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分数减法估算练习：判断差值与基准数的大小

分数减法估算练习：判断差值与基准数的大小
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2019-11-21 02:31
不等式
① 本范例是一个交互式数学练习，演示如何估算两个分数相减的结果与给定基准数（如1/2）的大小关系，并通过图形化反馈帮助学习者掌握估算策略。② 核心数学概念包括分数减法、有理数比较、估算与近似、数感培养，涉及分数、减法、不等式等基础算术运算。③ 作图要点：从构造摘要可见，使用了GeoGebra的If、Polygon、FractionText、Ellipse、Vector、Segment、Sequence等命令，创建了多个对象如AnsNotePolyPt、set、problem、sumBenchmarkSet1/2、sumBenchmarkValue、SR1-SR4、SRSkip、ansCorrect、ansSkip、sr1-sr4、SkipCorrectPt、AnsSelectedPt、SRSelect、example、directions、probTextClosestTo、probNumberTotal、ExPt、NextPt、nextPoly系列、buttonNext、term1num、term2num、term1denom等，用于生成题目、显示分数文本、绘制选择按钮和反馈图形。④ 适合小学高年级至初中阶段的学生，用于课堂练习或家庭作业，也可作为教师演示估算策略的教学工具，帮助学生直观理解分数减法估算。

