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选择合适的方程：文本情境到线性方程匹配

选择合适的方程：文本情境到线性方程匹配
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2022-01-31 16:42
函数几何作图函数图像
所属专题 Wiederholung: Variablen, Terme und Gleichungen Gleichungen lösen mit Umkehroperationen
这个范例演示如何根据给定文字情境去选择与之对应的方程，并通过对错反馈帮助学生建立“情境—等式”的对应关系。核心数学概念包括线性方程、由文字题列方程、将未知量设为变量、用等式刻画数量关系，以及在情境中正确表述方程含义。作图与交互构造要点来源于构造摘要：使用 Shuffle（打乱）与 Sequence（生成序列）来组织多组题目情境/选项；用 Element（抽取元素）与 Join（拼接）来组合题干与答案选项；借助 If（条件判断）实现根据学生选择判定对错；用 Point 与 Polygon 构造必要的几何/界面元素或标注区域；再结合文本对象（如 textCase*AnswerCorrect/Wrong）实现“选择正确/错误”的提示。适合5-6年级到初中早期的代数入门练习，用于课堂互动、作业巩固或GeoGebra教学活动中训练列一元一次方程的能力。

GeoGebra 命令及参数

  1. Shuffle(Sequence[Random[1, 5], i, 1, 100]) → randomNosPositionAnswerCorrect1, {5, 3, 4, 3, 5, 1, 3, 4, 1, 2, 5, 2, 4, 3, 1, 4, 4, 2, 2, 5, 1, 3, 2, 3, 3, 4, 3, 2, 1, 2, 1, 4, 4, 5, 1, 1, 5, 5, 3, 5, 5, 1, 4, 5, 1, 3, 5, 2, 5, 5, 5, 4, 2, 3, 1, 3, 2, 5, 2, 1, 5, 2, 3, 5, 4, 2, 2, 2, 5, 4, 1, 1, 5, 1, 4, 1, 4, 3, 4, 1, 1, 4, 3, 5, 2, 3, 5, 1, 2, 1, 1, 3, 3, 3, 2, 5, 1, 4, 1, 2}
  2. Sequence(RandomElement[Remove[Sequence[5], {randomNosPositionAnswerCorrect1(i)}]], i, 1, 100) → randomNosPositionAnswerWrong1, {1, 4, 3, 1, 3, 5, 5, 2, 2, 1, 2, 4, 3, 1, 5, 2, 5, 3, 1, 1, 4, 4, 4, 1, 2, 3, 1, 4, 3, 4, 2, 1, 1, 1, 4, 2, 2, 1, 5, 3, 1, 4, 2, 2, 5, 4, 3, 4, 3, 3, 2, 3, 3, 2, 2, 5, 5, 1, 3, 4, 4, 1, 1, 1, 5, 4, 3, 4, 4, 1, 5, 3, 2, 5, 2, 2, 2, 2, 5, 2, 4, 2, 4, 1, 4, 4, 2, 5, 1, 2, 5, 5, 2, 2, 1, 2, 4, 3, 2, 3}
  3. Element(randomNosPositionAnswerWrong1, Mod[questionCount, 100] + 1) → numPositionAnswerWrong1
  4. Sequence(RandomElement[Remove[Remove[Sequence[5], {randomNosPositionAnswerCorrect1(i)}], {randomNosPositionAnswerWrong1(i)}]], i, 1, 100) → randomNosPositionAnswerWrong2, {3, 2, 2, 5, 4, 2, 4, 5, 4, 5, 4, 1, 1, 5, 3, 3, 1, 1, 4, 4, 3, 5, 5, 2, 5, 5, 5, 3, 4, 3, 3, 2, 3, 3, 5, 4, 1, 3, 2, 1, 3, 3, 1, 1, 3, 1, 4, 5, 2, 1, 4, 1, 1, 5, 3, 1, 1, 4, 1, 5, 2, 5, 2, 4, 2, 5, 5, 3, 1, 2, 2, 5, 3, 3, 3, 3, 1, 5, 2, 5, 5, 3, 5, 2, 3, 5, 1, 2, 3, 5, 3, 2, 4, 4, 3, 4, 3, 1, 4, 1}
  5. Element(randomNosPositionAnswerWrong2, Mod[questionCount, 100] + 1) → numPositionAnswerWrong2
