024-12-16 19:45
所属专题 Gegenzahl und Betrag einer rationalen Zahl
Gegenzahl范例演示如何将分数转换为数轴上的位置。核心数学概念包括绝对值、数轴表示和分数转换。作图要点包括使用Textfield输入分数、Polygon绘制数轴、Shuffle随机排列点、Distance测量距离、Circle绘制圆圈等。适合小学7-8年级学生，用于理解分数与数轴的关系。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  4. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {6, 4, 8, 10, 3, 7, 4, 9, 5, 7, 3, 8, 4, 8, 3, 5, 1, 8, 2, 0, 9, 4, 9, 1, 2, 2, 6, 8, 8, 10, 5, 1, 0, 3, 8, 8, 2, 10, 0, 6, 4, 3, 9, 8, 5, 2, 8, 7, 5, 8, 2, 6, 4, 8, 3, 3, 8, 3, 1, 6, 5, 6, 1, 6, 1, 1, 8, 10, 10, 1, 10, 8, 9, 3, 7, 3, 0, 9, 10, 4, 0, 9, 9, 5, 0, 3, 8, 1, 0, 4, 10, 9, 3, 6, 2, 2, 2, 8, 0, 4}
  5. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  6. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 0, 0, 6, 4, 5, 1, 9, 2, 9, 1, 7, 0, 7, 7, 0, 7, 2, 3, 1, 10, 1, 2, 3, 7, 4, 3, 10, 5, 4, 0, 10, 7, 6, 9, 0, 7, 0, 3, 0, 6, 8, 7, 4, 0, 7, 0, 8, 2, 7, 7, 9, 0, 7, 10, 0, 10, 3, 3, 5, 8, 2, 8, 5, 10, 7, 4, 9, 8, 4, 4, 3, 8, 9, 0, 10, 7, 5, 7, 6, 9, 5, 6, 3, 4, 0, 3, 10, 7, 4, 10, 1, 2, 1, 10, 2, 1, 9, 3, 9}
  7. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  8. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  9. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  10. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  11. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  12. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  13. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  14. Shuffle(1…10) → ExNumList, {6, 4, 8, 9, 2, 5, 7, 3, 1, 10}
  15. Length(ExNumList) → questionCountMax
  16. Shuffle({1, 2, 3}) → NumListModMid, {3, 1, 2}
  17. If(questionCount ≤ 3, 1, 2) → metaprogression
  18. If(metaprogression ≟ 1, NumListModStart(questionCount), NumListModMid(modindex)) → mod
  19. Shuffle(Sequence[i, i, 1, If[mod ≟ 1, 1, mod ≟ 2, 3, 2]]) → SubGroupList, {1}
  20. If(mod ≟ 1, 15, 1 + 7 / 8, mod ≟ 2 ∧ subgroup ≟ 1, 7.5, mod ≟ 2 ∧ subgroup ≟ 2, 3, mod ≟ 2 ∧ subgroup ≟ 3, 1.5, mod ≟ 3 ∧ subgroup ≟ 1, 1.5) → grenze
  21. Sequence(GeradePLinks + ((Length[Segment[GeradePLinks, GeradePRechts]] * i / 30), 0), i, 0, 30) → GeradePoints
  22. Sequence(Segment[GeradePoints(i) + (0, dyStriche), GeradePoints(i) + (0, (-dyStriche))], i, 1, 31) → l2
  23. Segment(GeradePLinks + (-0.3, 0), GeradePRechts + (0.3, 0)) → g
  24. Shuffle(Sequence[i, i, -15, 15]) → NumListGanzeRaw, {-14, -10, 7, -7, 6, -12, -6, 4, -2, 13, 3, -1, -9, -13, 9, 5, 15, 12, 1, 11, 14, -5, -8, 8, 0, 2, -11, -15, -3, -4, 10}
