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绝对值的演示与解释

绝对值的演示与解释
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2024-12-16 19:46
所属专题 Gegenzahl und Betrag einer rationalen Zahl
①本范例演示了如何在 GeoGebra 中输入分数并解释绝对值的几何意义；②核心数学概念包括绝对值、数轴上的距离、整数运算；③构造要点：使用了 Textfield, Shuffle, If, Sequence, Distance, Point, Polygon, Element, Append, Remove, Length, Segment, Circle, Text 等命令和对象来创建交互式演示；④适合初中七、八年级学生，用于理解绝对值的定义和应用。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle({1, 2, 3}) → NumListModMid, {3, 2, 1}
  4. If(questionCount ≤ 3, 1, 2) → metaprogression
  5. If(metaprogression ≟ 1, NumListModStart(questionCount), NumListModMid(modindex)) → mod
  6. Shuffle(Sequence[i, i, 1, If[mod ≟ 1, 1, mod ≟ 2, 3, 2]]) → SubGroupList, {1}
  7. 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
  8. Sequence(GeradePLinks + ((Length[Segment[GeradePLinks, GeradePRechts]] * i / 30), 0), i, 0, 30) → GeradePoints
  9. Shuffle(Sequence[i, i, -15, 15]) → NumListGanzeRaw, {-10, -8, 3, -1, 15, -6, -4, -2, -3, 2, 12, -5, 6, -14, -9, 0, -13, 1, 5, 10, 14, -11, 8, 4, 13, -15, 9, -7, 7, -12, 11}
  10. Shuffle(Sequence[(0.5 * i), i, -15, 15]) → NumListDezi1Raw, {1.5, -1.5, 4.5, -5, -7, -0.5, -2, -7.5, 1, 0, 6, -6, 6.5, 7.5, 2, 5.5, 7, 4, -3, 5, 2.5, 3.5, -1, -5.5, -3.5, 0.5, 3, -6.5, -4, -4.5, -2.5}
  11. Shuffle(Sequence[(0.2 * i), i, -15, 15]) → NumListDezi2Raw, {-1.6, 1, 0.2, 0.8, 2.2, 1.4000000000000001, -3, -1.8, -0.6000000000000001, 0.6000000000000001, -2.2, -1.4000000000000001, 2, -2.8000000000000003, 3, 1.6, -1.2000000000000002, -2.6, 2.4000000000000004, -0.2, 1.8, 2.6, 0, -2, -0.8, 1.2000000000000002, -1, -2.4000000000000004, -0.4, 2.8000000000000003, 0.4}
  12. Shuffle(Sequence[(i * 0.1), i, -15, 15]) → NumListDezi3Raw, {-1.1, -1, -1.4000000000000001, -0.4, 0.4, 0.5, -0.2, 1.2000000000000002, -1.3, 0.8, -0.9, 0.30000000000000004, -0.6000000000000001, -0.1, 0.6000000000000001, 1, -1.2000000000000002, -0.5, 1.3, -0.30000000000000004, 1.1, -0.8, 0.1, 0, 0.2, -1.5, 0.7000000000000001, 1.4000000000000001, -0.7000000000000001, 1.5, 0.9}
  13. Shuffle({2, 5, 10}) → NumListFracNenner1, {5, 10, 2}
  14. Shuffle({2, 4, 8}) → NumListFracNenner2, {4, 2, 8}
  15. If(subgroup ≟ 1, NumListFracNenner1(1), NumListFracNenner2(1)) → nenner
  16. Shuffle(Sequence[i, i, (-floor((nenner * 1.5))), floor((nenner * 1.5))]) → NumListFracZaehlerRaw, {2, 6, -3, 0, -4, 3, 5, 4, 7, 1, -6, -5, -2, -7, -1}
  17. Shuffle({-1, 1}) → VorzeichenShuffle, {-1, 1}
  18. 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
  19. Distance(GeradePoints(1), GeradePoints(2)) → distP
  20. Point(GeradePointsAbove) → HintPunkt
  21. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  22. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 9, 3, 9, 10, 8, 3, 2, 5, 6, 6, 7, 10, 7, 5, 8, 3, 10, 3, 8, 4, 5, 7, 9, 8, 8, 7, 3, 5, 3, 3, 7, 3, 8, 8, 2, 10, 8, 4, 0, 6, 8, 0, 5, 2, 0, 3, 0, 0, 2, 1, 1, 2, 0, 3, 10, 7, 1, 2, 3, 10, 10, 2, 5, 6, 5, 10, 3, 5, 0, 1, 3, 8, 1, 5, 4, 10, 7, 2, 2, 4, 3, 8, 1, 8, 2, 0, 4, 9, 8, 4, 4, 6, 9, 1, 4, 1, 8, 4, 2}
  23. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  24. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {6, 6, 4, 10, 10, 0, 10, 10, 5, 7, 2, 10, 6, 9, 1, 1, 2, 4, 9, 8, 8, 8, 8, 6, 10, 9, 6, 4, 9, 1, 7, 1, 7, 10, 10, 10, 5, 8, 6, 4, 3, 1, 0, 7, 9, 3, 7, 3, 1, 9, 9, 8, 6, 7, 8, 4, 4, 6, 5, 10, 8, 9, 2, 0, 8, 5, 9, 5, 6, 8, 8, 1, 1, 2, 7, 0, 9, 5, 3, 3, 9, 9, 2, 1, 3, 4, 3, 3, 0, 9, 4, 8, 5, 7, 5, 2, 1, 9, 1, 9}
  25. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  26. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  27. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  28. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  29. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  30. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  31. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  32. Shuffle(1…10) → ExNumList, {9, 10, 8, 3, 1, 2, 4, 7, 6, 5}
  33. Length(ExNumList) → questionCountMax
  34. Sequence(Segment[GeradePoints(i) + (0, dyStriche), GeradePoints(i) + (0, (-dyStriche))], i, 1, 31) → l2
  35. Segment(GeradePLinks + (-0.3, 0), GeradePRechts + (0.3, 0)) → g
  36. Circle(SolMark, toleranz) → solCirc
  37. Text(solutionText, SolMark + (0, (dyBesch * 1.5)), false, true, 0, 0) → SolText
  38. Text(AngabeHelper, C, false, true, -1, 0) → AngabeMaster
  39. Segment(E, xPos) → h
  40. Mod(questionCount, 2) → b
  41. Segment(NullPunkt, D) → i
  42. Segment(E, HintPunkt) → f
  43. Text(correctText1, F, false, true, 0, 0) → correctText2
  44. Segment(xPos + (0, dyAbove) + (0, 0.4), NullPunkt + (0, dyAbove) + (0, 0.4)) → solSec
  45. Text(Text1, Midpoint[E, D] + (0, 1), false, true, 0, 0) → Text6
  46. Segment((x(HintPunkt), y(xPos)), HintPunkt) → j
  47. Distance(HintPunkt, xPos) → d
  48. Text(NumTxtMaster, xPos + (0, (2.3 * dyAbove)), false, true, 0, 0) → Text9
  49. Text(ZMHelper, HintPunkt + (0, 0.5), false, true, 0, 0) → Text7
  50. Text(ZMHelper, HintPunkt + (0.5, 0.5), false, true, 0, 0) → Text10
  51. Text(ZMHelper, HintPunkt + (-0.5, 0.5), false, true, 0, 0) → Text11
  52. Text(NumTxtMaster, xPos + (0, If[showZM, (2.3 * dyAbove), 1 + (0.6 * dyAbove)]), false, true, 0, 0) → Text2