  6. Sequence(RandomElement[Remove[Remove[Remove[Sequence[5], {randomNosPositionAnswerCorrect1(i)}], {randomNosPositionAnswerWrong1(i)}], {randomNosPositionAnswerWrong2(i)}]], i, 1, 100) → randomNosPositionAnswerCorrect2, {4, 1, 1, 4, 2, 3, 2, 1, 3, 4, 1, 3, 2, 4, 2, 1, 2, 4, 3, 2, 2, 1, 1, 5, 1, 1, 2, 1, 5, 5, 5, 5, 5, 2, 3, 3, 3, 4, 1, 4, 4, 5, 3, 3, 2, 5, 2, 1, 1, 2, 1, 5, 5, 1, 5, 4, 4, 3, 4, 3, 1, 4, 4, 3, 1, 1, 4, 5, 3, 3, 3, 4, 4, 2, 1, 4, 3, 4, 1, 4, 2, 1, 1, 4, 1, 2, 3, 4, 4, 3, 2, 1, 1, 1, 4, 1, 5, 5, 5, 4}
  7. Element(randomNosPositionAnswerCorrect2, Mod[questionCount, 100] + 1) → numPositionAnswerCorrect2
  8. Sequence(RandomElement[Remove[Remove[Remove[Remove[Sequence[5], {randomNosPositionAnswerCorrect1(i)}], {randomNosPositionAnswerWrong1(i)}], {randomNosPositionAnswerWrong2(i)}], {randomNosPositionAnswerCorrect2(i)}]], i, 1, 100) → randomNosPositionAnswerMixed, {2, 5, 5, 2, 1, 4, 1, 3, 5, 3, 3, 5, 5, 2, 4, 5, 3, 5, 5, 3, 5, 2, 3, 4, 4, 2, 4, 5, 2, 1, 4, 3, 2, 4, 2, 5, 4, 2, 4, 2, 2, 2, 5, 4, 4, 2, 1, 3, 4, 4, 3, 2, 4, 4, 4, 2, 3, 2, 5, 2, 3, 3, 5, 2, 3, 3, 1, 1, 2, 5, 4, 2, 1, 4, 5, 5, 5, 1, 3, 3, 3, 5, 2, 3, 5, 1, 4, 3, 5, 4, 4, 4, 5, 5, 5, 3, 2, 2, 3, 5}
  9. Element(randomNosPositionAnswerMixed, Mod[questionCount, 100] + 1) → numPositionAnswerMixed
  10. Element(randomNosPositionAnswerCorrect1, Mod[questionCount, 100] + 1) → numPositionAnswerCorrect1
  11. Join({{1, 4}, l2}) → reihenfolge
  12. Shuffle(Sequence[Random[1, 4], i, 1, 100]) → randomNosCase, {1, 1, 1, 2, 3, 4, 1, 3, 3, 4, 1, 4, 4, 3, 3, 1, 2, 1, 1, 1, 1, 4, 4, 3, 1, 1, 1, 2, 4, 3, 3, 2, 1, 1, 1, 4, 4, 4, 2, 3, 1, 1, 2, 3, 1, 4, 4, 1, 2, 4, 2, 1, 4, 2, 2, 2, 2, 4, 3, 3, 4, 1, 3, 1, 2, 2, 4, 2, 4, 2, 2, 3, 2, 3, 2, 2, 2, 3, 1, 3, 2, 3, 3, 3, 3, 2, 2, 1, 3, 3, 3, 4, 3, 3, 2, 2, 2, 4, 1, 3}
  13. If((numPositionAnswerCorrect1 ≟ 3 ∨ numPositionAnswerCorrect2 ≟ 3 ∨ MixedCorrect(numCase) ≟ true ∧ numPositionAnswerMixed ≟ 3) ∧ checkbox3 ≟ true, true, false) → c3
  14. If((numPositionAnswerCorrect1 ≟ 2 ∨ numPositionAnswerCorrect2 ≟ 2 ∨ MixedCorrect(numCase) ≟ true ∧ numPositionAnswerMixed ≟ 2) ∧ checkbox2 ≟ true, true, false) → c2
