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指数的匹配练习：把幂对应到重复乘法

指数的匹配练习：把幂对应到重复乘法
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2024-04-24 21:33
多边形数列几何作图滑块动画
所属专题 Potenzen - Einführung
这个范例通过交互式“匹配/排序”练习，帮助学生把正整数指数的幂表示与“同一个数的重复相乘”建立联系，并在图形反馈中巩固幂的含义。核心数学概念是：用正整数指数表示反复乘法（a^n 为 n 次重复乘以 a）、幂的读法与意义解释，以及用幂的表示进行简单应用。作图与交互要点主要来自构造摘要中的 GeoGebra 元素与命令：使用 Polygon 构造用于承载题目/区域的多边形外形；用 Sequence 生成可用的数值/位置序列；用 Shuffle 与随机重排来实现题块或选项的打乱；用 If 做条件判断以确定匹配结果；用 Textfield 让用户输入/选择；用 Element 与 Append/Remove 动态管理选项元素的集合；并通过 CountIf 统计匹配次数、Length 检查数据规模；结合 PointIn 判断对象是否落入指定区域，最终用 Text 标注与 optionsR/ optionsL、allowedRect1-4 等对象控制可操作区域与反馈逻辑。适合七到八年级（初中中段）作为指数运算概念理解与巩固练习，也适用于课堂互动或在线作业。

