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比较数值大小 - 小学数学入门

比较数值大小 - 小学数学入门
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2025-01-07 18:43
所属专题 Gegenzahl und Betrag einer rationalen Zahl
这个范例演示了如何通过几何图形直观比较两个数值的大小。核心数学概念包括绝对值、数轴上的距离以及数值比较的基本原理。作图要点包括使用GeoGebra命令如Join、Point、Distance和Translate来构造数轴和标记数值点。适合小学7-8年级学生用于学习整数概念和数轴表示。

GeoGebra 命令及参数

  1. Join({{1}, Shuffle[{2, 3}], Join[Sequence[Shuffle[Sequence[1, 3]], m, 1, 40]]}) → listBSP
  2. SelectedIndex(DropDown5) → input5
  3. Element({1, 0.5, 0.1}, bsp) → faktor
  4. Join({{1, 4, 3}, Join[Sequence[Shuffle[Sequence[1, 5]], m, 1, 30]]}) → listNumFall
  5. Element({1, 1, 1, 0, 1}, fall) → numVZY
  6. Element({0, 0, 0, 0, 1}, fall) → numVZX
  7. Sequence(RandomElement[listPossibleNumsBigger], m, 1, 130) → listNum1X, {16, 16, 14, 15, 15, 15, 16, 15, 16, 15, 13, 16, 15, 13, 13, 14, 14, 13, 15, 13, 14, 15, 14, 13, 16, 16, 15, 16, 15, 16, 14, 16, 13, 14, 15, 16, 16, 14, 14, 13, 13, 15, 16, 14, 16, 14, 15, 16, 13, 13, 13, 13, 14, 15, 15, 16, 16, 13, 15, 13, 14, 15, 14, 14, 15, 15, 14, 13, 16, 13, 13, 13, 14, 13, 15, 16, 13, 16, 16, 14, 13, 15, 16, 13, 13, 14, 15, 16, 15, 15, 16, 13, 14, 15, 13, 15, 15, 15, 14, 15, 13, 15, 14, 15, 15, 16, 16, 16, 13, 14, 14, 15, 14, 16, 13, 15, 13, 16, 16, 15, 14, 15, 13, 13, 16, 13, 14, 13, 14, 14}
  8. Zip(RandomElement[listPossibleNumsAll \ Sequence[m - absNum - 1, 18]], m, listNum1X) → listNum1Y
  9. Sequence(RandomElement[listPossibleNumsAll], m, 1, 130) → listNum3X, {14, 15, 6, 13, 4, 7, 15, 5, 14, 15, 15, 13, 15, 16, 16, 15, 14, 16, 4, 6, 5, 6, 6, 4, 7, 5, 14, 14, 4, 5, 6, 4, 13, 4, 6, 6, 4, 16, 15, 15, 13, 15, 4, 13, 13, 6, 4, 16, 7, 13, 14, 14, 6, 5, 5, 13, 7, 15, 15, 13, 13, 13, 16, 4, 6, 14, 14, 13, 16, 15, 6, 4, 13, 5, 5, 15, 6, 4, 14, 4, 7, 16, 4, 14, 5, 7, 4, 13, 7, 14, 14, 13, 5, 7, 15, 16, 15, 6, 14, 13, 15, 5, 15, 5, 5, 13, 7, 15, 5, 7, 7, 5, 15, 7, 15, 6, 7, 14, 7, 14, 7, 4, 4, 13, 4, 5, 5, 15, 6, 14}
  10. Element({num1x, num2x, num3x, num4x, num5x}, fall) → numXValue
  11. Element({num1y, num2y, num3y, num4y, num5y}, fall) → numYValue
  12. If(lenaX, numX, numY) → numLena
  13. If(lenaX, numY, numX) → numJanis
  14. Min({numLenaCorrect, numJanisCorrect}) → numLeft
  15. Max({numLenaCorrect, numJanisCorrect}) → numRight
  16. If(sol3 < sol4, 2, If[sol3 > sol4, 3, If[sol3 ≟ sol4, 4]]) → sol5
  17. Point(Line[PStart, xAxis]) → PEnd
  18. Distance(PStart, PEnd) → linelength
  19. Sequence(PStart + (m * (linelength / linedivision, 0)), m, -1, 41) → listLinePoints
  20. KeepIf(x(PStart) ≤ x(P) ≤ x(PEnd), P, listLinePoints) → listPoints