  15. If((numPositionAnswerCorrect1 ≟ 1 ∨ numPositionAnswerCorrect2 ≟ 1 ∨ MixedCorrect(numCase) ≟ true ∧ numPositionAnswerMixed ≟ 1) ∧ checkbox1 ≟ true, true, false) → c1
  16. If((numPositionAnswerCorrect1 ≟ 4 ∨ numPositionAnswerCorrect2 ≟ 4 ∨ MixedCorrect(numCase) ≟ true ∧ numPositionAnswerMixed ≟ 4) ∧ checkbox4 ≟ true, true, false) → c4
  17. If((numPositionAnswerCorrect1 ≟ 5 ∨ numPositionAnswerCorrect2 ≟ 5 ∨ MixedCorrect(numCase) ≟ true ∧ numPositionAnswerMixed ≟ 5) ∧ checkbox5 ≟ true, true, false) → c5
  18. If(MixedCorrect(numCase) ≟ true, checkboxes(numPositionAnswerMixed), true) → c6
  19. Point(Line[F11, Vector[(0, 0), (1, 0)]]) → F21
  20. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  21. Polygon(PtopLeftCornerFeedback_{1}, PtopRightCornerFeedback_{1}, PbottomRightCornerFeedback_{1}, PbottomLeftCornerFeedback_{1}) → rectangleCorrect_{1}, ptopleftcornerfeedback_{1}, ptoprightcornerfeedback_{1}, pbottomrightcornerfeedback_{1}, pbottomleftcornerfeedback_{1}
  22. Polygon(PtopLeftCornerFeedback_{2}, PtopRightCornerFeedback_{2}, PbottomRightCornerFeedback_{2}, PbottomLeftCornerFeedback_{2}) → rectangleCorrect_{2}, ptopleftcornerfeedback_{2}, ptoprightcornerfeedback_{2}, pbottomrightcornerfeedback_{2}, pbottomleftcornerfeedback_{2}
  23. Polygon(PtopLeftCornerFeedback_{3}, PtopRightCornerFeedback_{3}, PbottomRightCornerFeedback_{3}, PbottomLeftCornerFeedback_{3}) → rectangleCorrect_{3}, ptopleftcornerfeedback_{3}, ptoprightcornerfeedback_{3}, pbottomrightcornerfeedback_{3}, pbottomleftcornerfeedback_{3}
  24. Polygon(PtopLeftCornerFeedback_{4}, PtopRightCornerFeedback_{4}, PbottomRightCornerFeedback_{4}, PbottomLeftCornerFeedback_{4}) → rectangleCorrect_{4}, ptopleftcornerfeedback_{4}, ptoprightcornerfeedback_{4}, pbottomrightcornerfeedback_{4}, pbottomleftcornerfeedback_{4}

AI 绘图提示语参考

创建一个交互式学习界面，展示如何将文字问题描述与线性方程匹配。界面包含多个选项和即时反馈，通过随机生成问题情境和答案选项，用不同颜色区分正确与错误答案。用几何图形表示答案选项，正确答案用绿色边框矩形，错误答案用红色边框矩形，并配以文字说明反馈。先展示问题情境和选项，用户选择后显示正确或错误的视觉反馈，帮助学习者理解线性方程的应用。
以上提示语为根据原始绘图命令整理而来，仅供参考。