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自然数乘带分数：有理数乘法作图求值

自然数乘带分数：有理数乘法作图求值
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2023-05-22 17:04
函数不等式几何作图函数图像
所属专题 Natürliche Zahl mit Bruchzahl multiplizieren
本范例通过在 GeoGebra 中随机生成题目，让学习者观察“自然数 × 带分数”对应的代数化结果，并在界面中逐步核对计算分子与分母的变化。核心数学概念包括：带分数与假分数的表示、分子分母的乘法规则、最简分式（分子分母可能需要化简）、以及在随机参数下保证题目与答案一致的数论操作。作图与交互要点来自构造摘要：使用 Shuffle 与 Element 随机抽取参数（questionCount、randomNosForC/B/A 及其 numC/numD/numB/numA），用 Mod 控制取值范围与整除相关条件；借助 Numerator 与 Denominator 抽取结果分式的分子分母（solZaehler1/solZaehler2、solNenner1/solNenner2），并用 If 与 Textfield 生成条件化的提示文本与输入框；同时通过 Polygon、Segment、Corner、Text 等对象承载题面结构与几何/示意区域（Corner1/Corner2、PosBox1 等）。适合中学阶段的有理数运算与分数乘法复习，也可用于课堂练习系统或交互式作业生成。

GeoGebra 命令及参数

  1. Shuffle(Sequence[Random[1, 9], i, 1, 100]) → randomNosForC, {3, 1, 3, 9, 2, 9, 6, 2, 9, 2, 8, 3, 6, 9, 4, 9, 1, 7, 7, 1, 9, 7, 7, 2, 3, 9, 5, 5, 4, 3, 2, 3, 6, 3, 7, 2, 8, 7, 5, 5, 7, 6, 8, 7, 2, 5, 5, 7, 5, 7, 7, 5, 5, 7, 6, 5, 4, 1, 1, 2, 3, 3, 8, 6, 7, 1, 1, 6, 6, 9, 6, 6, 6, 5, 6, 7, 8, 5, 8, 5, 3, 7, 1, 9, 3, 3, 3, 8, 7, 5, 1, 2, 4, 5, 9, 2, 1, 6, 9, 4}
  2. Element(randomNosForC, Mod[questionCount, 100] + 1) → numC
  3. Shuffle(Sequence[Random[numC + 1, 10], i, 1, 100]) → randomNosForD, {10, 9, 10, 6, 10, 8, 8, 8, 6, 5, 9, 10, 9, 10, 6, 10, 6, 7, 5, 10, 8, 7, 10, 8, 6, 9, 5, 6, 8, 7, 5, 7, 7, 8, 8, 6, 8, 8, 7, 10, 6, 9, 6, 7, 5, 5, 7, 9, 6, 8, 10, 6, 8, 5, 6, 5, 6, 9, 5, 8, 8, 5, 9, 7, 8, 8, 6, 5, 5, 9, 10, 9, 9, 6, 10, 5, 5, 8, 9, 8, 9, 10, 10, 7, 9, 7, 5, 8, 6, 7, 9, 5, 10, 5, 8, 9, 10, 5, 10, 5}
  4. Element(randomNosForD, Mod[questionCount, 100] + 1) → numD
  5. Shuffle(Sequence[Random[2, 6], i, 1, 100]) → randomNosForB, {5, 3, 5, 2, 6, 2, 6, 4, 5, 6, 6, 3, 2, 3, 6, 2, 3, 3, 2, 5, 2, 6, 4, 6, 6, 5, 6, 5, 6, 5, 2, 4, 2, 4, 6, 5, 5, 3, 6, 2, 2, 5, 6, 4, 3, 5, 6, 3, 4, 6, 2, 2, 2, 4, 6, 4, 5, 6, 6, 4, 6, 2, 3, 6, 3, 5, 3, 5, 3, 3, 5, 3, 6, 2, 3, 4, 3, 6, 2, 6, 4, 2, 3, 6, 2, 3, 5, 6, 3, 2, 6, 5, 2, 3, 2, 6, 2, 4, 2, 5}
  6. Element(randomNosForB, Mod[questionCount, 100] + 1) → numB
  7. Shuffle(Sequence[Random[2, 8], i, 1, 100]) → randomNosForA, {3, 8, 6, 2, 2, 5, 7, 2, 5, 2, 6, 5, 4, 5, 4, 5, 3, 6, 6, 4, 8, 6, 8, 6, 4, 3, 3, 2, 4, 4, 7, 7, 8, 2, 8, 2, 3, 5, 8, 6, 5, 8, 6, 3, 6, 6, 3, 3, 4, 3, 6, 6, 2, 2, 6, 7, 2, 4, 8, 6, 8, 2, 2, 8, 7, 2, 8, 5, 5, 3, 4, 5, 3, 8, 2, 8, 3, 8, 4, 3, 5, 3, 7, 6, 5, 4, 8, 5, 6, 5, 5, 2, 4, 4, 6, 8, 8, 3, 7, 3}
  8. Element(randomNosForA, Mod[questionCount, 100] + 1) → zwischenNumA
  9. Mod(zwischenSolZaehler1, solNenner1) → zwischenSolZaehler2
  10. If(zwischenSolZaehler2 ≟ 0, zwischenNumA + 1, zwischenNumA) → numA
  11. Mod(solZaehler1, solNenner1) → solZaehler2
  12. Corner(text1, 3) → Corner1
  13. If(¬showhint, Corner1 + (0.8, 0), Corner1 + (0.3, 0)) → PosBox1
  14. Corner(text2, 3) → Corner2
  15. If(showhint, correctHint, input1 / input2 ≟ Dez1 ∨ ((input8 * input2) + input1) / input2 ≟ Dez1) → correct1
  16. Textfield(input1) → InputBox1
  17. Textfield(input2) → InputBox2
  18. If(solZaehler1 < solNenner1 ∨ ((input8 * input2) + input1) / input2 ≟ Dez1 ∧ input2 > input1, correct1, If[Mod[solZaehler1, solNenner1] ≟ 0, correct1 ∧ correct3, If[solZaehler1 > solNenner1, correct1 ∧ correct2 ∧ correct3]]) → correct
