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间接成比例情境判定与供给问题：认识比例关系

间接成比例情境判定与供给问题：认识比例关系
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2023-10-18 22:13
所属专题 Wiederholung: Direkte und Indirekte Proportionalität Indirekte Proportionalität
该范例通过多组文字情境（如猫粮/饲料的可用天数、采摘浆果的用时、两人同行的时间变化）来演示“数量变化与时间变化”是否满足间接成比例的判断过程，并配套开放题引导学生给出生活中的例子。核心数学概念包括：直接成比例与间接成比例的区别、间接比例关系的判定（如两量乘积是否保持不变）、以及在文字情境中建立量之间的联系并给出理由或反驳。作图与交互要点可从构造摘要提炼为：使用下拉选择与索引驱动题目流程（DropDown4/Index4、DropDown3/Index3、DropDown2/Index2、DropDown1/Index1），在过程中通过 Textfield 与文本标注（Text1、Text...）呈现题干与选项；并用几何绘制组件来承载界面与步骤展示（SpeechBubbleLeft/Right、Semicircle、Midpoint、Sequence）以及通过按钮与状态对象控制推进（btnS

GeoGebra 命令及参数

  1. SelectedIndex(DropDown4) → Index4
  2. SelectedIndex(DropDown3) → Index3
  3. SelectedIndex(DropDown2) → Index2
  4. SelectedIndex(OpZeichen1) → IndexOp1
  5. SelectedIndex(OpZeichen2) → IndexOp2
  6. SelectedIndex(OpZeichen3) → IndexOp3
  7. SelectedIndex(DropDown1) → Index1
  8. SpeechBubbleRight(G, 9, 1) → Speech1
  9. Midpoint(TableE1, TableE4) → L
  10. Midpoint(TableE2, TableE3) → M
  11. Sequence(TableE1 + (Vector[TableE1, TableE2] * i / 6), i, 0, 6) → TablePointsL
  12. Sequence(TableE4 + (Vector[TableE1, TableE2] * i / 6), i, 0, 6) → TablePointsR
  13. Textfield(input1) → InputBox1
  14. SpeechBubbleLeft(H, 9, 1) → Speech2
  15. Midpoint(TablePointsL(2), TablePointsL(3)) → TL1
  16. Midpoint(TablePointsL(3), TablePointsL(4)) → TL2
  17. SpeechBubbleRight(D, 10.3, 1.5) → Speech3
  18. Textfield(input2) → InputBox2
  19. Textfield(input3) → InputBox3
  20. Textfield(input4) → InputBox4
  21. Textfield(input5) → InputBox5
  22. Textfield(input6) → InputBox6
  23. Midpoint(TablePointsR(2), TablePointsR(3)) → TR1
  24. Midpoint(TablePointsR(3), TablePointsR(4)) → TR2
  25. Midpoint(TablePointsL(4), TablePointsL(5)) → TL3
  26. Midpoint(TablePointsR(4), TablePointsR(5)) → TR3
  27. Midpoint(TablePointsL(5), TablePointsL(6)) → TL4
  28. Midpoint(TablePointsL(6), TablePointsL(7)) → TL5
  29. Midpoint(TablePointsR(5), TablePointsR(6)) → TR4
  30. Midpoint(TablePointsR(6), TablePointsR(7)) → TR5
  31. SpeechBubbleRight(A, 9, 2) → Vieleck1
  32. Semicircle(TL2, TL1) → a
  33. Semicircle(TR1, TR2) → b
  34. Semicircle(TL3, TL2) → c
  35. Semicircle(TL4, TL3) → e
  36. Semicircle(TL5, TL4) → f
  37. Semicircle(TR2, TR3) → d
  38. Semicircle(TR3, TR4) → g
  39. Semicircle(TR4, TR5) → h