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分数等价可视化：条形图与随机生成练习

分数等价可视化：条形图与随机生成练习
几何画板及绘图内容加载中，请稍等……
2019-06-15 06:19
多边形函数数列几何作图滑块动画
① 本范例通过动态条形图直观展示分数等价的几何意义，用户可随机生成分数并观察其等价形式。② 核心数学概念是分数的等价性（如1/2 = 2/4），涉及最大公约数（GCD）化简、分子分母的随机生成与匹配。③ 作图要点：使用Random和Element命令随机选择分母种子，GCD计算最大公约数，Polygon和Segment绘制条形图，Textfield用于输入交互，Sequence生成多个条形，Slider控制重置（a01reset）等；对象包括SeedDenominators、ActualNumerator、BarFirst、ShadedFirst等，实现三组条形对比。④ 适合小学高年级至初中学生理解分数等价概念，也可用于教师课堂演示或学生自主探索。

GeoGebra 命令及参数

  1. Random(1, Length[SeedDenominators]) → WhichSeedDenominator
  2. Element(SeedDenominators, WhichSeedDenominator) → SeedDenominator
  3. Random(1, SeedDenominator - 1) → SeedNumerator
  4. GCD(SeedNumerator, SeedDenominator) → FixIt
  5. Polygon(A, A + (BarLength, 0), A + (BarLength, BarHeight), A + (0, BarHeight)) → BarFirst, a, f, g, h
  6. Polygon(B, B + (BarLength, 0), B + (BarLength, BarHeight), B + (0, BarHeight)) → BarSecond, b, i, j, k
  7. Polygon(C, C + (BarLength, 0), C + (BarLength, BarHeight), C + (0, BarHeight)) → BarThird, c, l, m, n
  8. Sequence(Segment[A + ((InitialPartitionLength * i), 0), A + ((InitialPartitionLength * i), 0) + (0, BarHeight)], i, 1, ActualDenominator - 1) → InitialPartitionsFirst
  9. Sequence(Segment[B + ((InitialPartitionLength * i), 0), B + ((InitialPartitionLength * i), 0) + (0, BarHeight)], i, 1, ActualDenominator - 1) → InitialPartitionsSecond
  10. Sequence(Segment[C + ((InitialPartitionLength * i), 0), C + ((InitialPartitionLength * i), 0) + (0, BarHeight)], i, 1, ActualDenominator - 1) → InitialPartitionsThird
  11. Polygon(A, A + ((InitialPartitionLength * ActualNumerator), 0), A + ((InitialPartitionLength * ActualNumerator), BarHeight), A + (0, BarHeight)) → ShadedFirst, a_1, p, q, r
  12. Polygon(B, B + ((InitialPartitionLength * ActualNumerator), 0), B + ((InitialPartitionLength * ActualNumerator), BarHeight), B + (0, BarHeight)) → ShadedSecond, b_1, s, t, d
  13. Polygon(C, C + ((InitialPartitionLength * ActualNumerator), 0), C + ((InitialPartitionLength * ActualNumerator), BarHeight), C + (0, BarHeight)) → ShadedThird, c_1, e, f_1, g_1
  14. Sequence(Segment[B + ((SecondPartitionLength * i), 0), B + ((SecondPartitionLength * i), 0) + (0, BarHeight)], i, 1, SecondPartitions - 1) → SecondPartitionLines
  15. Sequence(Segment[C + ((ThirdPartitionLength * i), 0), C + ((ThirdPartitionLength * i), 0) + (0, BarHeight)], i, 1, ThirdPartitions - 1) → ThirdPartitionLines
  16. Textfield(InputTextNumerator2) → a04BoxNum2
  17. Textfield(InputTextDenominator2) → a05BoxDenom2
  18. Textfield(InputTextNumerator3) → a09BoxNum3
  19. Textfield(InputTextDenominator3) → a10BoxDenom3
  20. Segment(D, D + (FractionBarLength, 0)) → FractionBar1
  21. Segment(D + (FractionBarLength + FractionBarGap, 0), D + ((2 * FractionBarLength) + FractionBarGap, 0)) → FractionBar2

AI 绘图提示语参考

绘制三个等长的矩形条，分别表示分数1/2、2/4和简化后的分数。每个矩形条都用线段分成若干等分，第一个矩形条用线段标出1/2，第二个矩形条用线段标出2/4，第三个矩形条用线段标出简化后的分数。每个矩形条还用阴影部分表示相应的分数值。
以上提示语为根据原始绘图命令整理而来，仅供参考。