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Adding Like & Unlike Fractions Visualized

Adding Like & Unlike Fractions Visualized
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2017-03-25 09:27
CircleSequenceGeometric ConstructionGraphing
In collections FRACTIONS
① This example uses pie charts (circle graphs) to visually demonstrate the addition of fractions with like and unlike denominators, clarifying the geometric meaning of fraction addition. ② Core math concepts include fractions, common denominators (least common multiple, LCM), rational number addition, and the part-whole relationship. ③ Construction highlights: GeoGebra commands include LCM for computing the least common multiple, Circle and Point to build circular pie charts, Sequence to generate equal-arc divisions, Segment to draw dividing lines, and multiple circles (c_1, c_2, c_3, c_4) with points (A_1, A_2, A_3, A_4) representing numerator parts; lists (list1, list2, etc.) store values, and text objects (text3, text5) display expressions and results. ④ Suitable for upper elementary to middle school students learning fraction operations, and for teachers to demonstrate in class, turning abstract fraction addition into intuitive visual manipulation.

GeoGebra Commands & Parameters

  1. LCM(d_1, d_2) → d_3
  2. Circle(O_1, r_1) → c_1
  3. Point(c_1) → A_1
  4. Sequence(Sector[c_1, Rotate[A_1, ((2 * π) * i / d_1), O_1], Rotate[A_1, ((2 * π) * (i + 1) / d_1), O_1]], i, 0, d_1 - 1) → list1
  5. Sequence(Sector[c_1, Rotate[A_1, ((2 * π) * i / d_1), O_1], Rotate[A_1, ((2 * π) * (i + 1) / d_1), O_1]], i, 0, n_1 - 1) → list2
  6. Circle(O_2, r_2) → c_2
  7. Point(c_2) → A_2
  8. Sequence(Sector[c_2, Rotate[A_2, ((2 * π) * i / d_2), O_2], Rotate[A_2, ((2 * π) * (i + 1) / d_2), O_2]], i, 0, n_2 - 1) → list4
  9. Circle(O_3, r_3) → c_3
  10. Point(c_3) → A_3
  11. Sequence(Sector[c_3, Rotate[A_3, ((2 * π) * i / d_3), O_3], Rotate[A_3, ((2 * π) * (i + 1) / d_3), O_3]], i, 0, p_1 - 1) → list5
  12. Sequence(Sector[c_3, Rotate[A_3, ((2 * π) * i / d_3), O_3], Rotate[A_3, ((2 * π) * (i + 1) / d_3), O_3]], i, 0, d_3 - 1) → list6
  13. Circle(O_4, r_3) → c_4
  14. Point(c_4) → A_4
  15. Sequence(Sector[c_4, Rotate[A_4, ((2 * π) * i / d_3), O_4], Rotate[A_4, ((2 * π) * (i + 1) / d_3), O_4]], i, 0, d_3 - 1) → list8
  16. Sequence(Sector[c_4, Rotate[A_4, ((2 * π) * i / d_3), O_4], Rotate[A_4, ((2 * π) * (i + 1) / d_3), O_4]], i, 0, p_3 - 1) → list9
  17. Sequence(Sector[c_3, Rotate[A_3, ((2 * π) * i / d_3), O_3], Rotate[A_3, ((2 * π) * (i + 1) / d_3), O_3]], i, p_1, Min[n_3 - 1, d_3 - 1]) → list7
  18. Sequence(Sector[c_2, Rotate[A_2, ((2 * π) * i / d_2), O_2], Rotate[A_2, ((2 * π) * (i + 1) / d_2), O_2]], i, 0, d_2 - 1) → list3
  19. Circle(O_3, A_3) → c
  20. Segment(O_1, A_1) → b
  21. Segment(O_2, A_2) → d
  22. Segment(O_3, A_3) → e
  23. Segment(O_4, A_4) → f