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分数比较 by Nicolette

分数比较 by Nicolette
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2020-06-07 10:22
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这个范例演示了如何比较两个分数的大小。核心数学概念包括分数、最小公倍数和等价分数。通过使用GeoGebra命令如Circle、Point、LCM、Sequence等，可以动态展示分数的比较过程。适合小学高年级和初中学生学习分数的基本概念和比较方法。

GeoGebra 命令及参数

  1. Circle(A_1, r) → c
  2. Point(c) → B
  3. Circle(A_2, r) → d
  4. LCM(denominator_1, denominator_2) → equivalentdenominator
  5. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_2) → PIEALL_2
  6. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{2E}
  7. 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}
  8. Midpoint(A_1, A_2) → A_{mid}
  9. Circle(A_1, r) → PIESECTION_{1whole}
  10. Circle(A_2, r) → PIESECTION_{2whole}
  11. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator_2)°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_{2subtract}
  12. 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}
  13. If(ShiftCircleLeftRight ≟ (2.5 * r), 1, 0) → trigger
  14. 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}
  15. Vector(A_2, A_{2end1}) → u
  16. Translate(PIESECTION_{finalsubtract1}, Vector[(DetachPie * u)]) → PIESECTION_{finalsubtract2}
  17. Vector(A_2, A_{2end2}) → v
  18. Circle(A_2, r) → PIESECTION_{whole1}
  19. 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}
  20. Circle(A_2, r) → PIESECTION_{whole2}
  21. Translate(PIESECTION_{whole2}, Vector[(DetachPie * v)]) → PIESECTION_{whole2v}
  22. Translate(PIESECTION_{part1}, Vector[(DetachPie * v)]) → PIESECTION_{part2}
  23. Translate(PIESECTION_{whole1}, Vector[(DetachPie * u)]) → PIESECTION_{whole1u}
  24. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  25. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  26. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  27. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, (4.5 * r), (3.5 * r)], If[ResultGCD ≟ 1, 0, (-2 * r)]) → x_{textEquivalentsign3}
  28. If(ResultGCD ≟ 1, (-0.25 * r), If[equivalentnumerator < equivalentdenominator, (5 * r), (-0.25 * r)]) → x_{textposition2}
  29. 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}
  30. Vector(A_2, A_{2end3}) → w
  31. Translate(PIESECTION_{negativefinalsubtract1}, Vector[(DetachPie * v)]) → PIESECTION_{negativefinalsubtract2}
  32. Textfield(numerator_1) → InputBox1
  33. Textfield(denominator_1) → InputBox2
  34. Textfield(numerator_2) → InputBox3
  35. Textfield(denominator_2) → InputBox4
  36. If(¬subtractfractions, " + ", " − ") → addsign2
  37. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / denominator_2)°, A_2], Rotate[C_2, (-(r°)), A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_2
  38. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator_2)°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_{2Compare}
  39. LCM(numerator_1, numerator_2) → equivalentnumerator_{compare}
  40. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{1E}
  41. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 360 / denominator_1, 360, 360 / denominator_1) → PIEALL_1
  42. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / denominator_1)°, A_1]], r, 0, (360 / denominator_1 * numerator_1) - 360 / denominator_1, 360 / denominator_1) → PIESECTION_1
  43. 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}
  44. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_{2Ecompare}) → PIEALL_{2samenumerator}
  45. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / denominator_{1Ecompare}) → PIEALL_{1samenumerator}

AI 绘图提示语参考

画两个大小不同的圆，用扇形表示两个分数的大小，通过动态旋转和比较扇形面积来展示分数比较的方法。首先画出两个圆，然后在第一个圆中画出代表第一个分数的扇形，在第二个圆中画出代表第二个分数的扇形。接着，通过旋转和调整扇形的大小，展示两个分数的最小公倍数和等价分数，最后比较两个扇形的面积大小。
以上提示语为根据原始绘图命令整理而来，仅供参考。