比较苹果与橙子的比率活动:通过图形理解比例关系

比较苹果与橙子的比率活动:通过图形理解比例关系
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2022-12-24 03:32
这个活动通过GeoGebra工具帮助学生理解比率的概念。演示内容包括绘制苹果和橙子的图形,并比较它们的数量关系。核心数学概念是比率和比例。作图要点包括使用Shuffle、Element、Sample等命令创建图形,以及通过InputBox输入数值。适合6-8年级学生用于数学教学和课堂互动。

GeoGebra 命令及参数

  1. Shuffle(Sequence[35]) → applesNums, {26, 19, 13, 33, 22, 2, 21, 15, 30, 7, 4, 23, 11, 24, 31, 32, 12, 1, 34, 9, 10, 18, 6, 28, 3, 8, 17, 5, 27, 20, 25, 14, 16, 35, 29}
  2. Element(applesNums, Mod[questionCount, Length[applesNums]] + 1) → applesShown
  3. Shuffle(Sequence[36 - applesShown]) → orangesNums, {6, 1, 5, 4, 7, 3, 8, 9, 10, 2}
  4. Sample(Sequence[36], applesShown, false) → applesPos, {20, 17, 32, 36, 2, 4, 14, 24, 28, 25, 6, 1, 21, 22, 9, 19, 11, 31, 27, 12, 15, 13, 7, 29, 34, 26}
  5. Element(orangesNums, 1) → orangesShown
  6. Sample(Sequence[36] \ applesPos, orangesShown, false) → orangesPos, {30, 23, 5, 8, 10, 18}
  7. Corner(5) → AppSize
  8. Polygon({(0, 0), (10, 0), (10, 4), (0, 4)}) → box
  9. Flatten(Sequence[Sequence[(0.5 + kk, 4 - (0.5 + jj)), kk, 0, 9], jj, 0, 4]) → positions
  10. Sequence(Circle[Element[positions, Element[applesPos, kk]], 0.25], kk, 1, Length[positions]) → apples_{2}
  11. Sequence(Circle[Element[positions, Element[orangesPos, kk]], 0.25], kk, 1, Length[orangesPos]) → oranges_{2}
  12. Textfield(appsNum) → InputBox1
  13. Textfield(orangesNum) → InputBox2
  14. Textfield(totalNum) → InputBox3
  15. If(correct1, "✓", "✘") → textFeedback1
  16. If(correct2, "✓", "✘") → textFeedback2
  17. If(correct3, "✓", "✘") → textFeedback3
  18. Translate(hGL, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → hGL'
  19. Translate(vGL, Vector[(Vector[Corner[1], Corner[2]] / 800 * 16)]) → vGL'
  20. Translate(vGL, Vector[(Vector[Corner[1], Corner[2]] / 800 * 64)]) → vGL'_{1}
  21. If(A1 ≟ 1, "Apple", "Apples") → B1
  22. If(A2 ≟ 1, "Orange", "Oranges") → B2
  23. Sequence((11.2, 4 - (0.5 + jj)), jj, 0, 2) → legendPos
  24. Translate(legendPos, (1, 0)) → departure
  25. Sequence((0.5, -2.6 + (kk * 0.75)), kk, 0, 1) → legendPos2
  26. Sequence((8.5, -2.7 + (kk * 0.75)), kk, 0, 1) → legendPos3
  27. Flatten(Translate[{legendPos2, legendPos3}, (If[stage ≟ 2, 4, 4.3], 0)]) → arrival
  28. Semicircle(departure(1), arrival(4)) → c1
  29. Semicircle(departure(1), arrival(1)) → c2
  30. Point(c1, 1 - Min[SlideToAnim - 1, 1]) → Panim2
  31. Point(c2, 1 - Min[SlideToAnim, 1]) → Panim1
  32. Text(Text[applesShown], Panim1, true, true, 0, 0) → textanim1
  33. Text(Text[applesShown], Panim2, true, true, 0, 0) → textanim2
  34. Semicircle(departure(2), arrival(2)) → c3
  35. Semicircle(departure(2), arrival(3)) → c4
  36. Point(c3, 3 - Min[SlideToAnim, 3]) → Panim3
  37. Point(c4, 4 - Min[SlideToAnim, 4]) → Panim4
  38. Text(Text[orangesShown], Panim3, true, true, 0, 0) → textanim3
  39. Text(Text[orangesShown], Panim4, true, true, 0, 0) → textanim4
  40. Point(c1, 1 - Min[SlideToAnim, 1]) → Panim5
  41. Point(c3, 2 - Min[SlideToAnim, 2]) → Panim6
  42. Semicircle(departure(3), arrival(1)) → c7
  43. Semicircle(departure(3), arrival(3)) → c8
  44. Point(c7, 3 - Min[SlideToAnim, 3]) → Panim7
  45. Point(c8, 4 - Min[SlideToAnim, 4]) → Panim8
  46. Text(Text[applesShown], Panim5, true, true, 0, 0) → textanim5
  47. Text(Text[totalNum], Panim7, true, true, 0, 0) → textanim7
  48. Text(Text[totalNum], Panim8, true, true, 0, 0) → textanim8
  49. Text(Text[orangesShown], Panim6, true, true, 0, 0) → textanim6
  50. Dilate(pic1, 0.1) → pic1'
  51. Zip(Translate[pic1', Vector[positions(kk)]], kk, applesPos) → l1
  52. Translate(pic1', Vector[legendPos(1)]) → pic1''
  53. Translate(pic1', Vector[legendPos(3) - (sep, 0)]) → pic1''_{1}
  54. Translate(pic1', Vector[legendPos2(1)]) → pic1''_{2}
  55. Translate(pic1', Vector[legendPos3(2)]) → pic1''_{3}
  56. Dilate(pic2, 0.1) → pic2'
  57. Zip(Translate[pic2', Vector[positions(kk)]], kk, orangesPos) → l2
  58. Translate(pic2', Vector[legendPos(2)]) → pic2''
  59. Translate(pic2', Vector[legendPos(3) + (sep, 0)]) → pic2''_{1}
  60. Translate(pic2', Vector[legendPos2(2)]) → pic2''_{2}
  61. Translate(pic2', Vector[legendPos3(1)]) → pic2''_{3}
  62. Translate(pic2', Vector[legendPos2(2) + (0, 0.2)]) → pic2''_{4}
  63. Translate(pic1', Vector[legendPos2(1)] + ((-sep), 0.15)) → pic1''_{5}
  64. Translate(pic2', Vector[legendPos2(1)] + (sep, 0.1)) → pic2''_{5}
  65. Translate(pic1''_{5}, (8, 0)) → pic4
  66. Translate(pic2''_{5}, (8, 0)) → pic3
  67. TableText({((("\bold\color{" * colorApple) * "}") * Text[applesShown]), "Apples\\\\\\"}, {((("\bold\color{" * colorOrange) * "}") * Text[orangesShown]), "Oranges\\\\\\"}, {((("\bold\color{" * colorTotal) * "}") * Text[totalNum]), "Fruit"}, "l") → text5
  68. Translate(pic1', Vector[legendPos3(2) + (0, 0.3)]) → pic1''_{4}

AI 绘图提示语参考

绘制一个包含苹果和橙子的图形,通过坐标几何展示比例关系。首先随机生成苹果的数量,然后随机生成橙子的数量,接着在坐标系中绘制苹果和橙子的位置,每个位置画一个半径为0.25的圆。最后在图形下方添加苹果和橙子的数量显示,以及比例关系的反馈信息。
以上提示语为根据原始绘图命令整理而来,仅供参考。