  21. Textfield(input1) → Eingabefeld1
  22. Textfield(input2) → Eingabefeld2
  23. Element({2, 2, 2}, step) → tries
  24. Segment(listLinePoints(1), Element[Last[listLinePoints], 1]) → line
  25. Element({5, 2, 5}, bsp) → lineabslong
  26. Sequence(PStart + ((lineabslong * m) * (linelength / linedivision, 0)), m, 0, linedivision / lineabslong) → listLinePointsLong
  27. KeepIf(x(PStart) < x(P) < x(PEnd) ∧ (¬(P ∈ listLinePointsLong)), P, listLinePoints) → listLinePointsShort
  28. Zip(Segment[P + (0, (-lineheightshort)), P + (0, lineheightshort)], P, listLinePointsShort) → listLinesShort
  29. Zip(Segment[P + (0, (-lineheightlong)), P + (0, lineheightlong)], P, listLinePointsLong) → listLinesLong
  30. Sequence(PStart + (m * (linelength / linedivision, 0)), m, 0, linedivision, linedivision / 4) → listLinePointsText
  31. Zip(m ≟ n, m, listNum1X, n, listNum1Y) → check
  32. Join({Zip[Text[(("\textsf\footnotesize{--}\textsf{" * n) * "}"), m + (0, -1), true, true, -0, 1], n, {((linedivision * 0.5) * faktor), ((linedivision * 0.25) * faktor)}, m, listLinePointsText], Zip[Text[(("\textsf\footnotesize{" * n) * "}"), m + (0, -1), true, true, -0, 1], n, {((linedivision * 0.25) * faktor), ((linedivision * 0.5) * faktor)}, m, Sequence[Element[listLinePointsText, m], m, 4, 5]]}) → listLineText
  33. Textfield(input3) → Eingabefeld3
  34. Textfield(input4) → Eingabefeld4
  35. If(numLeft ≟ numLenaCorrect, colourorange, colourlila) → colourLeft
  36. If(numRight ≟ numLenaCorrect, colourorange, colourlila) → colourRight
  37. If(numLenaSol > numJanisSol, "Lena", "Janis") → nameFurther
  38. If(nameFurther ≟ "Lena", "Janis", "Lena") → nameCloser
  39. PointIn(Circle[PosQuestion3, 10]) → PosQuestion3B
  40. PointIn(Circle[PosQuestion3, 10]) → PBogen1a
  41. Point(Line[PBogen1a, xAxis]) → PBogen2a
  42. CircleArc(Midpoint[PBogen1a, PBogen1b] + (bogensize, 0), PBogen1a, PBogen1b) → bogen1
  43. Translate(Mirror[bogen1, Line[PBogen1a, yAxis]], PBogen2a - PBogen1a) → bogen2
  44. Element({correctA, correctB, correctC}, step) → correctActual
  45. Segment(PHaus1, PJanis1) → janis1
  46. Segment(PJanis2, PHaus2) → janis2
  47. Segment(PHaus1, PLena1) → lena1
  48. Segment(PLena2, PHaus2) → lena2
  49. Zip(Text[(("\textsf\small\bold{" * n) * "}"), m + (0, -1), true, true, -0, 1], n, {0}, m, {listPoints(linedivision / 2 + 1)}) → listLineText0
  50. SelectedIndex(DropDown6) → input6
  51. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  52. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  53. 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