  25. Shuffle(Sequence[(0.5 * i), i, -15, 15]) → NumListDezi1Raw, {-2.5, 4.5, 4, 6.5, 2, -5, 7.5, -4, 3, 1.5, -2, 6, 7, 2.5, -5.5, 1, -1, -3, -4.5, -0.5, 0.5, -1.5, 0, 5.5, 5, -7.5, -6, -3.5, -6.5, 3.5, -7}
  26. Shuffle(Sequence[(0.2 * i), i, -15, 15]) → NumListDezi2Raw, {-1.2000000000000002, 1.8, -0.6000000000000001, -1.8, 2.6, 1, -2.8000000000000003, -0.4, 1.6, -0.2, 3, -3, -0.8, 2.2, 0.2, -1.6, 1.2000000000000002, 2.4000000000000004, 0.8, 2, -2.6, 0.4, -2.4000000000000004, 0, 0.6000000000000001, -2.2, -1, 1.4000000000000001, -1.4000000000000001, 2.8000000000000003, -2}
  27. Shuffle(Sequence[(i * 0.1), i, -15, 15]) → NumListDezi3Raw, {-1, -1.5, 0, -1.2000000000000002, 0.7000000000000001, 1.3, 1, -0.2, 1.2000000000000002, -1.1, 0.1, 0.9, 1.4000000000000001, 0.4, -0.7000000000000001, -0.4, 0.2, -1.4000000000000001, -0.9, -0.6000000000000001, 0.5, 0.30000000000000004, 1.1, -0.5, 0.8, -0.8, -0.1, 1.5, -1.3, -0.30000000000000004, 0.6000000000000001}
  28. Shuffle({2, 5, 10}) → NumListFracNenner1, {5, 2, 10}
  29. Shuffle({2, 4, 8}) → NumListFracNenner2, {8, 4, 2}
  30. If(subgroup ≟ 1, NumListFracNenner1(1), NumListFracNenner2(1)) → nenner
  31. Shuffle(Sequence[i, i, (-floor((nenner * 1.5))), floor((nenner * 1.5))]) → NumListFracZaehlerRaw, {-1, 5, 4, -5, -3, 0, -7, 7, 6, -2, -4, -6, 2, 3, 1}
  32. Shuffle({-1, 1}) → VorzeichenShuffle, {1, -1}
  33. If(mod ≟ 1, (vorzeichen * abs(NumListGanze(1))), mod ≟ 2 ∧ subgroup ≟ 1, (vorzeichen * abs(NumListDezi1(1))), mod ≟ 2 ∧ subgroup ≟ 2, (vorzeichen * abs(NumListDezi2(1))), mod ≟ 2 ∧ subgroup ≟ 3, (vorzeichen * abs(NumListDezi3(1))), mod ≟ 3, (vorzeichen * abs(zaehler / nenner))) → xvalue
  34. Distance(GeradePoints(1), GeradePoints(2)) → distP
  35. Circle(SolMark, toleranz) → solCirc
  36. Sequence(C + ((Length[Segment[GeradePLinks, GeradePRechts]] * i / 30), 0), i, 0, 30) → SoloStartGerade
  37. Join({SoloStartGerade, GeradePoints}) → InputPunktList
  38. Point(InputPunktList) → InputPunkt
  39. IsInRegion(InputPunkt, solCirc) → correct1
  40. Text(solutionText, SolMark + (0, (dyBesch * 1.5)), false, true, 0, 0) → SolText
  41. Text(NumTxtMaster, xPos + (0, (1.7 * dyBesch)), false, true, 0, 0) → Text2
  42. Segment(D, D + ((-dArrow), 0)) → f
  43. Polygon(InputPunkt, InputPunkt + (1, 1), 2) → Vieleck1, h_{1}, i_{1}
  44. Polygon(InputPunkt + (sizeVR, sizeVR), InputPunkt + (sizeVR, (-sizeVR)), InputPunkt + ((-sizeVR), (-sizeVR)), InputPunkt + ((-sizeVR), sizeVR)) → v1, h, i, j, k
  45. Text(NumTxtMasterGegen, SolMark + (0, (3.5 * dyBesch)), false, true, 0, 0) → Text9
  46. Text(solutionText, E, false, true, 0, 0) → SolTextZuWeitLinks
  47. If(¬zuweitlinks, (-0.6, 1), (-0.3, 1)) → F