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整数比较与排序练习 - 基础数学应用

整数比较与排序练习 - 基础数学应用
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2024-05-23 18:24
几何作图
所属专题 Ganze Zahlen & Arbeiten mit der Zahlengerade
这个范例演示了如何通过整数比较和排序来理解数字的大小关系。核心数学概念包括整数比较、排序以及在数轴上的表示。作图要点涉及使用GeoGebra命令如Join、Sequence、Random等来创建整数序列和比较工具。适合小学五年级到六年级学生，用于巩固整数运算和数感培养。

GeoGebra 命令及参数

  1. Join({{2}, Sequence[RandomElement[{2, 3, 4, 5}], k, 1, 99]}) → StepCList1
  2. Sequence(RandomElement[{2, 3, 4, 5}], k, 1, 100) → StepCList2, {3, 2, 2, 2, 4, 3, 2, 2, 5, 5, 3, 3, 2, 3, 3, 3, 5, 4, 4, 2, 2, 5, 4, 2, 4, 2, 3, 3, 4, 5, 4, 3, 2, 4, 5, 2, 3, 5, 2, 2, 5, 4, 5, 2, 3, 4, 2, 3, 3, 4, 2, 2, 5, 4, 3, 4, 4, 4, 4, 2, 2, 5, 3, 4, 4, 3, 2, 2, 4, 5, 2, 4, 2, 4, 3, 3, 5, 3, 5, 5, 2, 4, 4, 4, 4, 3, 4, 3, 3, 3, 3, 4, 3, 5, 5, 2, 4, 5, 4, 3}
  3. Random(-20, -10, 100) → StartList2, {-18, -16, -12, -15, -18, -13, -11, -12, -18, -15, -14, -16, -16, -17, -12, -16, -12, -11, -12, -17, -20, -16, -20, -18, -18, -10, -20, -17, -15, -10, -17, -18, -13, -14, -12, -13, -20, -10, -17, -10, -16, -12, -17, -12, -20, -12, -18, -13, -19, -12, -12, -10, -11, -18, -10, -16, -11, -19, -13, -10, -20, -14, -13, -17, -10, -17, -18, -19, -13, -13, -15, -12, -18, -19, -12, -10, -11, -15, -14, -13, -11, -17, -20, -12, -11, -11, -15, -18, -11, -12, -19, -12, -13, -18, -17, -18, -16, -13, -14, -10}
  4. Sequence(RandomElement[Remove[(StartList2(k))…(StartList2(k) + 20), Sequence[(m * StepCList2(k)), m, -25, 25]]], k, 1, 100) → NumberList2, {-10, -15, -7, -13, -11, -4, 5, -7, -4, 1, -10, -13, -1, -7, -1, -7, -8, 3, 6, -3, -9, -7, -15, -5, -9, -3, -17, -14, -13, -7, -7, -7, -11, -2, 2, -1, -16, -1, -5, -1, -2, -3, -9, 7, -10, -1, 1, 4, -1, 7, 7, 5, -8, 1, -7, -14, 3, 1, -2, 3, -11, 6, -10, -7, -2, 2, -3, -15, 6, -1, -9, -5, -7, -15, 2, -5, 3, -10, -14, 1, -11, -5, -10, -2, 5, 4, -3, -14, -8, 4, -8, 2, -13, -2, -13, -5, -2, -3, 6, 5}
  5. Sequence(RandomElement[{2, 3, 4, 5}], k, 1, 100) → StepCList3, {3, 5, 3, 3, 2, 5, 5, 5, 5, 3, 3, 2, 4, 3, 3, 5, 4, 5, 3, 4, 5, 3, 2, 2, 4, 4, 4, 4, 2, 3, 2, 2, 2, 2, 3, 3, 4, 3, 3, 5, 4, 5, 5, 3, 5, 4, 4, 5, 5, 5, 3, 4, 3, 5, 2, 3, 3, 5, 4, 4, 4, 3, 2, 3, 4, 2, 2, 2, 5, 3, 4, 5, 5, 2, 3, 5, 3, 5, 3, 5, 4, 2, 3, 4, 5, 5, 3, 4, 3, 4, 5, 3, 5, 4, 4, 4, 2, 3, 5, 2}
  6. Element(If[level ≟ 1, StepCList1, level ≟ 2, StepCList2, StepCList3], counter) → stepC
  7. If(level ≟ 1, 21, level ≟ 2, 21, 21) → anzahl
  8. Sequence(-10, k, 1, 100) → StartList1
  9. Random(-50, 30, 100) → StartList3, {28, 13, -11, 25, -48, 18, -49, 28, 4, -45, 25, -9, -5, 29, 28, -27, -3, 29, 27, 28, -47, 20, -49, -9, -47, -45, 21, 28, 0, -16, 11, 19, 11, -5, -28, -23, -16, -48, 17, -16, -36, 22, -46, -46, 13, 29, 2, 16, -14, -47, -44, 17, 7, -14, -46, 19, 15, 9, 3, -24, 19, -16, 1, -49, -19, -21, 19, -40, 9, -37, -4, 23, 30, 8, -46, 23, 23, -23, -36, -14, -45, -37, 22, -1, -6, -6, 19, -5, -32, -25, 2, 4, -15, -8, -29, 11, -7, -29, -23, 1}
  10. If(level ≟ 1, StartList1(counter), level ≟ 2, StartList2(counter), StartList3(counter)) → startNumber
  11. If(show0, Mod[(-startNumber), stepC], 0) → diff
  12. Sequence(RandomElement[Join[{Remove[-10…10, Sequence[(m * StepCList1(k)), m, -100, 100]], Remove[-10…-1, Sequence[(m * StepCList1(k)), m, -100, 100]]}]], k, 1, 100) → NumberList1, {-9, -7, 7, -7, -9, -1, -5, -3, -7, -9, 10, -9, -9, 7, 5, -9, 5, 5, 1, -7, -10, 7, 3, -8, -9, -4, -2, 1, 7, -2, -10, -3, 5, -7, -1, -4, -8, -7, -4, -6, 9, -5, -1, -1, -1, 3, -7, 9, -9, -3, -2, -1, 1, -1, 7, -1, 9, 2, -1, 3, -9, -3, -7, -1, -1, -1, -7, -3, -5, -8, -7, -5, -1, -9, 1, 4, -5, -6, -2, 2, 7, -5, 4, -1, 1, 9, -3, -2, -10, -9, 4, -5, -5, 9, -7, -9, -6, -7, -3, -9}
