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有理数排序与数轴表示

有理数排序与数轴表示
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2025-06-04 17:43
所属专题 Ordnen und Vergleichen von rationalen Zahlen
这个范例演示了如何输入和比较有理数，并在数轴上表示它们。涉及的核心数学概念包括有理数的比较和排序，以及数轴上的表示方法。作图要点使用了GeoGebra命令如Join, Shuffle, Sequence, KeepIf, If, Element, Unique, Textfield, Text等来创建问题、验证答案和显示结果。适合7-8年级学生学习有理数的比较和数轴表示。

GeoGebra 命令及参数

  1. Join(Sequence[Shuffle[{1, 2}], k, 1, 100]) → CaseList
  2. Shuffle(1…10) → Aufgaben1, {3, 2, 8, 4, 5, 9, 10, 7, 6, 1}
  3. Shuffle(11…20) → Aufgaben2, {15, 12, 20, 14, 17, 18, 19, 16, 13, 11}
  4. Sequence(If[Mod[k, 2] ≟ 0, Aufgaben2(k / 2), Aufgaben1((k + 1) / 2)], k, 1, 20) → Reihenfolge
  5. Join({Sequence[1, k, 1, 10], Sequence[2, k, 1, 10]}) → AnzahlInputList
  6. KeepIf(Mod[a, 1] ≠ 0, a, Join[{Sequence[-10 + (k * 1 / 2), k, 1, (20 * 2)], Sequence[-10 + (k * 1 / 3), k, 1, (20 * 3)], Sequence[-10 + (k * 1 / 4), k, 1, (20 * 4)], Sequence[-10 + (k * 1 / 5), k, 1, (20 * 5)], Sequence[-10 + (k * 1 / 6), k, 1, (20 * 6)], Sequence[-10 + (k * 1 / 8), k, 1, (20 * 8)], Sequence[-10 + (k * 1 / 10), k, 1, (20 * 10)]}]) → AllFractions
  7. If(Case ≟ 1, Number1, Number4) → number1
  8. If(Case ≟ 1, Number2, Number3) → number2
  9. If(Case ≟ 1, Number3, Number2) → number3
  10. If(Case ≟ 1, Number4, Number1) → number4
  11. Element(If[Case ≟ 1, {1, 2, 3, 4}, {4, 3, 2, 1}], Pos1List(counter)) → pos1
  12. Element(If[Case ≟ 1, {1, 2, 3, 4}, {4, 3, 2, 1}], If[AnzahlInput ≟ 1, Pos1List(counter), Pos2List(counter)]) → pos2
  13. Unique({pos1, pos2}) → PosList
  14. If(Case ≟ 1, If[1 ∈ PosList, input1, number1] < If[2 ∈ PosList, input2, number2] < If[3 ∈ PosList, input3, number3] < If[4 ∈ PosList, input4, number4], If[1 ∈ PosList, input1, number1] > If[2 ∈ PosList, input2, number2] > If[3 ∈ PosList, input3, number3] > If[4 ∈ PosList, input4, number4]) → correct1
  15. Textfield(input1) → InputBox1
  16. Textfield(input2) → InputBox2
  17. Textfield(input3) → InputBox3
  18. Textfield(input4) → InputBox4
  19. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 9, 2, 6, 5, 8, 6, 3, 4, 2}
  20. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  21. Textfield(input) → inputBox
  22. Sequence(If[Case ≟ 1, DenominatorN1(k), DenominatorN4(k)], k, 1, 20) → Denominator1
  23. Sequence(If[Case ≟ 1, DenominatorN2(k), DenominatorN3(k)], k, 1, 20) → Denominator2
  24. Sequence(If[Case ≟ 1, DenominatorN3(k), DenominatorN2(k)], k, 1, 20) → Denominator3
  25. Sequence(If[Case ≟ 1, DenominatorN4(k), DenominatorN1(k)], k, 1, 20) → Denominator4
  26. Text(txtN1, PosN1, false, true, 0, 0) → txtNumber1
  27. Text(txtN2, PosN2, false, true, 0, 0) → txtNumber2
  28. Text(txtN3, PosN3, false, true, 0, 0) → txtNumber3
  29. Text(txtN4, PosN4, false, true, 0, 0) → txtNumber4
  30. If(Case ≟ 1, If[1 ∈ PosList, input1, number1] < If[2 ∈ PosList, input2, number2], If[1 ∈ PosList, input1, number1] > If[2 ∈ PosList, input2, number2]) → Ineq1
  31. If(Case ≟ 1, If[2 ∈ PosList, input2, number2] < If[3 ∈ PosList, input3, number3], If[2 ∈ PosList, input2, number2] > If[3 ∈ PosList, input3, number3]) → Ineq2
  32. If(Case ≟ 1, If[3 ∈ PosList, input3, number3] < If[4 ∈ PosList, input4, number4], If[3 ∈ PosList, input3, number3] > If[4 ∈ PosList, input4, number4]) → Ineq3
  33. If(PosList ≟ {1, 2}, 1, 6, PosList ≟ {1, 3}, 2, PosList ≟ {1, 4}, 3, PosList ≟ {2, 3}, 4, PosList ≟ {2, 4}, 5) → Case2Input
  34. If(Defined[IndexOf[".", Text[InputBox2]]], 2, Defined[IndexOf["/", Text[InputBox2]]], 3, 1) → DarstellungInput2
  35. If(Defined[IndexOf[".", Text[InputBox1]]], 2, Defined[IndexOf["/", Text[InputBox1]]], 3, 1) → DarstellungInput1
  36. If(Defined[IndexOf[".", Text[InputBox3]]], 2, Defined[IndexOf["/", Text[InputBox3]]], 3, 1) → DarstellungInput3
  37. If(Defined[IndexOf[".", Text[InputBox4]]], 2, Defined[IndexOf["/", Text[InputBox4]]], 3, 1) → DarstellungInput4
  38. If(AnzahlInput ≟ 1, Remove[{1, 2, 3, 4}, {Pos1List(counter)}], Remove[{1, 2, 3, 4}, {Pos1List(counter), Pos2List(counter)}]) → Anzeige
  39. Sequence(Element[AlleDarstellungen, Element[Anzeige, k]], k, 1, Length[Anzeige]) → AnzeigeDarstellungen