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Adding Proper Fractions with Different Denominators

Adding Proper Fractions with Different Denominators
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2017-03-27 11:08
FunctionCoordinate Geometry
This example demonstrates the addition of proper fractions with different denominators using visual and interactive methods. Key math concepts include fraction addition, least common multiple (LCM), coordinate geometry representation, and dynamic geometric transformations. GeoGebra commands and objects like Point, Textfield, Polygon, Sequence, LCM, and RemoveUndefined are used to visualize the process through sliders and animations. Suitable for middle school and above students to understand the connection between fraction operations and geometric representations.

GeoGebra Commands & Parameters

  1. Point({(a1 * moveTimer), (-2 * moveTimer)}) → a2mover
  2. Point({0, 2 - (4 * moveTimer)}) → a1mover
  3. Textfield(a1text) → InputBox1
  4. Polygon(a1mover, a1mover + (a1, 0), a1mover + (a1, 1), a1mover + (0, 1)) → a1poly, f, g, h, i
  5. Polygon(a2mover, a2mover + (a2, 0), a2mover + (a2, 1), a2mover + (0, 1)) → a2poly, j, k, l, m
  6. Textfield(a2text) → InputBox2
  7. Polygon((0, 2), (a1, 2), (a1, 3), (0, 3)) → a1polyFixed, m_1, n_1, p_1, q_1
  8. Polygon((0, 0), (a2, 0), (a2, 1), (0, 1)) → a2polyFixed, r_1, s_1, t_1, f_2
  9. Point({0, 2 - (4 * barMoveTime)}) → a1barMover
  10. Point({0, (-2 * barMoveTime)}) → a2barMover
  11. Sequence(Segment[(i, 0), (i, 1)], i, 1 / a2denom, ceil(a2) - 1 / a2denom, 1 / a2denom) → list5
  12. Sequence(Segment[(i, 2), (i, 3)], i, 1 / a1denom, ceil(a1) - 1 / a1denom, 1 / a1denom) → list4
  13. LCM(a1denom, a2denom) → a
  14. Sequence(Segment[(0, -2) + (i, 0), (0, -2) + (i, growBarTimer)], i, 1 / a, ceil(a1 + a2) - 1 / a, 1 / a) → list7
  15. Sequence(Polygon[(i, -2), (i + 1, -2), 4], i, 0, ceil(a1 + a2) - 1) → list3
  16. Sequence(Polygon[(i, 0), (i + 1, 0), 4], i, 0, ceil(a2) - 1) → list1
  17. Sequence(Polygon[(i, 2), (i + 1, 2), 4], i, 0, ceil(a1) - 1) → list2
  18. RemoveUndefined(Join[{Sequence[Segment[a1barMover + (i, 0), a1barMover + (i, 1)], i, 1 / a1denom, ceil(a1) - 1 / a1denom, 1 / a1denom], Sequence[Segment[a2barMover + (i, 0), a2barMover + (i, 1)], i, 1 / a2denom, ceil(a2) - 1 / a2denom, 1 / a2denom]}]) → list6