GeoGebra 命令及参数

  1. Polygon(allowedRect4, allowedRect3, allowedRect2, allowedRect1) → allowedRect, a_1, b, c, d
  2. Max(widthsOptionsR) → widthR
  3. Max(heightsOptionsR) → heightR
  4. Max(heightR, Max[heightsOptionsL]) → heightL
  5. Max(widthsOptionsL) → widthL
  6. If(isShuffleOptionsLechts, Shuffle[1…numOptionsR], 1…numOptionsR) → indizesOptionsRechts
  7. If(isShuffleOptionsLinks, Shuffle[1…numOptionsL], 1…numOptionsL) → indizesOptionsLinks
  8. Textfield(input1) → InputBox1
  9. Textfield(input2) → InputBox2
  10. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 7, 8, 7, 7, 3, 9, 0, 7, 10, 7, 4, 5, 7, 10, 2, 9, 9, 3, 6, 3, 7, 4, 9, 5, 5, 9, 4, 10, 9, 0, 1, 3, 1, 7, 8, 3, 8, 2, 0, 5, 6, 1, 3, 4, 10, 3, 8, 9, 3, 0, 9, 3, 2, 0, 10, 2, 5, 10, 0, 10, 4, 2, 10, 5, 10, 7, 6, 3, 7, 7, 6, 8, 4, 1, 1, 2, 4, 8, 5, 8, 2, 5, 5, 2, 1, 5, 1, 0, 2, 10, 1, 1, 5, 7, 9, 0, 8, 6, 9}
  12. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {8, 5, 3, 3, 10, 0, 3, 3, 10, 3, 4, 10, 0, 4, 1, 2, 8, 7, 4, 3, 6, 1, 8, 9, 5, 4, 0, 3, 1, 6, 1, 7, 1, 4, 6, 9, 9, 9, 0, 9, 3, 3, 7, 7, 0, 5, 7, 3, 9, 2, 3, 6, 8, 0, 1, 0, 8, 3, 7, 7, 6, 6, 7, 7, 10, 5, 9, 3, 8, 6, 2, 9, 0, 10, 10, 0, 4, 2, 5, 6, 3, 0, 6, 1, 8, 0, 10, 5, 8, 10, 0, 8, 0, 0, 3, 5, 5, 8, 8, 9}
  14. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  15. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  16. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  17. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  18. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  19. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  20. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  21. Sequence(1) → positionsOptionsRechts
  22. Sequence(Element[optionsRAll, indizesOptionsRechts(i)], i, 1, numOptionsR) → optionsRActual
  23. Length(optionsRActual) → a
  24. Sequence(Element[optionsLAll, indizesOptionsLinks(i)], i, 1, numOptionsL) → optionsLActual
  25. Sequence(allOptionsL(indizesOptionsLinks(i)), i, 1, numOptionsL) → optionsL
  26. Sequence(allOptionsR(indizesOptionsLinks(i)), i, 1, numOptionsL) → optionsR
  27. Polygon((-10, -2), (10, -2), (10, 10), (-10, 10)) → q1, q_1, r_1, s_1, t_1
  28. Polygon(E, F, G, H) → q2, e_1, f_2, g_2, h_2
  29. Polygon(I, J, K, L) → q3, i_2, j_2, k_1, l_1
  30. Sequence(optionsLoesungAll(indizesOptionsLinks(i)), i, 1, numOptionsL) → optionsLoesung
  31. Text(optionsLActual(1), CenterOptionL1, true, true, 0, 0) → opL1
  32. Text(optionsLActual(2), CenterOptionL2, true, true, 0, 0) → opL2
  33. Text(optionsLActual(3), CenterOptionL3, true, true, 0, 0) → opL3
  34. Text(optionsLActual(4), CenterOptionL4, true, true, 0, 0) → opL4
  35. Text(optionsLActual(5), CenterOptionL5, true, true, 0, 0) → opL5
  36. PointIn(allowedRect) → CenterOptionR1
  37. Text(optionsRActual(1), CenterOptionR1, true, true, 0, 0) → opR1
  38. Polygon(CenterOptionR1, CenterOptionR1 - (widthR / 2, heightR / 2), CenterOptionR1 + (widthR / 2, ((-heightR)) / 2), CenterOptionR1 + (widthR / 2, heightR / 2), CenterOptionR1 - (widthR / 2, ((-heightR)) / 2), CenterOptionR1 - (widthR / 2, heightR / 2)) → rectRMove1, centeroptionr1, f, g, h, i, j
  39. PointIn(allowedRect) → CenterOptionR2
  40. Text(optionsRActual(2), CenterOptionR2, true, true, 0, 0) → opR2
  41. Polygon(CenterOptionR2, CenterOptionR2 - (widthR / 2, heightR / 2), CenterOptionR2 + (widthR / 2, ((-heightR)) / 2), CenterOptionR2 + (widthR / 2, heightR / 2), CenterOptionR2 - (widthR / 2, ((-heightR)) / 2), CenterOptionR2 - (widthR / 2, heightR / 2)) → rectRMove2, centeroptionr2, k, l, m, n, p
  42. PointIn(allowedRect) → CenterOptionR3
  43. Text(optionsRActual(3), CenterOptionR3, true, true, 0, 0) → opR3
  44. Polygon(CenterOptionR3, CenterOptionR3 - (widthR / 2, heightR / 2), CenterOptionR3 + (widthR / 2, ((-heightR)) / 2), CenterOptionR3 + (widthR / 2, heightR / 2), CenterOptionR3 - (widthR / 2, ((-heightR)) / 2), CenterOptionR3 - (widthR / 2, heightR / 2)) → rectRMove3, centeroptionr3, q, r, s, t, e
  45. PointIn(allowedRect) → CenterOptionR4
  46. Text(optionsRActual(4), CenterOptionR4, true, true, 0, 0) → opR4
  47. Polygon(CenterOptionR4, CenterOptionR4 - (widthR / 2, heightR / 2), CenterOptionR4 + (widthR / 2, ((-heightR)) / 2), CenterOptionR4 + (widthR / 2, heightR / 2), CenterOptionR4 - (widthR / 2, ((-heightR)) / 2), CenterOptionR4 - (widthR / 2, heightR / 2)) → rectRMove4, centeroptionr4, f_1, g_1, h_1, i_1, j_1
  48. PointIn(allowedRect) → CenterOptionR5
  49. Text(optionsRActual(5), CenterOptionR5, true, true, 0, 0) → opR5
  50. Polygon(CenterOptionR5, CenterOptionR5 - (widthR / 2, heightR / 2), CenterOptionR5 + (widthR / 2, ((-heightR)) / 2), CenterOptionR5 + (widthR / 2, heightR / 2), CenterOptionR5 - (widthR / 2, ((-heightR)) / 2), CenterOptionR5 - (widthR / 2, heightR / 2)) → rectRMove5, centeroptionr5, m_1, n_1, b_1, c_1, d_1
  51. PointIn(allowedRect) → CenterOptionR6
  52. Text(optionsRActual(6), CenterOptionR6, true, true, 0, 0) → opR6
  53. Polygon(CenterOptionR6, CenterOptionR6 - (widthR / 2, heightR / 2), CenterOptionR6 + (widthR / 2, ((-heightR)) / 2), CenterOptionR6 + (widthR / 2, heightR / 2), CenterOptionR6 - (widthR / 2, ((-heightR)) / 2), CenterOptionR6 - (widthR / 2, heightR / 2)) → rectRMove6, centeroptionr6, k_2, l_2, m_2, n_2, p_2
  54. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR1] ≟ 4, 1, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR1] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR1] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR1] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR1] ≟ 4, 5) → indexAnswerR1
  55. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR2] ≟ 4, 1, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR2] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR2] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR2] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR2] ≟ 4, 5) → indexAnswerR2
  56. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR3] ≟ 4, 1, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR3] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR3] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR3] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR3] ≟ 4, 5) → indexAnswerR3
  57. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR4] ≟ 4, 1, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR4] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR4] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR4] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR4] ≟ 4, 5) → indexAnswerR4
  58. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR5] ≟ 4, 1, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR5] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR5] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR5] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR5] ≟ 4, 5) → indexAnswerR5
  59. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR6] ≟ 4, 1, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR6] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR6] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR6] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR6] ≟ 4, 5) → indexAnswerR6
  60. CountIf(ind ≠ -1, ind, indizesAnswerR) → numAnswersDraggedToLeft
  61. If(correct, "\vphantom{✘}✓ Richtig", If[correctpartially, "\vphantom{✓}✘ Teilweise richtig", "\vphantom{✓}✘ Falsch"]) → correctTextTemp
  62. Text((("\textsf{" * correctTextTemp) * "}"), PStartCorrectText, true, true, 1, 0) → correctText

AI 绘图提示语参考

创建一个交互式图形，展示正整数指数与重复乘法的关联。包含多个矩形区域和选项，通过拖拽选项到对应区域进行匹配。图形中心有一个大矩形，周围分布着多个小矩形作为选项区域，每个区域通过文字标注显示对应的指数表达式。用户需要理解指数的意义，将表达式拖拽到表示正确乘法结果的区域。图形设计应清晰展示指数运算的概念，适合中年级学生理解。
以上提示语为根据原始绘图命令整理而来，仅供参考。