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同分母带分数加法

同分母带分数加法
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2019-04-17 13:20
①本范例演示了同分母带分数或真分数的加法运算过程；②涉及核心数学概念包括带分数、真分数、分数加法、最小公倍数等；③作图要点提炼自GeoGebra命令：使用了LCM（最小公倍数）、Sequence（数列）、Rotate（旋转）、Circle（圆）、Vector（向量）、Translate（平移）、Segment（线段）、CircleSector（扇形）、CircleArc（圆弧）、If（条件判断）、Text（文本）、Ray（射线）等命令及对象；④适合初中数学教学，用于帮助学生直观理解分数加法运算和几何表示。

GeoGebra 命令及参数

  1. LCM(d1, d2) → d
  2. Sequence(A + (((2.5 * (maxi - 1)) * r), 0) - (((2.5 * r) * k), 0), k, 0, i1 - 1) → points
  3. Rotate(P, ((360 * ° / d1) * n1), O) → Q
  4. Circle(O, r) → c1
  5. Vector(Center[c1], B) → u
  6. Translate(Vector[(If[move1 > 1, 1, move1] * u)], O) → v
  7. Segment(O, P) → f
  8. Sequence(Segment[Rotate[O, k°, O], Rotate[P, k°, O]], k, 0, 360, 360 / d1) → cut1
  9. Translate(cut1, v) → cut1'
  10. CircleSector(O, P, Q) → seg1
  11. Circle(O, r) → disc1
  12. Translate(disc1, v) → disc1'
  13. CircleArc(O, P, Q) → arc1
  14. Translate(c1, v) → c1'
  15. Sequence(Circle[points(k), r], k, 1, i1) → circles
  16. If(i1 > 0, Text[i1], "") → int1
  17. Segment(C + (0, r), C - (0, (6.5 * r))) → h
  18. Sequence(A + (((2.5 * (maxi - 1)) * r), 0) - (((2.5 * r) * k), (2.5 * r)), k, 0, i2 - 1) → points2
  19. Sequence(Circle[points2(k), r], k, 1, i2) → circles2
  20. Rotate(P2, ((-360 * ° / d1) * n2), O2) → Q2
  21. Sequence(Segment[Rotate[O2, k°, O2], Rotate[P2, k°, O2]], k, 0, 360, 360 / d2) → cut2
  22. Circle(O2, r) → c2
  23. If(i2 > 0, Text[i2], "") → int2
  24. Vector(Center[c2], B) → u2
  25. Circle(O2, r) → disc2
  26. Sequence(CircleSector[O2, Rotate[P2, ((360 * ° / d2) * k), O2], Rotate[P2, ((360 * ° / d2) * (k + 1)), O2]], k, 0, n2 - 1) → segs2
  27. Sequence(If[move1 ≤ k, 0, If[move1 ≥ k + 1, 1, Mod[move1, 1]]], k, 1, n1) → scales1
  28. Sequence(If[move2 ≤ k, 0, If[move2 ≥ k + 1, 1, Mod[move2, 1]]], k, 1, n2) → scales2
  29. CircleSector(O2, P2, Q2) → seg2
  30. CircleArc(O2, P2, Q2) → arc2
  31. Sequence(CircleSector[O, Rotate[P, (θ1 * k), O], Rotate[P, (θ1 * (k + 1)), O]], k, 0, n1 - 1) → segs1
  32. Sequence(A + (((2.5 * (maxi - 1)) * r), 0) - (((2.5 * r) * k), (5.5 * r)), k, 0, i2 + i1 - 1 + floor((n1 + n2) / d)) → points3
  33. Sequence(Translate[Rotate[CircleSector[O2, Rotate[P2, (θ2 * k), O2], Rotate[P2, (θ2 * (k + 1)), O2]], ((n1 * θ2) * scales2(k + 1)), O2], (u2 * scales2(k + 1))], k, d - n1, If[carry, n2 - 1, 0]) → segs2b'
  34. Sequence(Translate[Translate[Rotate[CircleSector[O2, Rotate[P2, (θ2 * k), O2], Rotate[P2, (θ2 * (k + 1)), O2]], ((n1 * θ2) * scales2(k + 1)), O2], (u2 * scales2(k + 1))], w], k, 0, If[carry, d - n1, n2] - 1) → segs2a'
  35. Text(If[doneCarry, "1", ""]) → text10
  36. Sequence(Vector[points2(k), points3(k + If[carry, 1, 0])], k, 1, i2) → vectors2
  37. Sequence(Vector[points(k), points3(k + i2 + If[carry, 1, 0])], k, 1, i1) → vectors1
  38. Sequence(Translate[Circle[points(k), r], (If[move_i > 1, 1, move_i] * vectors1(k))], k, 1, i1) → circles'
  39. Sequence(Translate[Circle[points2(k), r], (If[move_i < 1, 0, move_i - 1] * vectors2(k))], k, 1, i2) → circles2'
  40. Text(If[eng, "Dotted line", "虛線"]) → text12
  41. Ray((x(O) + (3 * r), y(O) - (7 * r)), Vector[O, O + (0, 1)]) → k
  42. Sequence(Translate[Translate[CircleSector[O, Rotate[P, ((360 * ° / d) * k), O], Rotate[P, ((360 * ° / d) * (k + 1)), O]], (u * scales1(k + 1))], w], k, 0, n - 2) → segs1'
  43. If(i > 0, Text[i], "") → int