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TR KAY - Fraction Division Visualization

TR KAY - Fraction Division Visualization
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2016-11-30 15:24
TrianglePolygonSequenceGeometric Construction
This GeoGebra example demonstrates a visual and geometric construction of fraction division, turning the abstract arithmetic operation into an interactive diagram. The core mathematical concept is fraction division, where dividing by a fraction is equivalent to multiplying by its reciprocal, and the construction integrates elements such as equilateral triangles, orthocenters, quadrilaterals, and bar charts to represent the division process. Key construction steps involve using GeoGebra commands like Point, Segment, Sequence, and Polygon to create points, segments, sequences, and polygons; defining the dividend (DİVİDEND) and divisor (DİVİDER) along with their variants; and organizing geometric objects through multiple lists (list1, list2, liste2, etc.) and loop variables (i, j, k, l, m). The use of equilateral triangles and orthocenter properties aids in the geometric layout, and the final result is presented as a bar chart or bar graph. This resource is suitable for middle school mathematics (grades 6-8) for teaching fraction operations, and can be used by teachers to create interactive lessons that help students grasp the geometric meaning and rules of fraction division.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Segment(C, F) → a
  4. Segment(E, F) → b
  5. Segment(E, B) → c
  6. Segment(B, C) → d
  7. Segment(A, G) → e
  8. Segment(G, H) → f
  9. Segment(D, H) → g
  10. Segment(A, D) → h
  11. Sequence((x(A) + (i * x(G) / DİVİDEND), y(A)), i, 1, DİVİDEND) → list1
  12. Sequence((x(D) + (i * x(H) / DİVİDEND), y(D)), i, 1, DİVİDEND) → list2
  13. Sequence((x(B) + (i * x(E) / DİVİDER), y(B)), i, 1, DİVİDER) → liste2
  14. Sequence((x(C) + (i * x(F) / DİVİDER), y(C)), i, 1, DİVİDER) → liste3
  15. Polygon(A, D, Element[list2, DİVİDEND_1], Element[list1, DİVİDEND_1]) → liste5, liste5_2, liste5_3, liste5_4, liste5_5
  16. Sequence(Segment[Element[liste2, i], Element[liste3, i]], i, 1, DİVİDER) → liste4
  17. Sequence(Segment[Element[list1, i], Element[list2, i]], i, 1, DİVİDEND) → liste1
  18. Polygon(B, C, Element[liste3, DİVİDER_1], Element[liste2, DİVİDER_1]) → çokgen1, i, j, k, l
  19. Sequence((x(A) + (i * x(G) / m), y(A)), i, 1, m) → liste6
  20. Sequence((x(D) + (i * x(H) / m), y(D)), i, 1, m) → liste7
  21. Sequence(Segment[Element[liste6, i], Element[liste7, i]], i, 1, m) → liste8
  22. Sequence((x(B) + (i * x(E) / m), y(B)), i, 1, m) → liste9
  23. Sequence((x(C) + (i * x(F) / m), y(C)), i, 1, m) → liste10
  24. Sequence(Segment[Element[liste9, i], Element[liste10, i]], i, 1, m) → liste11