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比较绝对值

比较绝对值
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2025-03-26 20:42
所属专题 Gegenzahl und Betrag einer rationalen Zahl
本范例通过比较两个负数的绝对值，帮助学生理解绝对值的概念及其在数轴上的意义。涉及 GeoGebra 命令包括 Point, Distance, Sequence, KeepIf, RandomElement 等。适合初中7-8年级学生学习。

GeoGebra 命令及参数

  1. Point(Line[PStart, xAxis]) → PEnd
  2. Distance(PStart, PEnd) → linelength
  3. Sequence(PStart + (m * (linelength / linedivision, 0)), m, -1, 41) → listLinePoints
  4. KeepIf(x(PStart) ≤ x(P) ≤ x(PEnd), P, listLinePoints) → listPoints
  5. Point(listPoints) → PLena
  6. Point(listPoints) → PJanis
  7. RandomElement(possibleValuesJanis) → randomNumJanis
  8. SelectedIndex(DropDown4) → input4
  9. SelectedIndex(DropDown7) → input7
  10. SelectedIndex(DropDown3) → input3
  11. SelectedIndex(DropDown8) → input8
  12. SelectedIndex(DropDown9) → input9
  13. SelectedIndex(DropDown10) → input10
  14. SelectedIndex(DropDown11) → input11
  15. Element({listPoints(21 - 13), listPoints(21 - 13), listPoints(21 - 13), listPoints(21 - 13), listPoints(21 - 13), listPoints(21 + numsLenaJanis(1, 1)), listPoints(21 + numsLenaJanis(2, 1)), listPoints(21 + numsLenaJanis(3, 1))}, step) → PLenaFix
  16. Element({listPoints(-21 + 13), listPoints(-21 + 13), listPoints(-21 + 13), listPoints(21 + randomNumJanis), listPoints(21 + randomNumJanis), listPoints(21 + numsLenaJanis(1, 2)), listPoints(21 + numsLenaJanis(2, 2)), listPoints(21 + numsLenaJanis(3, 2))}, step) → PJanisFix
  17. If(moveableJanis, PLena, PLenaFix) → PLenaPos
  18. If(moveableJanis, PJanis, PJanisFix) → PJanisPos
  19. If(abs(numLena) < abs(numJanis), 3, If[abs(numLena) > abs(numJanis), 2, 1]) → compare
  20. Element({0, 0, 0, 0, 0, 1, 2, 3, 0}, step) → exnum
  21. Textfield(input1) → Eingabefeld1
  22. Textfield(input2) → Eingabefeld2
  23. Segment(listLinePoints(1), Element[Last[listLinePoints], 1]) → line
  24. Sequence(PStart + ((lineabslong * m) * (linelength / linedivision, 0)), m, 0, linedivision / lineabslong) → listLinePointsLong
  25. KeepIf(x(PStart) < x(P) < x(PEnd) ∧ (¬(P ∈ listLinePointsLong)), P, listLinePoints) → listLinePointsShort
  26. Zip(Segment[P + (0, (-lineheightlong)), P + (0, lineheightlong)], P, listLinePointsLong) → listLinesLong
  27. Zip(Segment[P + (0, (-lineheightshort)), P + (0, lineheightshort)], P, listLinePointsShort) → listLinesShort
  28. Zip(Text[(("\textsf\small\bold{" * n) * "}"), m + (0, -1), true, true, -0, 1], n, {0}, m, {listPoints(linedivision / 2 + 1)}) → listLineText0
  29. Translate(listPoints, ((-0.5 * sizejanisx), 0)) → listLinePointsGirls
  30. Segment(PJanisH, PHaus2) → janis2
  31. Segment(PLenaH, PHaus1) → lena1
  32. Segment(PHaus2, PMitte) → linehaus
  33. Point(Line[Birne1, xAxis]) → Birne2
  34. Zip(Text[(((("\textsf\footnotesize{" * If[x(m) < x(PMitte), "--", "+"]) * "}\textsf{") * n) * "}"), m + (0, -1), true, true, -0, 1], n, {((linedivision * 0.5) * faktor), ((linedivision * 0.25) * faktor), ((linedivision * 0.25) * faktor), ((linedivision * 0.5) * faktor)}, m, listLinePointsText) → listLineText
  35. Text("\textsf\small{Janis}", PJanisPos + (0, heightlena + 0.95) + (0, -1), true, true, -0, 1) → textJanis
  36. Point(Line[AP1a, xAxis]) → AP2a
  37. CircleArc(Midpoint[AP1a, AP1b] + (arrowdepth, 0), AP1a, AP1b) → arrow1
  38. CircleArc(Midpoint[AP2a, AP2b] - (arrowdepth, 0), AP2b, AP2a) → arrow2
  39. PointIn(Circle[Pos3, 10]) → Pos4
  40. Textfield(input5) → Eingabefeld5
  41. Textfield(input6) → Eingabefeld6
  42. Point(Line[Birne3, xAxis]) → Birne4
  43. LaTeX(step, true, true) → TextStep
  44. Zip(Text[(((("\textsf\footnotesize\bold{" * If[n < 0, "--", If[n > 0, "+", ""]]) * "}{") * abs(n)) * "}"), PJanisPos + (0, -1), true, true, -0, 1], n, {numJanis}) → listTextNumJanis
  45. Text("\textsf\small{Lena}", PLenaPos + (0, heightlena + 0.95) + (0, -1), true, true, -0, 1) → textLena
  46. Zip(Text[(((("\textsf\footnotesize\bold{" * If[n < 0, "--", If[n > 0, "+", ""]]) * "}{") * abs(n)) * "}"), PLenaPos + (0, -1), true, true, -0, 1], n, {numLena}) → listTextNumLena
  47. If(step < 6, Pos3, Pos3 + (-0.5, -1.2)) → Pos3a
  48. If(step < 6, Pos3 + (2.42, 0), Pos3a + (3.4, 0)) → Pos3b
  49. Zip(Text[(("\textsf\small{" * m) * " }"), P + (0.05, 0), true, true, 0], m, {abs(numLena), abs(numJanis)}, P, listPMitte) → listTextNumMitte