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Fraction Division by Amy Brodesky

Fraction Division by Amy Brodesky
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2017-11-26 02:52
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the process of fraction division. It involves the core mathematical concept of fraction division. Using GeoGebra commands such as If, Polygon, Ellipse, Segment, Vector, Sequence, etc., a geometric model of fraction division can be constructed. Suitable for middle school and above students to learn the geometric meaning of fraction division.

GeoGebra Commands & Parameters

  1. If(set ≟ 1, {4, 5, 6, 0.25, 0.5, SRset1prob6num / SRset1prob6denom, 5, 30, 80, 20}, {2, 2, 2, 2, 1, 12, 5, 4, 1, 0.5}) → SR1
  2. If(set ≟ 1, {4, 5, 6, 0.25, 0.5, SRset1prob6num / SRset1prob6denom, 5, 30, 80, 20}, {2, 2, 2, 2, 1, 12, 5, 4, 1, 0.5}) → SR2
  3. If(set ≟ 1, {2, 1, 2, 1, 1, 2, 2, 1, 2, 2}, {2, 2, 1, 1, 1, 2, 2, 2, 1, 2}) → ansCorrect
  4. If(sr1, (10, 5.6), (10, 3.2)) → AnsSelectedPt
  5. If(sr1, SR1, SR2) → SRSelect
  6. Polygon(ExPt + (0.2, 0), ExPt + (5.4, 0), ExPt + (5.6, 0.2), ExPt + (5.6, 0.8), ExPt + (5.4, 1), ExPt + (0.2, 1), ExPt + (0, 0.8), ExPt + (0, 0.2)) → examplePoly, exPolyBottom, exPolyBR, exPolyR, exPolyTR, exPolyTop, exPolyTL, exPolyL, exPolyBL
  7. Polygon(NextPt + (0, 0.2), NextPt + (0.2, 0), NextPt + (2, 0), NextPt + (2, -0.5), NextPt + (4, 0.5), NextPt + (2, 1.5), NextPt + (2, 1), NextPt + (0.2, 1), NextPt + (0, 0.8)) → nextPoly, nextPoly_2, nextPoly_3, nextPoly_4, nextPoly_5, nextPoly_6, nextPoly_7, nextPoly_8, nextPoly_9, nextPoly_{10}
  8. If(set ≟ 1, {0, 0, 0, 1, 7, 5, 0, 0, 0, 0}, {11, 3, 2, 11, 1, 1, 9, 13, 3, 3}) → term1num
  9. If(set ≟ 1, {1, 11, 5, 0, 0, 0, 7, 3, 1, 8}, {1, 1, 1, 9, 3, 1, 7, 1, 5, 7}) → term2num
  10. If(set ≟ 1, {0, 0, 0, 2, 8, 9, 0, 0, 0, 0}, {12, 4, 3, 12, 2, 2, 10, 7, 4, 4}) → term1denom
  11. If(set ≟ 1, {4, 12, 8, 0, 0, 0, 8, 7, 12, 9}, {4, 9, 2, 10, 4, 4, 8, 3, 2, 8}) → term2denom
  12. Polygon(ProbSetSelect1Pt, ProbSetSelect1Pt + (0.5, 0), ProbSetSelect1Pt + (0.5, 0.5), ProbSetSelect1Pt + (0, 0.5)) → probSetSelect1Poly, probSetSelect1polySeg, probSetSelect1polySeg_1, probSetSelect1polySeg_2, probSetSelect1polySeg_3
  13. Polygon(ProbSetSelect2Pt, ProbSetSelect2Pt + (0.5, 0), ProbSetSelect2Pt + (0.5, 0.5), ProbSetSelect2Pt + (0, 0.5)) → probSetSelect2Poly, probSetSelect2polySeg_1, probSetSelect2polySeg_2, probSetSelect2polySeg_3, probSetSelect2polySeg
  14. If(set ≟ 1, {3, 3, 6, 0, 0, 0, 5, 10, 8, 20}, {0, 0, 0, 0, 0, 3, 5, 0, 0, 0}) → term1mixedWhole
  15. If(set ≟ 1, {0, 0, 0, 5, 3, 4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}) → term2mixedWhole
  16. If(sr1, 1, 2) → srSelect
  17. If(srSelect ≟ Element[ansCorrect, problem], 1, 0) → correct
  18. Polygon(AnsSelectedPt + If[Element[SRSelect, problem] ≥ 1, (0, 0), (0, -0.5)], AnsSelectedPt + (5.8, 0) + If[Element[SRSelect, problem] ≥ 1, (0, 0), (0, -0.5)], AnsSelectedPt + (5.8, 1.2) + If[Element[SRSelect, problem] ≥ 1, (0, 0), (0, 0.5)], AnsSelectedPt + (0, 1.2) + If[Element[SRSelect, problem] ≥ 1, (0, 0), (0, 0.5)]) → ansSelectedPoly, ansSelectedPolySegBottom, ansSelectedPolySegR, ansSelectedPolySegTop, ansSelectedPolySegL
  19. If(sr1 ∨ sr2, true, false) → ansSelected
  20. If(Element[ansCorrect, problem] ≟ 1, (15.6, 6.1), (15.6, 3.7)) → CorrectEllipsePt2
  21. If(Element[ansCorrect, problem] ≟ 1, (10.1, 6.1), (10.1, 3.7)) → CorrectEllipsePt1
  22. Ellipse(CorrectEllipsePt1, CorrectEllipsePt2, CorrectEllipsePt3) → correctEllipse
  23. Segment((12.8, 8), (16.4, 8)) → exSegOriginal
  24. Segment((17.4, 8), (19.8, 8)) → exSegBenchmark
  25. Vector(CorrectEllipsePt1 + (-1.8, -0.2), CorrectEllipsePt1 + (-0.5, -0.2)) → ansNoteIncCorrVector
  26. Vector((18.2, 1.2), (19, 1.7)) → exCorrectArrow
  27. Sequence((16.2 + i, 0.3), i, 1, 7.3, 0.7) → scorePtsEmpty
  28. Sequence((16.5 + (0.7 * i), 0.3), i, 1, scoreTotal) → scorePts
  29. If(example ≟ false ∧ ansSelected ≟ true ∧ correct ≟ 0, true, false) → note