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Locating Fractions on a Number Line by EDC Interactive Math

Locating Fractions on a Number Line by EDC Interactive Math
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2018-09-20 22:56
Coordinate GeometryGeometric Construction
This example demonstrates how to place fractions accurately on number lines and provides feedback. Key mathematical concepts include rational numbers, real numbers, and point positioning on a number line. Construction involves GeoGebra commands such as Polygon, PointIn, If, Vector, Sequence, and objects like onLineHeight, set, restrictPts. Suitable for middle or high school mathematics teaching to practice fraction placement on number lines.

GeoGebra Commands & Parameters

  1. Polygon((-0.05, 0.4), (2.05, 0.4), (2.05, 3.3), (-0.05, 3.3)) → restrictPts, f, g, h, i
  2. PointIn(restrictPts) → Frac1PtSet1
  3. PointIn(restrictPts) → Frac1PtSet2
  4. PointIn(restrictPts) → Frac1PtSet3
  5. PointIn(restrictPts) → Frac1PtSet4
  6. PointIn(restrictPts) → Frac1PtSet5
  7. PointIn(restrictPts) → Frac1PtSet6
  8. If(set ≟ 1, Frac1PtSet1, If[set ≟ 2, Frac1PtSet2, If[set ≟ 3, Frac1PtSet3, If[set ≟ 4, Frac1PtSet4, If[set ≟ 5, Frac1PtSet5, Frac1PtSet6]]]]) → frac1MasterPt
  9. PointIn(restrictPts) → Frac2PtSet6
  10. PointIn(restrictPts) → Frac2PtSet5
  11. PointIn(restrictPts) → Frac2PtSet4
  12. PointIn(restrictPts) → Frac2PtSet3
  13. PointIn(restrictPts) → Frac2PtSet2
  14. PointIn(restrictPts) → Frac2PtSet1
  15. If(set ≟ 1, Frac2PtSet1, If[set ≟ 2, Frac2PtSet2, If[set ≟ 3, Frac2PtSet3, If[set ≟ 4, Frac2PtSet4, If[set ≟ 5, Frac2PtSet5, Frac2PtSet6]]]]) → frac2MasterPt
  16. PointIn(restrictPts) → Frac3PtSet6
  17. PointIn(restrictPts) → Frac3PtSet5
  18. PointIn(restrictPts) → Frac3PtSet4
  19. PointIn(restrictPts) → Frac3PtSet3
  20. PointIn(restrictPts) → Frac3PtSet2
  21. PointIn(restrictPts) → Frac3PtSet1
  22. If(set ≟ 1, Frac3PtSet1, If[set ≟ 2, Frac3PtSet2, If[set ≟ 3, Frac3PtSet3, If[set ≟ 4, Frac3PtSet4, If[set ≟ 5, Frac3PtSet5, Frac3PtSet6]]]]) → frac3MasterPt
  23. PointIn(restrictPts) → Frac4PtSet6
  24. PointIn(restrictPts) → Frac4PtSet5
  25. PointIn(restrictPts) → Frac4PtSet4
  26. PointIn(restrictPts) → Frac4PtSet3
  27. PointIn(restrictPts) → Frac4PtSet2
  28. PointIn(restrictPts) → Frac4PtSet1
  29. If(set ≟ 1, Frac4PtSet1, If[set ≟ 2, Frac4PtSet2, If[set ≟ 3, Frac4PtSet3, If[set ≟ 4, Frac4PtSet4, If[set ≟ 5, Frac4PtSet5, Frac4PtSet6]]]]) → frac4MasterPt
  30. If(set ≟ 1 ∧ ckPlaceSet1, true, If[set ≟ 2 ∧ ckPlaceSet2, true, If[set ≟ 3 ∧ ckPlaceSet3, true, If[set ≟ 4 ∧ ckPlaceSet4, true, If[set ≟ 5 ∧ ckPlaceSet5, true, If[set ≟ 6 ∧ ckPlaceSet6, true, false]]]]]) → placeMasterYN
  31. If(x(frac4MasterPt) < x(dotA) + snapHorAmt ∧ x(frac4MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac4MasterPt) < x(dotB) + snapHorAmt ∧ x(frac4MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac4MasterPt) < x(dotC) + snapHorAmt ∧ x(frac4MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac4MasterPt) < x(dotD) + snapHorAmt ∧ x(frac4MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac4MasterPt) < x(dotE) + snapHorAmt ∧ x(frac4MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac4MasterPt) < x(dotF) + snapHorAmt ∧ x(frac4MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac4MasterPt) < x(dotG) + snapHorAmt ∧ x(frac4MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac4MasterPt)]]]]]]) → frac4X
