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用长方体体积公式进行计算与错误诊断

用长方体体积公式进行计算与错误诊断
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2023-03-23 22:45
所属专题 Quader und Würfel - Volumen Wiederholung: Quader und Würfel
该范例通过长方体与立方体的体积计算情境，展示体积公式 V= a·b·c 的正确用法，并提出开放题让学习者解释计算步骤与纠正常见错误。核心数学概念包括：立体几何的体积（单位立方体计数）、长方体体积公式的由来与应用、用代数方程/比例关系求未知棱长，以及对“维度”或“乘法顺序/幂次误用”的错误进行原因分析。作图与交互要点：①使用输入框（InputBox）让学生输入边长或填写缺失量，并用逻辑判断（If、Max）控制题目是否判定正确（inputCorrect）以及题目数量（questionCount）或取值范围；②通过随机数机制（Shuffle、randomNosForA/B/C、randomNosFork）生成 a、b、c 的不同取值，实现可变题；③用文本标注/气泡呈现题干与反馈，包含文本输入（Textfield）、用于提问的文本块（text1）与对话气泡（SpeechBubbleRight），并

GeoGebra 命令及参数

  1. Textfield(vol) → InputBox4
  2. Shuffle(Sequence[Random[3, 7], i, 1, 100]) → randomNosFork, {4, 5, 4, 4, 3, 4, 3, 7, 3, 6, 7, 6, 5, 7, 6, 4, 4, 4, 5, 7, 4, 4, 7, 5, 5, 3, 4, 3, 4, 7, 6, 3, 3, 6, 5, 5, 4, 3, 6, 6, 6, 4, 4, 3, 3, 4, 6, 7, 5, 3, 7, 3, 4, 7, 4, 3, 6, 5, 6, 6, 3, 7, 6, 5, 5, 7, 5, 6, 5, 7, 5, 3, 7, 5, 4, 4, 4, 4, 6, 5, 5, 3, 6, 7, 3, 4, 3, 7, 3, 3, 4, 7, 4, 5, 4, 3, 4, 7, 3, 6}
  3. Element(randomNosFork, Mod[questionCount, 100] + 1) → k
  4. Shuffle(Sequence[Random[1, 7], i, 1, 100]) → randomNosForB, {7, 1, 6, 2, 2, 1, 1, 2, 3, 6, 3, 6, 3, 5, 7, 5, 1, 4, 4, 3, 1, 3, 7, 1, 7, 2, 7, 1, 4, 5, 5, 1, 5, 4, 2, 7, 6, 1, 6, 6, 7, 6, 6, 4, 4, 3, 6, 7, 6, 1, 6, 2, 3, 6, 5, 7, 5, 4, 5, 2, 2, 6, 7, 1, 7, 4, 6, 3, 4, 4, 5, 3, 6, 5, 4, 4, 3, 2, 5, 2, 6, 6, 7, 6, 3, 4, 3, 5, 1, 1, 3, 4, 1, 4, 5, 7, 6, 3, 5, 3}
  5. Shuffle(Sequence[Random[10, 59], i, 1, 100]) → randomNosForA, {20, 23, 51, 21, 23, 43, 13, 40, 31, 14, 28, 52, 40, 41, 39, 45, 41, 51, 23, 46, 56, 12, 10, 28, 25, 37, 12, 27, 57, 50, 25, 11, 17, 52, 59, 43, 17, 20, 33, 44, 43, 35, 34, 25, 45, 49, 21, 24, 50, 34, 57, 37, 48, 32, 56, 11, 42, 20, 14, 35, 37, 53, 43, 19, 47, 49, 35, 14, 53, 15, 31, 46, 56, 34, 43, 23, 38, 55, 21, 55, 47, 40, 58, 31, 58, 28, 15, 30, 23, 48, 31, 23, 30, 26, 13, 36, 29, 59, 21, 18}
  6. Element(randomNosForA, Mod[questionCount, 100] + 1) → a
  7. Shuffle(Sequence[Random[6, 9], i, 1, 100]) → randomNosForC, {7, 8, 6, 8, 7, 7, 6, 9, 9, 9, 8, 6, 8, 8, 8, 6, 9, 6, 8, 8, 8, 7, 9, 6, 6, 7, 6, 8, 7, 9, 9, 8, 8, 6, 6, 6, 6, 9, 9, 6, 8, 8, 7, 8, 8, 7, 6, 6, 6, 9, 6, 7, 9, 7, 7, 6, 7, 8, 8, 9, 9, 8, 7, 6, 9, 8, 8, 6, 9, 9, 6, 7, 7, 9, 7, 6, 9, 9, 7, 7, 7, 7, 7, 9, 6, 7, 9, 6, 6, 7, 8, 7, 8, 8, 8, 9, 6, 6, 9, 9}
  8. Element(randomNosForC, Mod[questionCount, 100] + 1) → c
  9. Max(groessen) → maxNum
  10. Shuffle(Sequence[Random[1, 4], i, 1, 100]) → randomNosForEinheit, {1, 2, 2, 2, 1, 4, 1, 3, 3, 4, 2, 3, 4, 4, 1, 2, 2, 2, 4, 1, 1, 1, 2, 4, 3, 1, 2, 3, 4, 4, 4, 4, 2, 3, 1, 2, 2, 2, 4, 2, 2, 2, 2, 1, 3, 1, 2, 4, 3, 1, 4, 2, 3, 3, 1, 3, 4, 1, 4, 3, 3, 3, 3, 4, 1, 2, 1, 4, 2, 1, 1, 1, 4, 3, 4, 1, 2, 1, 2, 3, 4, 4, 2, 3, 1, 1, 3, 2, 1, 1, 3, 1, 1, 2, 1, 3, 3, 1, 2, 3}
  11. Element(randomNosForEinheit, Mod[questionCount, 100] + 1) → Einheit
  12. If(maxNum > 20, 0.03, 0.1) → kuerzung
  13. Rotate(B + (((b * kuerzung) * verzerrung), 0), winkel, B) → C
  14. Rotate(A + (((b * kuerzung) * verzerrung), 0), winkel, A) → D
  15. Rotate(F + (((b * kuerzung) * verzerrung), 0), winkel, F) → G
  16. Rotate(E + (((b * kuerzung) * verzerrung), 0), winkel, E) → H
  17. Segment(A, B) → ab
  18. Segment(B, C) → bc
  19. Segment(C, D) → cd
  20. Segment(A, E) → ae
  21. Segment(B, F) → bf
  22. Segment(E, F) → ef
  23. Segment(E, H) → eh
  24. Segment(F, G) → fg
  25. Segment(G, H) → gh
  26. Segment(A, D) → ad
  27. Segment(D, H) → dh
  28. Segment(C, G) → cg
  29. SpeechBubbleRight(Bubble + (0.47, -0.1), 10.7, 1.3) → bubble2
  30. Textfield(aInput) → InputBox1
  31. Textfield(bInput) → InputBox2
  32. Textfield(cInput) → InputBox3
  33. SelectedIndex(selectedDrop) → index
  34. SpeechBubbleRight(PBubble4, 4.6, 1.7) → bubble3
  35. SpeechBubbleRight(Bubble1, 8, 1.5) → poly1
  36. SpeechBubbleRight(PBubble3, 8, 2.5) → poly2