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Different Cases in Comparing Rational Numbers

Different Cases in Comparing Rational Numbers
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2025-06-04 17:40
In collections Ordnen und Vergleichen von rationalen Zahlen
This example demonstrates different cases in comparing rational numbers, focusing on the concepts of comparing and ordering rational numbers and representing them on the number line. Using GeoGebra commands such as Join, Sequence, and Zip, it dynamically shows the positions and comparison results of rational numbers on the number line. Suitable for 7-8 grade students for practice and learning.

GeoGebra Commands & Parameters

  1. Join({Sequence[Q0 + (m * (absnotes, 0)), m, 0, 2], {(0, -5), (0, -5), (0, -5)}}) → listPointsNotes
  2. Sequence(Random[1, 1], m, 1, 110) → listCorrect1, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
  3. Zip(RandomElement[{2, 2} \ {m}], m, listCorrect1) → listCorrect2
  4. If(shuffled, Join[Sequence[Shuffle[Sequence[1, 15]], m, 1, 9]], Join[{1…15, 1…15, 1…15, 1…15}]) → listExnums
  5. If(listsolhelp ≟ {0, 0, 1}, RandomElement[{{1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}}], If[listsolhelp ≟ {0, 1, 1}, RandomElement[{{2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}], {1, 2, 3}]) → listChangedPositions
  6. If(shuffle, IndexOf[1, listChangedPositions], listCorrect1(Mod[questionCount, 100] + 1)) → posC1
  7. If(shuffle, IndexOf[2, listChangedPositions], listCorrect2(Mod[questionCount, 100] + 1)) → posC2
  8. RemoveUndefined({If[selected1, 1], If[selected2, 2], If[selected3, 3]}) → listselected
  9. Zip(RandomElement[{3, 3} \ {m, n}], m, listCorrect1, n, listCorrect2) → listCorrect3
  10. If(shuffle, IndexOf[3, listChangedPositions], listCorrect3(Mod[questionCount, 100] + 1)) → posC3
  11. RemoveUndefined({If[listsolhelp(1) ≟ 1, posC1], If[listsolhelp(2) ≟ 1, posC2], If[listsolhelp(3) ≟ 1, posC3]}) → listsol
  12. Sequence(Random[1, 4], m, 1, 110) → listNote1, {2, 3, 3, 4, 2, 3, 1, 2, 4, 1, 4, 1, 2, 4, 1, 4, 3, 1, 2, 1, 1, 4, 2, 2, 2, 1, 4, 1, 2, 2, 2, 3, 1, 2, 1, 4, 3, 3, 2, 4, 4, 3, 2, 3, 1, 1, 4, 1, 4, 3, 4, 3, 4, 1, 2, 4, 1, 3, 2, 2, 1, 3, 3, 4, 2, 4, 2, 3, 3, 1, 4, 1, 3, 4, 2, 4, 4, 3, 4, 1, 1, 3, 3, 1, 2, 3, 1, 2, 1, 1, 4, 4, 2, 2, 2, 1, 4, 4, 3, 2, 4, 3, 2, 4, 1, 3, 3, 4, 4, 1}
  13. Zip(RandomElement[{5} \ {m}], m, listNote1) → listNote2
  14. Zip(RandomElement[{1, 2, 3, 4} \ {m, n}], m, listNote1, n, listNote2) → listNote3
  15. Zip(RandomElement[{1, 2, 3, 4} \ {m, n, j}], m, listNote1, n, listNote2, j, listNote3) → listNote4
  16. Sequence(P0 + (m * (abstext, 0)), m, 0, 2) → listPointsText
  17. Zip(RandomElement[{1, 2, 3} \ {m, n}], m, listCorrect1, n, listCorrect2) → listWrong3
  18. Textfield(input1) → InputBox1
  19. Textfield(input2) → InputBox2
  20. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  21. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {10, 7, 8, 1, 9, 3, 8, 2, 8, 3, 9, 6, 10, 8, 10, 1, 2, 5, 7, 0, 2, 2, 10, 3, 1, 1, 2, 0, 2, 7, 9, 8, 5, 5, 6, 3, 0, 2, 6, 3, 8, 8, 1, 0, 0, 0, 9, 8, 7, 1, 2, 1, 9, 8, 2, 4, 1, 4, 0, 8, 10, 9, 2, 2, 2, 5, 7, 1, 6, 4, 4, 5, 1, 2, 5, 0, 1, 4, 2, 3, 1, 7, 4, 4, 1, 2, 10, 9, 8, 5, 4, 1, 3, 2, 7, 10, 6, 10, 6, 6}
  22. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {7, 10, 0, 6, 0, 10, 8, 8, 2, 2, 7, 1, 10, 2, 8, 7, 1, 3, 10, 5, 5, 9, 6, 10, 8, 7, 6, 7, 7, 5, 1, 0, 0, 9, 2, 5, 3, 8, 6, 4, 3, 0, 10, 0, 3, 9, 6, 2, 10, 3, 6, 5, 7, 8, 9, 0, 10, 2, 7, 7, 9, 1, 2, 0, 6, 2, 6, 2, 9, 0, 5, 0, 3, 7, 0, 5, 4, 5, 10, 2, 2, 2, 8, 9, 6, 0, 0, 4, 9, 5, 7, 8, 3, 7, 8, 1, 2, 8, 4, 2}
  23. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  24. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  25. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  26. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  27. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  28. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  29. NumberSeparationComma(numX) → Text3
  30. NumberSeparationComma(numY) → Text4
  31. NumberSeparationComma(numZ) → Text5
  32. Zip(RandomElement[{6} \ {m, n, j, l}], m, listNote1, n, listNote2, j, listNote3, l, listNote4) → listNote5
  33. Zip(RandomElement[{1, 2, 3, 4} \ {m, n, j, l, k}], m, listNote5, listNote1, n, listNote2, j, listNote3, l, listNote4, k) → listNote6
  34. Length(listsol) → numSol
  35. Defined(IndexOf[IndexOf[3, listChangedPositions], listselected]) → selectedShuffle3
  36. Defined(IndexOf[IndexOf[2, listChangedPositions], listselected]) → selectedShuffle2
  37. Defined(IndexOf[IndexOf[1, listChangedPositions], listselected]) → selectedShuffle1
  38. Text((("\bold{" * numAHelpText) * "}"), midPointQuestionNumber, true, true, 0, 0) → Text1
  39. Text(TextC1, Midpoint[Vertex[s1(1), 1], Vertex[s1(1), 3]] + vec, false, true, 0, 0) → TxtSelection1
  40. Text(TextC2, Midpoint[Vertex[s2(1), 1], Vertex[s2(1), 3]] + vec, false, true, 0, 0) → TxtSelection2
  41. Text(TextC3, Midpoint[Vertex[s3(1), 1], Vertex[s3(1), 3]] + vec, false, true, 0, 0) → TxtSelection3