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Rational Number Ordering Chain

Rational Number Ordering Chain
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2025-06-04 17:43
In collections Ordnen und Vergleichen von rationalen Zahlen
This example demonstrates the ordering chain of rational numbers, involving key math concepts such as comparing and ordering rational numbers. Using GeoGebra commands like Shuffle and Sort, it dynamically shows the arrangement of rational numbers on the number line. Suitable for 7-8 grade students to practice comparing and ordering rational numbers, as well as representing them on the number line.

GeoGebra Commands & Parameters

  1. Shuffle({1, 2}) → ModusListe, {2, 1}
  2. Shuffle({1, 2, 3, 4, 5, 6, 7, 8, 9, 10}) → RandoNumListe, {8, 1, 9, 7, 2, 6, 3, 5, 4, 10}
  3. Polygon((-5, -8), (7.5, -8), (7.5, 0.5), (-5, 0.5)) → ZiehBereich, segZB1, segZB2, segZB3, segZB4
  4. Polygon(Q1E1, Q1E2, 4) → Box1, f, g, h, i, Q1E3, Q1E4
  5. IsInRegion(PosZettel4, Box1) → Z4inB1
  6. IsInRegion(PosZettel2, Box1) → Z2inB1
  7. IsInRegion(PosZettel1, Box1) → Z1inB1
  8. IsInRegion(PosZettel3, Box1) → Z3inB1
  9. Polygon(Q2E1, Q2E2, 4) → Box2, j, k, l, m, Q2E3, Q2E4
  10. IsInRegion(PosZettel4, Box2) → Z4inB2
  11. IsInRegion(PosZettel2, Box2) → Z2inB2
  12. IsInRegion(PosZettel1, Box2) → Z1inB2
  13. IsInRegion(PosZettel3, Box2) → Z3inB2
  14. Polygon(Q3E1, Q3E2, 4) → Box3, n, p, q, r, Q3E3, Q3E4
  15. IsInRegion(PosZettel4, Box3) → Z4inB3
  16. IsInRegion(PosZettel2, Box3) → Z2inB3
  17. IsInRegion(PosZettel1, Box3) → Z1inB3
  18. IsInRegion(PosZettel3, Box3) → Z3inB3
  19. Polygon(Q4E1, Q4E2, 4) → Box4, s, t, a, b, Q4E3, Q4E4
  20. IsInRegion(PosZettel3, Box4) → Z3inB4
  21. IsInRegion(PosZettel4, Box4) → Z4inB4
  22. IsInRegion(PosZettel2, Box4) → Z2inB4
  23. IsInRegion(PosZettel1, Box4) → Z1inB4
  24. Shuffle({1, 2}) → ZufallslisteZettel1, {1, 2}
  25. Shuffle({1, 2}) → ZufallslisteZettel2, {1, 2}
  26. Shuffle({1, 2}) → ZufallslisteZettel3, {2, 1}
  27. Shuffle({1, 2}) → ZufallslisteZettel4, {2, 1}
  28. Sort(NumberList) → NumberListModus1
  29. Reverse(NumberListModus1) → NumberListModus2
  30. Sequence(IndexOf[NumberList(k), If[modus ≟ 1, NumberListModus1, NumberListModus2]], k, 1, 4) → IndexNumber
  31. Element(B1List, IndexOf[1, IndexNumber]) → correctB1
  32. Element(B2List, IndexOf[2, IndexNumber]) → correctB2
  33. Element(B3List, IndexOf[3, IndexNumber]) → correctB3
  34. Element(B4List, IndexOf[4, IndexNumber]) → correctB4
  35. Polygon(Z1VieleckE1, Z1VieleckE2, Zettel1Anchor_1, Z1VieleckH, Z1VieleckE3, Z1VieleckE4) → Vieleck1, z1vielecke1, z1vielecke2, zettel1anchor_1, z1vieleckh, z1vielecke3, z1vielecke4
  36. Polygon(Z2VieleckE1, Z2VieleckE2, Zettel2Anchor_1, Z2VieleckH, Z2VieleckE3, Z2VieleckE4) → Vieleck2, z2vielecke1, z2vielecke2, zettel2anchor_1, z2vieleckh, z2vielecke3, z2vielecke4
  37. Polygon(Z3VieleckE1, Z3VieleckE2, Zettel3Anchor_1, Z3VieleckH, Z3VieleckE3, Z3VieleckE4) → Vieleck3, z3vielecke1, z3vielecke2, zettel3anchor_1, z3vieleckh, z3vielecke3, z3vielecke4
  38. Polygon(Z4VieleckE1, Z4VieleckE2, Zettel4Anchor_1, Z4VieleckH, Z4VieleckE3, Z4VieleckE4) → Vieleck4, z4vielecke1, z4vielecke2, zettel4anchor_1, z4vieleckh, z4vielecke3, z4vielecke4
  39. Text(FeedbackText, A, false, true, 0) → Text3
  40. Sequence(IndexOf[NumberList(k), If[modus ≟ 2, NumberListModus1, NumberListModus2]], k, 1, 4) → InvIndexNumber
  41. Element(B4List, IndexOf[4, InvIndexNumber]) → invB4
  42. Element(B3List, IndexOf[3, InvIndexNumber]) → invB3
  43. Element(B2List, IndexOf[2, InvIndexNumber]) → invB2
  44. Element(B1List, IndexOf[1, InvIndexNumber]) → invB1
  45. Text(Bruch1Text, Midpoint[Zettel1Anchor_1, Zettel1Anchor_2] + (0, 4.15), false, true, 0, 0) → txtN1
  46. Text(Bruch2Text, Midpoint[Zettel2Anchor_1, Zettel2Anchor_2] + (0, 4.15), false, true, 0, 0) → txtN2
  47. Text(Bruch3Text, Midpoint[Zettel3Anchor_1, Zettel3Anchor_2] + (0, 4.15), false, true, 0, 0) → txtN3
  48. Text(Bruch4Text, Midpoint[Zettel4Anchor_1, Zettel4Anchor_2] + (0, 4.15), false, true, 0, 0) → txtN4
  49. If(modus ≟ 1, "<", ">") → txtSign
  50. Sequence(IndexOf[k, IndexNumber], k, 1, 4) → IndexZettel
  51. Segment(Midpoint[Corner[CapZiehMich1, 1], Corner[CapZiehMich1, 2]], Midpoint[Corner[CapZiehMich1, 1], Corner[CapZiehMich1, 2]] + (0, -0.5)) → segZiehMich1
  52. Segment(Midpoint[Corner[CapZiehMich2, 1], Corner[CapZiehMich2, 4]], Midpoint[Corner[CapZiehMich2, 1], Corner[CapZiehMich2, 4]] + (-0.5, 0)) → segZiehMich2
  53. Sort(NumberList) → SortNumberList
  54. Reverse(SortNumberList) → InvSortNumberList
  55. If(modus ≟ 1, SortNumberList, InvSortNumberList) → OrderNumbers
  56. Sequence(IndexOf[NumberList(k), OrderNumbers], k, 1, 4) → IndexOrderNumbers