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2 和 5 的整除性

2 和 5 的整除性
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2024-01-23 15:06
不等式
所属专题 Teilbarkeitsregeln
本范例演示了如何使用 GeoGebra 来探索 2 和 5 的整除性规则。核心数学概念包括整除性、因数和倍数。作图要点包括使用 Polygon、Shuffle、Midpoint 等 GeoGebra 命令来创建图形。适合的学段或用途包括初中数学教育，特别是整除性和因数的学习。

GeoGebra 命令及参数

  1. Polygon(Q1E1, Q1E2, 4) → Q1, q1_1, q1_2, q1_3, q1_4, Q1E3, Q1E4
  2. Polygon(Q2E1, Q2E2, 4) → Q2, q2_1, q2_2, q2_3, q2_4, Q2E3, Q2E4
  3. Polygon(Q3E1, Q3E2, 4) → Q3, q3_4, q3_1, q3_2, q3_3, Q3E3, Q3E4
  4. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 5), k, 1, 20]], i], i, 1, 6]) → RandomList5, {20, 25, 15, 50, 65, 75}
  5. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 2), k, 1, 50]], i], i, 1, 6]) → RandomList2, {22, 20, 98, 4, 44, 32}
  6. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 10), k, 1, 10]], i], i, 1, 6]) → RandomList10, {80, 90, 30, 30, 50, 50}
  7. Shuffle(Unique[Join[{RandomList2, RandomList5, RandomList10}]]) → RandomListNum, {22, 25, 15, 80, 75, 50, 32, 65, 4, 98, 90, 44, 20, 30}
  8. Midpoint(Corner[NumText7, 1], Corner[NumText7, 3]) → Pos7
  9. Midpoint(Corner[NumText10, 1], Corner[NumText10, 3]) → Pos10
  10. Midpoint(Corner[T1830, 1], Corner[T1830, 3]) → Pos1830
  11. Midpoint(Corner[NumText6, 1], Corner[NumText6, 3]) → Pos6
  12. Midpoint(Corner[NumText3, 1], Corner[NumText3, 3]) → Pos3
  13. Midpoint(Corner[T1826, 1], Corner[T1826, 3]) → Pos1826
  14. Midpoint(Corner[NumText5, 1], Corner[NumText5, 3]) → Pos5
  15. Midpoint(Corner[NumText9, 1], Corner[NumText9, 3]) → Pos9
  16. Midpoint(Corner[T2628, 1], Corner[T2628, 3]) → Pos2628
  17. Midpoint(Corner[NumText8, 1], Corner[NumText8, 3]) → Pos8
  18. Midpoint(Corner[NumText4, 1], Corner[NumText4, 3]) → Pos4
  19. Midpoint(Corner[NumText2, 1], Corner[NumText2, 3]) → Pos2
  20. Midpoint(Corner[NumText1, 1], Corner[NumText1, 3]) → Pos1
  21. Textfield(aInput) → InputBox1
  22. Textfield(bInput) → InputBox2
  23. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  24. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 10, 10, 2, 5, 1, 1, 3, 0, 9, 4, 0, 2, 2, 2, 1, 0, 7, 0, 5, 1, 8, 8, 3, 7, 1, 9, 2, 2, 1, 6, 6, 0, 4, 4, 8, 4, 10, 2, 2, 8, 7, 10, 7, 7, 7, 9, 0, 10, 8, 5, 1, 0, 2, 2, 8, 6, 1, 6, 0, 5, 8, 10, 0, 6, 4, 7, 7, 0, 8, 10, 7, 2, 0, 5, 9, 0, 2, 5, 10, 3, 2, 10, 9, 7, 7, 1, 3, 5, 6, 4, 8, 6, 8, 1, 6, 2, 10, 7, 1}
  25. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  26. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {10, 7, 9, 9, 1, 5, 8, 1, 6, 1, 10, 2, 3, 5, 7, 7, 2, 8, 2, 9, 9, 5, 3, 1, 6, 5, 8, 1, 8, 4, 5, 3, 7, 6, 8, 10, 0, 6, 7, 10, 5, 9, 8, 5, 4, 4, 5, 0, 9, 1, 8, 0, 7, 7, 10, 2, 5, 3, 4, 1, 0, 5, 6, 0, 9, 4, 5, 7, 6, 6, 7, 1, 2, 3, 6, 8, 6, 4, 1, 10, 2, 3, 0, 10, 8, 5, 3, 8, 10, 8, 0, 5, 4, 6, 1, 7, 0, 1, 9, 8}
