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有理数比较的不同情况

有理数比较的不同情况
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2025-06-04 17:40
所属专题 Ordnen und Vergleichen von rationalen Zahlen
这个范例展示了有理数比较的不同情况，涉及的核心数学概念包括有理数的大小比较和数轴上的表示。通过使用GeoGebra命令如Join、Sequence、Zip等，可以动态地展示有理数在数轴上的位置和比较结果。适合7-8年级的学生进行练习和学习。

GeoGebra 命令及参数

  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