  19. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  20. If(¬showBoxes, Defined[(input1 * input2)], If[showBoxes ∧ showhint ∧ Mod[input6, input7] ≟ 0, Defined[((((input1 * input2) * input6) * input7) * input3)], If[showBoxes ∧ showhint ∧ Mod[input6, input7] ≠ 0 ∧ input6 > input7, Defined[((((((input1 * input2) * input3) * input4) * input5) * input6) * input7)], If[showBoxes ∧ showhint ∧ Mod[input6, input7] ≠ 0 ∧ input6 < input7, Defined[(((input1 * input2) * input6) * input7)], If[showBoxes ∧ Mod[input1, input2] ≟ 0, Defined[((input1 * input2) * input3)], If[showBoxes ∧ Mod[input1, input2] ≠ 0, Defined[((((input1 * input2) * input3) * input4) * input5)]]]]]]) → fixed
  21. Segment(Corner1 + (0.3, -0.63), Corner1 + (1.03, -0.63)) → f
  22. Textfield(input3) → InputBox3
  23. Textfield(input4) → InputBox4
  24. Textfield(input5) → InputBox5
  25. If(showBoxes ∧ input6 > input7, Corner2 + (3.2, -1.45), Corner2 + (1.71, -1.45)) → PbottomRightCornerFeedback_{1}
  26. If(showBoxes ∧ input6 > input7, Corner2 + (2.29, 0.17), Corner2 + (0.82, 0.17)) → PtopLeftCornerFeedback_{1}
  27. Polygon(PtopLeftCornerFeedback_{1}, PtopRightCornerFeedback_{1}, PbottomRightCornerFeedback_{1}, PbottomLeftCornerFeedback_{1}) → rectangleCorrect_{1}, ptopleftcornerfeedback_{1}, ptoprightcornerfeedback_{1}, pbottomrightcornerfeedback_{1}, pbottomleftcornerfeedback_{1}
  28. If(showBoxes ∧ input6 > input7, Corner2 + (2.2, -0.2), Corner2 + (0.78, -0.2)) → PtopLeftCornerFeedback_{2}
  29. If(showBoxes ∧ input6 > input7, Corner2 + (1.3, -1.05), Corner2 + (-0.05, -1.05)) → PbottomRightCornerFeedback_{2}
  30. Polygon(PtopLeftCornerFeedback_{2}, PtopRightCornerFeedback_{2}, PbottomRightCornerFeedback_{2}, PbottomLeftCornerFeedback_{2}) → rectangleCorrect_{2}, ptopleftcornerfeedback_{2}, ptoprightcornerfeedback_{2}, pbottomrightcornerfeedback_{2}, pbottomleftcornerfeedback_{2}
  31. If(showBoxes ∧ Mod[input1, input2] ≟ 0, Corner2 + (-0.5, -1.5), If[showBoxes ∧ Mod[input1, input2] ≠ 0, Corner2 + (-0.5, -1.5), Corner1 + (0, -1.5)]) → PointTextCorrect
  32. Textfield(input6) → InputBox6
  33. Textfield(input7) → InputBox7
  34. Segment(Corner2 + (0, -0.63), Corner2 + (0.7, -0.63)) → h
  35. If(showhint ∧ input6 > input7, Corner2 + (2.4, -0.8), Corner2 + (0.9, -0.8)) → Pos3
  36. If(showhint ∧ input6 > input7, Segment[Corner2 + (2.4, -0.63), Corner2 + (3.15, -0.63)], Segment[Corner2 + (0.91, -0.63), Corner2 + (1.63, -0.63)]) → g
  37. Polygon(PtopLeftCornerFeedback_{3}, PtopRightCornerFeedback_{3}, PbottomRightCornerFeedback_{3}, PbottomLeftCornerFeedback_{3}) → rectangleCorrect_{3}, ptopleftcornerfeedback_{3}, ptoprightcornerfeedback_{3}, pbottomrightcornerfeedback_{3}, pbottomleftcornerfeedback_{3}
  38. If(showhint ∧ input6 > input7, Corner2 + (2.4, 0), Corner2 + (0.9, 0)) → Pos2
  39. Textfield(input8) → InputBox0
  40. Segment(PosBox1 + (0.04, -0.63), PosBox1 + (0.7, -0.63)) → PosLine
  41. Numerator(Dez2) → KuerzZaehler
  42. Denominator(Dez2) → KuerzNenner
  43. If(showhint ∧ input6 > input7, Corner2 + (1.4, -0.4), If[showhint ∧ input6 ≟ input7, Corner2 + (1.4, -0.4), Corner2 + (0, -0.4)]) → Pos1

AI 绘图提示语参考

画一个数学问题，包含一个自然数和一个带分数的乘法。首先展示随机生成的自然数和带分数，带分数通过几何图形（如多边形）表示。接着，用几何方法（如分割和组合图形）展示乘法过程，将带分数转换为假分数，然后进行分数乘法。最后，用文本框显示输入和解释，并用几何图形（如矩形）表示计算结果，确保结果分数正确且简化。
以上提示语为根据原始绘图命令整理而来，仅供参考。