GeoGebra 命令及参数

  1. If(set ≟ 1, Element[sumBenchmarkSet1, problem], Element[sumBenchmarkSet2, problem]) → sumBenchmarkValue
  2. If(set ≟ 1, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 0, 0, 0, 0}) → SR1
  3. If(set ≟ 1, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}) → SR2
  4. If(set ≟ 1, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 1, 0, 0, 0, 0, 0, 0}) → SR3
  5. If(set ≟ 1, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 0, 0, 0, 0}) → SR4
  6. If(set ≟ 1, {2, 1, 4, 2, 3, 1, 1, 1, 1, 1}, {2, 1, 2, 4, 3, 1, 1, 1, 1, 1}) → ansCorrect
  7. If(Element[ansCorrect, problem] ≟ 1, (2, 1.8), If[Element[ansCorrect, problem] ≟ 2, (8, 1.8), If[Element[ansCorrect, problem] ≟ 3, (14, 1.8), (20.1, 1.8)]]) → SkipCorrectPt
  8. If(ansSkip ≟ 1, SkipCorrectPt, If[sr1, (5.9, 1.9), If[sr2, (9.3, 1.9), If[sr3, (12.65, 1.9), If[sr4, (16, 1.9)]]]]) → AnsSelectedPt
  9. If(sr1, SR1, If[sr2, SR2, If[sr3, SR3, SR4]]) → SRSelect
  10. 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}
  11. If(set ≟ 1, {9, 5, 5, 5, 5, 1, 1, 1, 1, 1}, {1, 12, 11, 8, 14, 1, 1, 1, 1, 1}) → term1num
  12. If(set ≟ 1, {3, 2, 3, 3, 2, 1, 1, 1, 1, 1}, {7, 9, 5, 9, 4, 1, 1, 1, 1, 1}) → term2num
  13. If(set ≟ 1, {10, 8, 6, 9, 7, 1, 1, 1, 1, 1}, {10, 11, 12, 3, 5, 1, 1, 1, 1, 1}) → term1denom
  14. If(set ≟ 1, {8, 7, 16, 11, 9, 1, 1, 1, 1, 1}, {9, 10, 8, 8, 7, 1, 1, 1, 1, 1}) → term2denom
  15. Polygon(ProbSetSelect1Pt, ProbSetSelect1Pt + (0.5, 0), ProbSetSelect1Pt + (0.5, 0.5), ProbSetSelect1Pt + (0, 0.5)) → probSetSelect1Poly, probSetSelect1polySeg, probSetSelect1polySeg_1, probSetSelect1polySeg_2, probSetSelect1polySeg_3
  16. Polygon(ProbSetSelect2Pt, ProbSetSelect2Pt + (0.5, 0), ProbSetSelect2Pt + (0.5, 0.5), ProbSetSelect2Pt + (0, 0.5)) → probSetSelect2Poly, probSetSelect2polySeg_1, probSetSelect2polySeg_2, probSetSelect2polySeg_3, probSetSelect2polySeg
  17. If(set ≟ 1, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {2, 0, 3, 0, 0, 0, 0, 0, 0, 0}) → term1mixedWhole
  18. If(set ≟ 1, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 2, 0, 1, 0, 0, 0, 0, 0}) → term2mixedWhole
  19. If(sr1, 1, If[sr2, 2, If[sr3, 3, If[sr4, 4, 0]]]) → srSelect
  20. If(srSelect ≟ Element[ansCorrect, problem], 1, 0) → correct
  21. Polygon(AnsSelectedPt + If[Element[SRSelect, problem] ≟ 0, (0, 0), (0, 0.8)], AnsSelectedPt + (2, 0) + If[Element[SRSelect, problem] ≟ 0, (0, 0), (0, 0.8)], AnsSelectedPt + (2, 2.5), AnsSelectedPt + (0, 2.5)) → ansSelectedPoly, ansSelectedPolyBottom, ansSelectedPolyR, ansSelectedPolyTop, ansSelectedPolyL
  22. If(sr1 ∨ sr2 ∨ sr3 ∨ sr4, true, false) → ansSelected
  23. If(set ≟ 1, {1, 0.5, 1, 0.5, 0.6666666666666666, 1, 1, 1, 1, 1}, {2, 1, 4, 3, 3, 1, 1, 1, 1, 1}) → term1Benchmark
  24. If(set ≟ 1, {0.5, 0.25, 0.25, 0.25, 0.3333333333333333, 1, 1, 1, 1, 1}, {1, 1, 2.5, 1, 1.5, 1, 1, 1, 1, 1}) → term2Benchmark
  25. FractionText(If[set ≟ 1, Element[sumBenchmarkSet1, problem], Element[sumBenchmarkSet2, problem]]) → sumBenchmark
  26. If(Element[ansCorrect, problem] ≟ 1, (6.9, 3.8), If[Element[ansCorrect, problem] ≟ 2, (10.25, 3.8), If[Element[ansCorrect, problem] ≟ 3, (13.65, 3.8), (17, 3.8)]]) → CorrectEllipsePt2
  27. Ellipse(CorrectEllipsePt1, CorrectEllipsePt2, CorrectEllipsePt3) → correctEllipse
  28. Vector((14.5, 0.5), (13.7, 1)) → exCorrectArrow
  29. Segment((17.3, 8), (19.7, 8)) → exSegBenchmark
  30. Segment((12.8, 8), (16.4, 8)) → exSegOriginal
  31. Vector(CorrectEllipsePt2 + (1.9, 0), CorrectEllipsePt2 + (0.9, 0)) → ansNoteIncCorrVector
  32. Polygon(AnsNotePolyPt + (0, If[sumBenchmarkValue ≥ 1, 0.5, 0]), AnsNotePolyPt + (7, If[sumBenchmarkValue ≥ 1, 0.5, 0]), AnsNotePolyPt + (7, 5), AnsNotePolyPt + (0, 5)) → ansNotePoly, ansNotePolySegBottom, ansNotePolySegR, ansNotePolySegTop, ansNotePolySegL
  33. If(set ≟ 1, {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {-1, 0, 1, -1, 0, -1, -1, -1, -1, -1}) → SR1whole
  34. If(set ≟ 1, {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, -1, 1, -1, -1, -1, -1, -1, -1, -1}) → SR2whole
  35. If(set ≟ 1, {1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 1, 2, 1, 1, -1, -1, -1, -1, -1}) → SR3whole
  36. If(set ≟ 1, {6, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {-1, -1, 2, 2, 13, -1, -1, -1, -1, -1}) → SR4whole
  37. If(set ≟ 1, {2, 2, 10, 4, 4, 1, 1, 1, 1, 1}, {0, 2, 2, 8, 2, 1, 1, 1, 1, 1, 1}) → SR2denom
  38. If(set ≟ 1, {1, 1, 2, 1, 1, 1, 1, 1, 1, 1}, {-1, 1, 1, 3, 1, 1, 1, 1, 1, 1}) → SR2num
  39. If(set ≟ 1, {8, 4, 16, 9, 8, 1, 1, 1, 1, 1}, {9, 0, 8, 5, 0, 1, 1, 1, 1, 1}) → SR1denom
  40. If(set ≟ 1, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {6, -1, 1, 1, -1, 1, 1, 1, 1, 1}) → SR1num
  41. If(set ≟ 1, {-1, 3, 1, 3, 1, 1, 1, 1, 1, 1}, {-1, -1, 1, -1, 1, 1, 1, 1, 1, 1}) → SR3num
  42. If(set ≟ 1, {-1, 4, 2, 4, 3, 1, 1, 1, 1, 1}, {-1, -1, 2, -1, 2, 1, 1, 1, 1, 1}) → SR3denom
  43. If(set ≟ 1, {-1, 3, 3, 2, 3, 1, 1, 1, 1, 1}, {14, 7, 3, -1, -1, 1, 1, 1, 1, 1}) → SR4num
  44. If(set ≟ 1, {-1, 1, 4, 2, 4, 1, 1, 1, 1, 1}, {1, 5, 4, -1, -1, 1, 1, 1, 1, 1}) → SR4denom
  45. Sequence((17.8 + i, 0.6), i, 1, 4.5, 0.81) → scorePtsEmpty
  46. Sequence((17.8 + i, 0.6), i, 1, scoreTotal, 0.81) → scorePts

AI 绘图提示语参考

画一个分数减法估算练习的交互式图形，包含两个分数的分子和分母，以及一个基准数1/2。用户输入两个分数，计算它们的差，并判断这个差是否小于或大于1/2。图形中包含箭头、椭圆、多边形和段落，用于显示计算结果和反馈。分数以文本形式显示，箭头和椭圆用于指示正确答案的方向。
以上提示语为根据原始绘图命令整理而来，仅供参考。