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Comparing Values - Level 1

Comparing Values - Level 1
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2025-01-07 18:43
In collections Gegenzahl und Betrag einer rationalen Zahl
This example demonstrates how to visually compare two numerical values using geometric figures. The key mathematical concepts involve absolute value, distance on the number line, and basic principles of numerical comparison. Construction points include using GeoGebra commands such as Join, Point, Distance, and Translate to create the number line and mark value points. Suitable for students in grad

GeoGebra Commands & Parameters

  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