披萨分着玩:可视化分数与除法入门

披萨分着玩:可视化分数与除法入门
几何画板及绘图内容加载中,请稍等……
2023-04-19 21:52
所属专题 Arithmetic and Algebra
本范例通过披萨分给多个孩子的趣味场景,演示如何用圆形图可视化理解分数与除法概念。核心数学概念包括:分数的基本意义、分数与除法的关系、分数的比较、约分与通分等。作图要点:从构造摘要提取可知,使用Circle绘制圆面表示披萨,用CircleSector绘制圆扇形表示等分后的每一份,通过Sequence自动生成多个孩子的分饼序列,用Polygon绘制辅助线,用Translate实现披萨块的移动动画,用RandomElement增加互动的随机性。适合小学中高年级学生理解分数概念,或作为教师讲授分数入门时的直观演示工具,也可用于亲子数学启蒙教育。

GeoGebra 命令及参数

  1. Vector(C1, C2) → cTra
  2. Corner(5) → dims
  3. RandomElement({3, 2}) → bFive
  4. Circle(C1, rCfr) → c
  5. Circle(C2, rCfr) → d
  6. Translate(C2, cTra) → C3
  7. Circle(C3, rCfr) → e
  8. Translate(C3, cTra) → C4
  9. Circle(C4, rCfr) → f
  10. Translate(C4, cTra) → C5
  11. Circle(C5, rCfr) → g
  12. Vector(R1, F) → qTra
  13. Polygon(R1, R2, R3, R4) → q1, r1, r2, r3, r4
  14. Translate(R1, qTra) → R1'
  15. Translate(R2, qTra) → R2'
  16. Translate(R3, qTra) → R3'
  17. Translate(R4, qTra) → R4'
  18. Polygon(R1', R2', R3', R4') → q2, r1', r2', r3', r4'
  19. Translate(R1', qTra) → R1''
  20. Translate(R2', qTra) → R2''
  21. Translate(R3', qTra) → R3''
  22. Translate(R4', qTra) → R4''
  23. Polygon(R1'', R2'', R3'', R4'') → q3, r1'', r2'', r3'', r4''
  24. Sequence(Rotate[A, ((2 * pi / b) * k), C1], k, 1, b) → settCfr1
  25. CircleSector(C1, A, settCfr1(1)) → settc1pu
  26. CircleSector(C1, settCfr1(1), settCfr1(2)) → settc1pi
  27. CircleSector(C1, settCfr1(2), settCfr1(3)) → settc1bl
  28. Translate(settc1pu, cTra) → settc2pu
  29. Translate(settc1pu, Vector[(2 * cTra)]) → settc3pu
  30. Translate(settc1pu, Vector[(3 * cTra)]) → settc4pu
  31. Translate(settc1pu, Vector[(4 * cTra)]) → settc5pu
  32. Translate(settc1pi, cTra) → settc2pi
  33. Translate(settc1pi, Vector[(2 * cTra)]) → settc3pi
  34. Translate(settc1pi, Vector[(3 * cTra)]) → settc4pi
  35. Translate(settc1pi, Vector[(4 * cTra)]) → settc5pi
  36. Translate(settc1bl, cTra) → settc2bl
  37. Translate(settc1bl, Vector[(2 * cTra)]) → settc3bl
  38. Translate(settc1bl, Vector[(3 * cTra)]) → settc4bl
  39. Translate(settc1bl, Vector[(4 * cTra)]) → settc5bl
  40. Translate(CT1, qTra) → CT1'
  41. Translate(CT2, qTra) → CT2'
  42. Translate(CT3, qTra) → CT3'
  43. Translate(CT4, qTra) → CT4'
  44. Translate(CT5, qTra) → CT5'
  45. Translate(CT1, Vector[(2 * qTra)]) → CT1'_{1}
  46. Translate(CT2, Vector[(2 * qTra)]) → CT2'_{1}
  47. Translate(CT3, Vector[(2 * qTra)]) → CT3'_{1}
  48. Translate(CT4, Vector[(2 * qTra)]) → CT4'_{1}
