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用图形演示分数加法：饼图与等价分数

用图形演示分数加法：饼图与等价分数
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2016-03-22 08:03
圆数列变换滑块动画
所属专题 Jessica's Fraction Book
① 该范例通过饼图（圆形分区）直观展示两个分数的加法过程，并利用图形平移和等价分数转换帮助学生理解异分母分数相加的几何意义。② 核心数学概念包括分数加法、通分（最小公倍数）、等价分数、最大公约数化简以及带分数表示。③ 作图要点：使用GeoGebra的Circle、Point、Sequence、Midpoint、Vector、Translate等命令构造饼图分区，通过LCM计算公分母，GCD化简分数，并用If和文本对象动态显示分数表达式及等价分数；对象包括PIESECTION系列、textFraction、equivalentfraction等。④ 适合小学高年级至初中阶段学习分数运算，也可用于教师课堂演示或学生自主探索，通过可视化操作加深对分数加法规则的理解。

GeoGebra 命令及参数

  1. Circle(A_1, r) → c
  2. Point(c) → B
  3. Circle(A_2, r) → d
  4. LCM(denominator1, denominator2) → equivalentdenominator
  5. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator2) → PIEALL_2
  6. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 360 / denominator1, 360, 360 / denominator1) → PIEALL_1
  7. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / denominator1)°, A_1]], r, 0, (360 / denominator1 * numerator1) - 360 / denominator1, 360 / denominator1) → PIESECTION_1
  8. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / denominator2)°, A_2], Rotate[C_2, ((-r))°, A_2]], r, 0, (360 / denominator2 * numerator2_1) - 360 / denominator2, 360 / denominator2) → PIESECTION_2
  9. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{1E}
  10. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{2E}
  11. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / equivalentdenominator)°, A_1]], r, 0, (360 / equivalentdenominator * numerator_{1E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{1E}
  12. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / equivalentdenominator)°, A_2], Rotate[C_2, ((-r))°, A_2]], r, 0, (360 / equivalentdenominator * numerator_{2E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2E}
  13. Midpoint(A_1, A_2) → A_{mid}
  14. Circle(A_1, r) → PIESECTION_{1whole}
  15. Circle(A_2, r) → PIESECTION_{2whole}
  16. If(¬subtractfractions, "+", "−") → addsign2
  17. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator2)°, A_2]], r, 0, (360 / denominator2 * numerator2_1) - 360 / denominator2, 360 / denominator2) → PIESECTION_{2subtract}
  18. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, 0, (360 / equivalentdenominator * numerator_{2E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2Esubtract}
  19. If(ShiftCircleLeftRight ≟ (2.5 * r), 1, 0) → trigger
  20. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (numerator_{2E} * 360 / equivalentdenominator), (360 / equivalentdenominator * (numerator_{1E} - 1)), 360 / equivalentdenominator) → PIESECTION_{finalsubtract1}
  21. Vector(A_2, A_{2end1}) → u
  22. Translate(PIESECTION_{finalsubtract1}, Vector[(DetachPie * u)]) → PIESECTION_{finalsubtract2}
  23. Vector(A_2, A_{2end2}) → v
  24. Circle(A_2, r) → PIESECTION_{whole1}
  25. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, ((equivalentdenominator - numerator_{2E}) * 360 / equivalentdenominator), (360 / equivalentdenominator * (mixednumerator + equivalentdenominator - numerator_{2E} - 1)), 360 / equivalentdenominator) → PIESECTION_{part1}
  26. Circle(A_2, r) → PIESECTION_{whole2}
  27. Translate(PIESECTION_{whole2}, Vector[(DetachPie * v)]) → PIESECTION_{whole2v}
  28. Translate(PIESECTION_{part1}, Vector[(DetachPie * v)]) → PIESECTION_{part2}
  29. Translate(PIESECTION_{whole1}, Vector[(DetachPie * u)]) → PIESECTION_{whole1u}
  30. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  31. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  32. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  33. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, (4.5 * r), (3.5 * r)], If[ResultGCD ≟ 1, 0, (-2 * r)]) → x_{textEquivalentsign3}
  34. If(ResultGCD ≟ 1, (-0.25 * r), If[equivalentnumerator < equivalentdenominator, (5 * r), (-0.25 * r)]) → x_{textposition2}
  35. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (numerator_{1E} * 360 / equivalentdenominator), (360 / equivalentdenominator * (numerator_{2E} - 1)), 360 / equivalentdenominator) → PIESECTION_{negativefinalsubtract1}
  36. Vector(A_2, A_{2end3}) → w
  37. Translate(PIESECTION_{negativefinalsubtract1}, Vector[(DetachPie * v)]) → PIESECTION_{negativefinalsubtract2}

AI 绘图提示语参考

绘制两个分数相加的饼图，包括两个圆心分别为A1和A2的圆，每个圆分成若干等分扇形，表示分数的大小。通过调整角度和半径，将两个圆的扇形部分重叠，形成一个共同的分母，展示分数相加的过程。最后，通过移动和旋转，将多余的扇形部分移除，展示最终的加法结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。