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Fraction Addition Estimation Practice

Fraction Addition Estimation Practice
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2019-11-21 00:47
InequalityGeometric Construction
This example demonstrates how to estimate whether the sums of fraction addition problems are less than or more than a given number, with feedback and examples of estimation strategies provided. Core math concepts include fraction addition, inequality judgment, and mathematical estimation. Construction highlights use of GeoGebra commands like If, Polygon, FractionText, Ellipse, Vector, Segment, Sequence for creating problem interfaces, displaying results, and interactive feedback. Suitable for middle school and above mathematics education, fostering students' estimation skills and fraction operation understanding.

GeoGebra Commands & Parameters

  1. If(set ≟ 1, Element[sumBenchmarkSet1, problem], Element[sumBenchmarkSet2, problem]) → sumBenchmarkValue
  2. If(set ≟ 1, {0.25, 1, 0.5, 0.5, 8}, {0.25, 0.1111111111111111, 1, 0.5, 0.5}) → SR1
  3. If(set ≟ 1, {0.5, 2, 1, 1, 0.5}, {0.5, 0.25, 2, 1, 6}) → SR2
  4. If(set ≟ 1, {1, 19, 2, 8, 0.5}, {1, 0.5, 15, 2, 0.5}) → SR3
  5. If(set ≟ 1, {18, 21, 6, 16, 0.5}, {16, 1, 17, 8, 11}) → SR4
  6. If(set ≟ 1, {1, 2, 3, 2, 3}, {1, 4, 2, 3, 3}) → 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, {1, 11, 3, 4, 3}, {1, 3, 4, 1, 4}) → term1num
  12. If(set ≟ 1, {1, 8, 8, 4, 4}, {1, 4, 11, 7, 7}) → term2num
  13. If(set ≟ 1, {9, 12, 4, 7, 4}, {7, 5, 5, 5, 9}) → term1denom
  14. If(set ≟ 1, {10, 9, 7, 9, 7}, {9, 9, 12, 4, 8}) → term2denom
  15. FractionText(Element[SR1, problem]) → SR1text
  16. FractionText(Element[SR2, problem]) → SR2text
  17. FractionText(Element[SR3, problem]) → SR3text
  18. FractionText(Element[SR4, problem]) → SR4text
  19. If(set ≟ 1, {0, 0, 0, 0, 5}, {0, 0, 0, 0, 3}) → term1mixedWhole
  20. If(set ≟ 1, {0, 0, 0, 0, 3}, {0, 0, 0, 0, 2}) → term2mixedWhole
  21. If(sr1, 1, If[sr2, 2, If[sr3, 3, If[sr4, 4, 0]]]) → srSelect
  22. If(srSelect ≟ Element[ansCorrect, problem], 1, 0) → correct
  23. Polygon(AnsSelectedPt + If[Element[SRSelect, problem] < 1, (0, 0), (0, 0.8)], AnsSelectedPt + (2, 0) + If[Element[SRSelect, problem] < 1, (0, 0), (0, 0.8)], AnsSelectedPt + (2, 2.5), AnsSelectedPt + (0, 2.5)) → ansSelectedPoly, ansSelectedPoly_2, ansSelectedPolyR, ansSelectedPolyTop, ansSelectedPolyL
  24. If(sr1 ∨ sr2 ∨ sr3 ∨ sr4, true, false) → ansSelected
  25. If(set ≟ 1, {0.125, 1, 1, 0.5, 6}, {0.125, 0.5, 1, 0.25, 3}) → term1Benchmark
  26. If(set ≟ 1, {0.125, 1, 1, 0.5, 3}, {0.125, 0.5, 1, 2, 3}) → term2Benchmark
  27. FractionText(If[set ≟ 1, Element[sumBenchmarkSet1, problem], Element[sumBenchmarkSet2, problem]]) → sumBenchmark
  28. 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
  29. Ellipse(CorrectEllipsePt1, CorrectEllipsePt2, CorrectEllipsePt3) → correctEllipse
  30. Vector((14.5, 0.5), (13.7, 1)) → exCorrectArrow
  31. Segment((17.3, 8), (19.7, 8)) → exSegBenchmark
  32. Segment((12.8, 8), (16.4, 8)) → exSegOriginal
  33. Vector(CorrectEllipsePt2 + (1.9, 0), CorrectEllipsePt2 + (0.9, 0)) → ansNoteIncCorrVector
  34. Polygon(AnsNotePolyPt + (0, If[sumBenchmarkValue ≥ 1, 0.5, 0]), AnsNotePolyPt + (6.75, If[sumBenchmarkValue ≥ 1, 0.5, 0]), AnsNotePolyPt + (6.75, 5), AnsNotePolyPt + (0, 5)) → ansNotePoly, f, g, h, i
  35. If(set ≟ 1, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 5}) → SR1mixedWhole
  36. If(set ≟ 1, {0, 0, 0, 0, 8}, {0, 0, 0, 0, 0}) → SR2mixedWhole
  37. If(set ≟ 1, {0, 0, 0, 0, 9}, {0, 0, 0, 0, 6}) → SR3mixedWhole
  38. If(set ≟ 1, {0, 0, 0, 0, 10}, {0, 0, 0, 0, 0}) → SR4mixedWhole
  39. Sequence((17.8 + i, 0.6), i, 1, 4.5, 0.81) → scorePtsEmpty
  40. Sequence((17.8 + i, 0.6), i, 1, scoreTotal, 0.81) → scorePts