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Addition of Fractions with the Same Denominator by Anthony OR 柯志明

Addition of Fractions with the Same Denominator by Anthony OR 柯志明
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2018-04-29 09:51
PolygonVectorGeometric ConstructionSlider AnimationGraphing
This example demonstrates the geometric representation of addition of fractions with the same denominator, visually showing the process of adding fractions through shapes. It involves core mathematical concepts such as fraction addition, geometric representation, and vector operations. The construction uses GeoGebra commands and objects like Point, Translate, Vector, Polygon, Sequence, Segment, If to create and manipulate geometric elements. Suitable for middle school mathematics teaching, helping students understand the geometric meaning of fraction addition and enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Point(yAxis) → C
  2. Point(yAxis) → B
  3. Translate(B, Vector[(t2 * Vector[B, D])]) → B'
  4. Vector((0, 0), (-2.2, 0)) → u
  5. Point(yAxis) → A
  6. Polygon({A, A + (2, 0), A + (2, 1), A + (0, 1)}) → q1
  7. Polygon({B, B + (2, 0), B + (2, 1), B + (0, 1)}) → q2
  8. Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_1
  9. Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_2
  10. Polygon({A, A + ((2 * b / a), 0), A + ((2 * b / a), 1), A + (0, 1)}) → q3
  11. Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_5
  12. Polygon({B, B + ((2 * c / a), 0), B + ((2 * c / a), 1), B + (0, 1)}) → q4
  13. Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_6
  14. Sequence(Segment[A + ((i * 2 / a), 0), A + ((i * 2 / a), 1)], i, 1, a - 1) → L_3
  15. Sequence(Segment[B + ((i * 2 / a), 0), B + ((i * 2 / a), 1)], i, 1, a - 1) → L_4
  16. Polygon({C, C + (2, 0), C + (2, 1), C + (0, 1)}) → q5
  17. Translate(q3, Vector[(t1 * Vector[A, C])]) → q3'
  18. Translate(A, Vector[(t1 * Vector[A, C])]) → A'
  19. Sequence(Segment[A' + ((i * 2 / a), 0), A' + ((i * 2 / a), 1)], i, 0, b) → L_7
  20. Translate(q5, Vector[(-u)]) → q5'
  21. Sequence(Segment[A' + (0, i), A' + ((2 * b / a), i)], i, 0, 1) → L_9
  22. Polygon({B'', B'' + ((If[b + c > a, b + c - a, 0] * 2 / a), 0), B'' + ((If[b + c > a, b + c - a, 0] * 2 / a), 1), B'' + (0, 1)}) → q9
  23. Polygon({B', B' + ((If[b + c > a, a - b, c] * 2 / a), 0), B' + ((If[b + c > a, a - b, c] * 2 / a), 1), B' + (0, 1)}) → q8
  24. Sequence(Segment[B'' + ((i * 2 / a), 0), B'' + ((i * 2 / a), 1)], i, 0, If[b + c > a, b + c - a, 0]) → L_{11}
  25. Sequence(Segment[B' + (0, i), B' + ((If[b + c > a, a - b, c] * 2 / a), i)], i, 0, 1) → L_{12}
  26. Sequence(Segment[B'' + (0, i), B'' + ((If[b + c > a, b + c - a, 0] * 2 / a), i)], i, 0, 1) → L_{13}
  27. Translate(L_5, Vector[(t4 * Vector[A, C])]) → L_{14}
  28. Translate(L_1, Vector[(t4 * Vector[A, C])]) → L_{15}
  29. Translate(C, Vector[(m * u)]) → C'
  30. Translate(L_6, Vector[(t5 * Vector[B, C'])]) → L_{16}
  31. Translate(L_2, Vector[(t5 * Vector[B, C'])]) → L_{17}
  32. Sequence(Segment[B' + ((i * 2 / a), 0), B' + ((i * 2 / a), 1)], i, 0, If[b + c > a, a - b, c]) → L_{10}
  33. Sequence(Segment[C + ((i * 2 / a), 0), C + ((i * 2 / a), 1)], i, 1, a - 1) → L_{18}
  34. Sequence(Segment[E + ((i * 2 / a), 0), E + ((i * 2 / a), 1)], i, 1, a - 1) → L_8
  35. Segment(H, I) → f
  36. If(b > 0, 1, 0) → s1
  37. If(c > 0, 1, 0) → s2
  38. If(b + c > a, 1, 0) → s3
  39. If(m > 0, 1, 0) → s4
  40. If(n > 0, 1, 0) → s5
  41. If(s1 + s2 + s3 + s4 + s5 ≤ t1 + t2 + t3 + t4 + t5, true, false) → finished