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Comparing Fractions Using Pie Model

Comparing Fractions Using Pie Model
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2016-10-10 12:31
Circle
This example demonstrates how to compare fractions using a pie model. Key mathematical concepts include fractions and geometric construction. Commands used include Circle, Segment, Rotate, CircleSector, and Sequence. Suitable for upper elementary and middle school students learning fraction comparison and geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, C) → circle
  2. Segment(A, C) → cut
  3. Rotate(C, ((2 * π) * 1 / d), A) → C'
  4. CircleSector(A, C, C') → slice
  5. Sequence(Segment[A, Rotate[C, k, A]], k, ((2 * π) * 1 / d), (2 * π), ((2 * π) * 1 / d)) → AllCuts
  6. Sequence(Rotate[slice, k, A], k, 0, ((2 * π) * (n - 1) / d), (2 * π / d)) → Slices
  7. Rotate(C, If[n ≟ d, ((2 * π) * 0.999999), ((2 * π) * n / d)], A) → C''
  8. CircleSector(A, C, C'') → SlicesMergedTogether
  9. Circle(A_1, C_1) → circle_1
  10. Segment(A_1, C_1) → cut_1
  11. Rotate(C_1, ((2 * π) * 1 / d'), A_1) → C'_1
  12. CircleSector(A_1, C_1, C'_1) → slice_1
  13. Sequence(Segment[A_1, Rotate[C_1, k, A_1]], k, ((2 * π) * 1 / d'), (2 * π), ((2 * π) * 1 / d')) → AllCuts'
  14. Sequence(Rotate[slice_1, k, A_1], k, 0, ((2 * π) * (n' - 1) / d'), (2 * π / d')) → Slices'
  15. Rotate(C_1, If[n' ≟ d', ((2 * π) * 0.999999), ((2 * π) * n' / d')], A_1) → C''_1
  16. CircleSector(A_1, C_1, C''_1) → SlicesMergedTogether'