  49. Translate(CT5, Vector[(2 * qTra)]) → CT5'_{1}
  50. Vector(C1, CT1) → toq1c1
  51. Vector(C2, CT2) → toq1c2
  52. Vector(C3, CT3) → toq1c3
  53. Vector(C4, CT4) → toq1c4
  54. Vector(C5, CT5) → toq1c5
  55. Vector(C1, CT1') → toq2c1
  56. Vector(C2, CT2') → toq2c2
  57. Vector(C3, CT3') → toq2c3
  58. Vector(C4, CT4') → toq2c4
  59. Vector(C5, CT5') → toq2c5
  60. Vector(C1, CT1'_{1}) → toq3c1
  61. Vector(C2, CT2'_{1}) → toq3c2
  62. Vector(C3, CT3'_{1}) → toq3c3
  63. Vector(C4, CT4'_{1}) → toq3c4
  64. Vector(C5, CT5'_{1}) → toq3c5
  65. Take({settc1bl, settc2bl, settc3bl, settc4bl, settc5bl}, 1, a) → allSecBlu
  66. Take({settc1pi, settc2pi, settc3pi, settc4pi, settc5pi}, 1, a) → allSecPink
  67. Take({settc1pu, settc2pu, settc3pu, settc4pu, settc5pu}, 1, a) → allSecPu
  68. Take({CircleSector[C1, settCfr1(2), settCfr1(3)], Translate[settc1bl, cTra], Translate[settc1bl, Vector[(2 * cTra)]], Translate[settc1bl, Vector[(3 * cTra)]], Translate[settc1bl, Vector[(4 * cTra)]]}, 1, a) → allOutlinesBlu
  69. Take({CircleSector[C1, settCfr1(1), settCfr1(2)], Translate[settc1pi, cTra], Translate[settc1pi, Vector[(2 * cTra)]], Translate[settc1pi, Vector[(3 * cTra)]], Translate[settc1pi, Vector[(4 * cTra)]]}, 1, a) → allOutlinesPink
  70. Take({CircleSector[C1, A, settCfr1(1)], Translate[settc1pu, cTra], Translate[settc1pu, Vector[(2 * cTra)]], Translate[settc1pu, Vector[(3 * cTra)]], Translate[settc1pu, Vector[(4 * cTra)]]}, 1, a) → allOutlinesPu
  71. Zip(Translate[p, Vector[q]], p, allSecBlu, q, If[2 ≤ aniSli ≤ 3, (allq3Vec * (aniSli - 2))]) → allTraBlu
  72. Zip(Translate[p, Vector[q]], p, allOutlinesBlu, q, If[2 ≤ aniSli ≤ 3, (allq3Vec * (aniSli - 2))]) → allTraOutBlu
  73. Zip(Translate[p, Vector[q]], p, allOutlinesPu, q, If[0 ≤ aniSli ≤ 1, (allq1Vec * aniSli), allq1Vec]) → allTraOutPu
  74. Zip(Translate[p, Vector[q]], p, allSecPu, q, If[0 ≤ aniSli ≤ 1, (allq1Vec * aniSli), allq1Vec]) → allTraPu
  75. Zip(Translate[p, Vector[q]], p, allSecPink, Vector[q], If[1 ≤ aniSli ≤ 2, (allq2Vec * (aniSli - 1)), 2 < aniSli ≤ 3, allq2Vec]) → allTraPink
  76. Zip(Translate[p, Vector[q]], p, allOutlinesPink, Vector[q], If[1 ≤ aniSli ≤ 2, (allq2Vec * (aniSli - 1)), 2 < aniSli ≤ 3, allq2Vec]) → allTraOutPink
  77. SelectedIndex(ddMenu) → is

AI 绘图提示语参考

这是一个关于披萨分给孩子的视觉介绍场景。画面中央是一个圆形披萨,披萨被分成多个相等的切片,每个切片代表一部分披萨。旁边有辅助线,用于标记切片的边界。披萨切片可以移动,模拟分给不同孩子的过程。还可以随机化切片数量,让用户体验不同的划分方式。整个场景旨在帮助理解分数和除法的概念,适合小学高年级学生或教师使用。
以上提示语为根据原始绘图命令整理而来,仅供参考。