  27. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  28. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  29. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  30. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  31. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  32. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  33. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  34. If(Mod[num1, 10] ≟ 0, 1, Mod[num1, 5] ≟ 0, 3, 2) → num1meta
  35. If(Mod[num2, 10] ≟ 0, 1, Mod[num2, 5] ≟ 0, 3, 2) → num2meta
  36. If(Mod[num3, 10] ≟ 0, 1, Mod[num3, 5] ≟ 0, 3, 2) → num3meta
  37. If(Mod[num4, 10] ≟ 0, 1, Mod[num4, 5] ≟ 0, 3, 2) → num4meta
  38. If(Mod[num5, 10] ≟ 0, 1, Mod[num5, 5] ≟ 0, 3, 2) → num5meta
  39. If(Mod[num6, 10] ≟ 0, 1, Mod[num6, 5] ≟ 0, 3, 2) → num6meta
  40. If(Mod[num7, 10] ≟ 0, 1, Mod[num7, 5] ≟ 0, 3, 2) → num7meta
  41. If(Mod[num8, 10] ≟ 0, 1, Mod[num8, 5] ≟ 0, 3, 2) → num8meta
  42. If(Mod[num9, 10] ≟ 0, 1, Mod[num9, 5] ≟ 0, 3, 2) → num9meta
  43. If(Mod[num10, 10] ≟ 0, 1, Mod[num10, 5] ≟ 0, 3, 2) → num10meta
  44. IsInRegion(Pos1, If[num1meta ≟ 1, Q1, num1meta ≟ 2, Q2, Q3]) → correct1
  45. IsInRegion(Pos2, If[num2meta ≟ 1, Q1, num2meta ≟ 2, Q2, Q3]) → correct2
  46. IsInRegion(Pos3, If[num3meta ≟ 1, Q1, num3meta ≟ 2, Q2, Q3]) → correct3
  47. IsInRegion(Pos4, If[num4meta ≟ 1, Q1, num4meta ≟ 2, Q2, Q3]) → correct4
  48. IsInRegion(Pos5, If[num5meta ≟ 1, Q1, num5meta ≟ 2, Q2, Q3]) → correct5
  49. IsInRegion(Pos6, If[num6meta ≟ 1, Q1, num6meta ≟ 2, Q2, Q3]) → correct6
  50. IsInRegion(Pos7, If[num7meta ≟ 1, Q1, num7meta ≟ 2, Q2, Q3]) → correct7
  51. IsInRegion(Pos8, If[num8meta ≟ 1, Q1, num8meta ≟ 2, Q2, Q3]) → correct8
  52. IsInRegion(Pos9, If[num9meta ≟ 1, Q1, num9meta ≟ 2, Q2, Q3]) → correct9
  53. IsInRegion(Pos10, If[num10meta ≟ 1, Q1, num10meta ≟ 2, Q2, Q3]) → correct10
  54. Join(Sequence[Element[Sequence[Sequence[Q2E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge2
  55. Join(Sequence[Element[Sequence[Sequence[Q1E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge1
  56. Join(Sequence[Element[Sequence[Sequence[Q3E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge3
  57. Text(CorrHelper, A, false, true, 0, 0) → Text11
  58. Length(RandomListNum) → a

AI 绘图提示语参考

画一个图形来探索2和5的整除规则。首先画出三个多边形Q1、Q2和Q3，分别代表2和5的倍数。然后随机生成一些数字，将它们分布在Q1、Q2和Q3中。接着，根据这些数字是否能被2或5整除，将它们放置在相应的多边形内。最后，通过拖动点Pos1到Pos10，检查它们是否位于正确的多边形内，以验证整除规则。
以上提示语为根据原始绘图命令整理而来，仅供参考。