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有理数的比较和排序

有理数的比较和排序
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2025-06-04 17:40
所属专题 Ordnen und Vergleichen von rationalen Zahlen
这个 GeoGebra 范例演示了如何比较和排序有理数。学生可以通过选择正确的选项来回答问题，例如哪个数字小于 -4。范例还包括一个开放式问题，要求学生将两个有理数按大小排序。这个范例适合 7-8 年级学生，帮助他们理解有理数的比较和排序的概念。范例使用 GeoGebra 命令，如 SelectedIndex、Point、Join 等，来创建有理数的图形。范例还包括一个策略问题，要求学生使用有理数的比较和排序来解决问题。

GeoGebra 命令及参数

  1. SelectedIndex(DropDown21) → input21
  2. SelectedIndex(DropDown12) → input12
  3. SelectedIndex(DropDown2) → input2
  4. SelectedIndex(DropDown1) → input1
  5. SelectedIndex(DropDown6) → input6
  6. SelectedIndex(DropDown7) → input7
  7. SelectedIndex(DropDown8) → input8
  8. SelectedIndex(DropDown9) → input9
  9. SelectedIndex(DropDown16) → input16
  10. SelectedIndex(DropDown17) → input17
  11. SelectedIndex(DropDown18) → input18
  12. Point(Line[Start, xAxis]) → Ende
  13. Join(Zip[Translate[Sequence[Start + (m * (Distance[Start, Ende] / (nummax - nummin), 0)), m, 0, nummax - nummin, 0.1], Vector[(n * (0, 0.45))]], n, Sequence[0, 3]]) → listOptionsK
  14. Point(listOptionsK) → K15
  15. IndexOf(K15, listOptionsK) → input15
  16. Point(listOptionsK) → K14
  17. IndexOf(K14, listOptionsK) → input14
  18. Point(listOptionsK) → K11
  19. IndexOf(K11, listOptionsK) → input11
  20. Point(listOptionsK) → K10
  21. IndexOf(K10, listOptionsK) → input10
  22. Point(Line[Chris2a, yAxis]) → Chris3a
  23. Point(Line[Chris2a, yAxis]) → Chris7a
  24. SelectedIndex(DropDown22) → input22
  25. Element({0, 0, 0, 1, 2, 4, 3, 0, 0}, step) → exnum
  26. Textfield(input3) → Eingabefeld3
  27. Textfield(input4) → Eingabefeld4
  28. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, RasterMaxX / RasterStepXY, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, RasterMaxY / RasterStepXY, RasterMaxY / RasterStepXY]}) → RasterAussen
  29. Segment(Dilate[Start, 1.05, Midpoint[Start, Ende]], Dilate[Ende, 1.05, Midpoint[Start, Ende]]) → line
  30. Sequence(Start + (m * (Distance[Start, Ende] / (nummax - nummin), 0)), m, 0, nummax - nummin, 0.5) → listPointsBig
  31. Zip(Segment[P + (0, (-linesize)), P + (0, linesize)], P, listPointsBig) → listLines
  32. Sequence(Start + (m * (Distance[Start, Ende] / (nummax - nummin), 0)), m, 0.5, nummax - nummin) → listPointsText
  33. Join({Zip[Text[(("\textsf{" * m) * " }"), P + (0.08, -0.9), true, true, 0], m, Sequence[0, nummax], P, Sequence[listPointsText(n), n, nummitte / 2 + 1, nummitte + nummax]], Zip[Text[((("\textsf{" * "--") * abs(m)) * " }"), P + (0, -0.9), true, true, 0], m, Sequence[nummin, -1], P, listPointsText]}) → listText
  34. Midpoint(Start, Ende) → Mitte
  35. Zip(Mitte + (m * (Distance[Start, Ende] / (nummax - nummin), 0)), m, {num1, num2, num3, num4}) → listPoints2
  36. Translate(Segment[(0, 0), (arrowlength, 0)], Start + (0.7, arrowheight)) → arrowlinks
  37. Translate(Segment[(0, 0), (arrowlength, 0)], Ende + (-2.9, arrowheight)) → arrowrechts
  38. Join({Zip[Text[(("\textsf\small\bold\textcolor{db6114}{" * m) * " }"), P + (0, -0.9), true, true, 0], m, {"--0,75", "~2,2"}, P, {listPoints2(2), listPoints2(4)}], Zip[Text[(("\textsf\small\bold\textcolor{db6114}{" * m) * " }"), P + (0, 0.2), true, true, 0], m, {"--1\frac{1}{3}", "~~\frac{4}{5}"}, P, {listPoints2(1), listPoints2(3)}]}) → listText2
  39. Textfield(input5) → Eingabefeld5
  40. Element({Chris1a, Chris2a, Chris2a, Chris3a, Chris2a, Chris2a, Chris2a, Chris2a, Chris7a}, step + 1) → Chrisa
  41. Point(Line[Chrisa, xAxis]) → Chrisb
  42. Zip(Segment[P + (0, (-linesizesmall)), P + (0, linesizesmall)], P, listPointsSmall) → listLinesSmall
  43. Zip(Mitte + (m * (Distance[Start, Ende] / (nummax - nummin), 0)), m, {num5, num6}) → listPoints4
  44. Point(Line[SB3, yAxis]) → SB4
  45. Point(Line[SB3, yAxis]) → SB5
  46. Textfield(input13) → Eingabefeld13
  47. LaTeX(step, true, true) → Text2
  48. Zip(Text[(("\textsf\small\textcolor{616161}{" * m) * " }"), P + (0, arrowheight - 0.32), true, true, 0], m, {"links", "rechts"}, P, {Start, Ende}) → listLinksRechts
  49. Sequence(Start + (m * (Distance[Start, Ende] / (nummax - nummin), 0)), m, 0, nummax - nummin, 0.1) → listPoints
  50. Point(listPoints) → P1
  51. Point(listPoints) → P2
  52. Text(If[checkP1dezi, TextP1Dezimal, TextP1Bruch], P1 + (0.05, 0.8), false, true, 0, 0) → TextP1X
  53. Text(If[checkP2dezi, TextP2Dezimal, TextP2Bruch], P2 + (0.05, 0.8), false, true, 0, 0) → TextP2X
  54. If(checkP1dezi, TextP1Dezimal, TextP1Bruch) → TextP1
  55. If(checkP2dezi, TextP2Dezimal, TextP2Bruch) → TextP2
  56. Join({Zip[Text[(("\textsf\small\bold\textcolor{db6114}{" * m) * " }"), P + (0, -0.9), true, true, 0], m, {"2,2"}, P, {listPoints4(2)}], Zip[Text[(("\textsf\small\bold\textcolor{db6114}{" * m) * " }"), P + (0, 0.2), true, true, 0], m, {"--\frac{3}{4}"}, P, {listPoints4(1)}]}) → listText4
  57. Translate(Segment[(0, 0), ((0.7 * arrowlength), 0)], Start + (-0.1, arrowheight)) → arrowlinksklein
  58. Translate(Segment[(0, 0), ((0.7 * arrowlength), 0)], Ende + (-1.3, arrowheight)) → arrowrechtsklein
  59. Point(listOptionsK) → K19
  60. Point(listOptionsK) → K20
  61. IndexOf(K19, listOptionsK) → input19
  62. IndexOf(K20, listOptionsK) → input20
  63. IndexOf(K10, listOptionsK) → a