  13. Sequence(RandomElement[Remove[(StartList3(k))…(StartList3(k) + 20), Sequence[(m * StepCList3(k)), m, -25, 25]]], k, 1, 100) → NumberList3, {29, 14, 7, 40, -41, 38, -31, 33, 7, -37, 28, 11, 6, 38, 31, -26, 1, 29, 46, 41, -31, 35, -43, 7, -42, -45, 25, 33, 5, 2, 21, 27, 17, -3, -28, -22, -5, -34, 17, 1, -29, 31, -27, -31, 23, 39, 10, 22, -14, -46, -29, 18, 19, 6, -35, 32, 16, 13, 14, -22, 27, -10, 5, -37, -17, -19, 31, -33, 13, -22, 15, 34, 36, 13, -28, 33, 23, -22, -25, -3, -35, -35, 25, 18, -2, -3, 32, 9, -17, -19, 18, 20, -1, -5, -21, 25, 1, -10, -18, 3}
  14. Element(If[level ≟ 1, NumberList1, level ≟ 2, NumberList2, NumberList3], counter) → number
  15. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 10, 6, 10, 6, 1, 7, 2, 9, 9}
  16. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  17. Textfield(input) → inputBox
  18. Defined(input) → clickableBtnValidate
  19. Segment(Origin + ((-lengthAxis) - 0.5, 0), Origin + (lengthAxis + 0.5, 0)) → segAxis
  20. Sequence(Origin + ((-lengthAxis), 0) + (((k * 2) * lengthAxis / (anzahl - 1)), 0), k, 0, anzahl - 1) → PointsList
  21. Sequence(Origin + ((-lengthAxis), 0) + (((k * 2) * lengthAxis / (anzahl - 1)), 0), k, 0, anzahl - 1, stepM) → SelectablePoints
  22. Sequence(Segment[PointsList(k) + (0, If[Mod[NumbersOnAxis(k), stepC] ≟ 0, (-segLength2), (-segLength1)]), PointsList(k) + (0, If[Mod[NumbersOnAxis(k), stepC] ≟ 0, segLength2, segLength1])], k, 1, 21, stepM) → SegAxisList
  23. Sequence((If[startNumber < 0, ceil(startNumber / stepC), startNumber > 0, floor(startNumber / stepC), 0] * stepC) + (k * stepC), k, 0, floor(anzahl / stepC)) → NumbersCap, {-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10}
  24. Sequence(Text[(((((("\textsf{" * If[k < 0, "\(", ""]) * "") * k) * "") * If[k < 0, "\)", ""]) * "\vphantom{2}}"), PointsList(k - startNumber + 1) + (If[k < 0, -0.166, 0], (-segLength2)), false, true, 0, -1], k, startNumber + diff, startNumber + anzahl - 1 + diff, stepC) → CapList
  25. Sequence(Text[(((((("\textcolor{" * If[NumbersOnAxis(k) ∈ NumbersCap, "#000000", NumbersOnAxis(k) ≟ number, "#006758", "616161"]) * "}{\textsf{") * If[NumbersOnAxis(k) ∈ NumbersCap, "\small{\(", NumbersOnAxis(k) ≟ number, "\small{\(", "\scriptsize{\("]) * "") * NumbersOnAxis(k)) * "\)}}}"), SelectablePoints(k) + (If[NumbersOnAxis(k) < 0, -0.166, 0], (-segLength2)) + If[NumbersOnAxis(k) ≥ 0 ∧ (NumbersOnAxis(k) ∈ NumbersCap ∨ NumbersOnAxis(k) ≟ number), (0, 0), NumbersOnAxis(k) ≥ 0, (-0.02, 0), (0.05, 0)], false, true, 0, -1], k, 1, Length[NumbersOnAxis], 1) → CapListSol
  26. Translate(imgChilliRot1, Vector[PosImgChilliRot1, PosImgChilliRot1 + ((0.8 * dimChilli), 0)]) → imgChilliRot2
  27. Translate(imgChilliRot1, Vector[(2 * Vector[PosImgChilliRot1, PosImgChilliRot1 + ((0.8 * dimChilli), 0)])]) → imgChilliRot3
  28. Translate(imgChilliGrau1, Vector[PosImgChilliRot1, PosImgChilliRot1 + ((0.8 * dimChilli), 0)]) → imgChilliGrau2

AI 绘图提示语参考

在坐标平面上画一条水平数轴，数轴上按等距放置一排可选的刻度点，并在刻度处显示对应的整数标记（包含负数、零与正数）。同时在数轴下方给出一组离散整数集合：从一组预设起点生成起始数字与若干候选整数，并用这些整数作为“比较/排序”的输入。让某些刻度点按给定步长与位置规则形成可交互的分段小线段，使整条数轴呈现被选中整数所在的位置高亮与对齐。最后再叠加一个比较指示：当选定层级为不同模式时，选择对应的整数序列用于标注“当前题目”的目标数值。
以上提示语为根据原始绘图命令整理而来，仅供参考。