  32. If(x(frac3MasterPt) < x(dotA) + snapHorAmt ∧ x(frac3MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac3MasterPt) < x(dotB) + snapHorAmt ∧ x(frac3MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac3MasterPt) < x(dotC) + snapHorAmt ∧ x(frac3MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac3MasterPt) < x(dotD) + snapHorAmt ∧ x(frac3MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac3MasterPt) < x(dotE) + snapHorAmt ∧ x(frac3MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac3MasterPt) < x(dotF) + snapHorAmt ∧ x(frac3MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac3MasterPt) < x(dotG) + snapHorAmt ∧ x(frac3MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac3MasterPt)]]]]]]) → frac3X
  33. If(x(frac2MasterPt) < x(dotA) + snapHorAmt ∧ x(frac2MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac2MasterPt) < x(dotB) + snapHorAmt ∧ x(frac2MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac2MasterPt) < x(dotC) + snapHorAmt ∧ x(frac2MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac2MasterPt) < x(dotD) + snapHorAmt ∧ x(frac2MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac2MasterPt) < x(dotE) + snapHorAmt ∧ x(frac2MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac2MasterPt) < x(dotF) + snapHorAmt ∧ x(frac2MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac2MasterPt) < x(dotG) + snapHorAmt ∧ x(frac2MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac2MasterPt)]]]]]]) → frac2X
  34. If(x(frac1MasterPt) < x(dotA) + snapHorAmt ∧ x(frac1MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac1MasterPt) < x(dotB) + snapHorAmt ∧ x(frac1MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac1MasterPt) < x(dotC) + snapHorAmt ∧ x(frac1MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac1MasterPt) < x(dotD) + snapHorAmt ∧ x(frac1MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac1MasterPt) < x(dotE) + snapHorAmt ∧ x(frac1MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac1MasterPt) < x(dotF) + snapHorAmt ∧ x(frac1MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac1MasterPt) < x(dotG) + snapHorAmt ∧ x(frac1MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac1MasterPt)]]]]]]) → frac1X
  35. Vector((1, 0), (-0.2, 0)) → numLnL
  36. Vector((1, 0), (2.2, 0)) → numLnR
  37. Sequence((k - 0.037, -0.25), k, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → labelPtList
  38. If(y(frac1MasterPt) ≤ onLineHeight ∧ y(frac2MasterPt) < onLineHeight ∧ y(frac3MasterPt) < onLineHeight ∧ y(frac4MasterPt) < onLineHeight, true, false) → allOnLine
  39. If(x(Frac4PtLn) / Element[numLnMax, set] ≥ Element[frac4Num, set] / Element[frac4Denom, set] - 0.016 ∧ x(Frac4PtLn) / Element[numLnMax, set] ≤ Element[frac4Num, set] / Element[frac4Denom, set] + 0.016, true, false) → frac4PlaceYN
  40. If(x(Frac3PtLn) / Element[numLnMax, set] ≥ Element[frac3Num, set] / Element[frac3Denom, set] - 0.016 ∧ x(Frac3PtLn) / Element[numLnMax, set] ≤ Element[frac3Num, set] / Element[frac3Denom, set] + 0.016, true, false) → frac3PlaceYN
  41. If(x(Frac2PtLn) / Element[numLnMax, set] ≥ Element[frac2Num, set] / Element[frac2Denom, set] - 0.016 ∧ x(Frac2PtLn) / Element[numLnMax, set] ≤ Element[frac2Num, set] / Element[frac2Denom, set] + 0.016, true, false) → frac2PlaceYN
  42. If(x(Frac1PtLn) / Element[numLnMax, set] ≥ Element[frac1Num, set] / Element[frac1Denom, set] - 0.016 ∧ x(Frac1PtLn) / Element[numLnMax, set] ≤ Element[frac1Num, set] / Element[frac1Denom, set] + 0.016, true, false) → frac1PlaceYN
  43. If(set ≟ 1 ∧ ckHintSet1, true, If[set ≟ 2 ∧ ckHintSet2, true, If[set ≟ 3 ∧ ckHintSet3, true, If[set ≟ 4 ∧ ckHintSet4, true, If[set ≟ 5 ∧ ckHintSet5, true, If[set ≟ 6 ∧ ckHintSet6, true, false]]]]]) → hintMasterYN
  44. Sequence(Segment[(i, 0.28), (i, -0.28)], i, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → scaleHashXaxis
  45. If(set ≟ 1 ∧ ckHintSet1b, true, If[set ≟ 2 ∧ ckHintSet2b, true, If[set ≟ 3 ∧ ckHintSet3b, true, If[set ≟ 4 ∧ ckHintSet4b, true, If[set ≟ 5 ∧ ckHintSet5b, true, If[set ≟ 6 ∧ ckHintSet6b, true, false]]]]]) → hintMasterYNb
  46. Sequence((0.26 + j, 3), j, 0, 1.5, 0.498) → fracAlignPts