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分数除法 by Amy Brodesky

分数除法 by Amy Brodesky
几何画板及绘图内容加载中，请稍等……
2017-11-26 02:52
函数解析几何几何作图
这个范例演示了分数除法的过程。它涉及的核心数学概念是分数的除法运算。通过使用GeoGebra命令如If, Polygon, Ellipse, Segment, Vector, Sequence等，可以构造出分数除法的几何模型。适合初中及以上学生学习分数除法的几何意义。

GeoGebra 命令及参数

  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