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Locating Decimals on a Number Line (2)

Locating Decimals on a Number Line (2)
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2018-09-20 23:13
FunctionTrigonometryCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates how to correctly place decimal fractions on a number line and get instant feedback. This is a more challenging version using different endpoints. Key math concepts include number line, decimals, rational numbers, and real numbers. Construction highlights using GeoGebra commands/objects from the summary: Polygon, PointIn, If, Vector, Sequence; objects: set, restrictPts, f, h, i, j, Frac4PtSet1-6, Frac4PtSet1, frac4MasterPt, numLnMax, PtA-F, dotA-F, ckPlaceSet1-6, placeMasterYN, snapHorAmt, frac4X, snapHorHeight, snapVertAmt, Frac3PtSet1. Suitable for middle school and above mathematics education, helping students understand and master the placement of decimals 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, h, i, j
  2. PointIn(restrictPts) → Frac4PtSet1
  3. PointIn(restrictPts) → Frac4PtSet2
  4. PointIn(restrictPts) → Frac4PtSet3
  5. PointIn(restrictPts) → Frac4PtSet4
  6. PointIn(restrictPts) → Frac4PtSet5
  7. PointIn(restrictPts) → Frac4PtSet6
  8. If(set ≟ 1, Frac4PtSet1, If[set ≟ 2, Frac4PtSet2, If[set ≟ 3, Frac4PtSet3, If[set ≟ 4, Frac4PtSet4, If[set ≟ 5, Frac4PtSet5, Frac4PtSet6]]]]) → frac4MasterPt
  9. 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
  10. 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
  11. PointIn(restrictPts) → Frac3PtSet1
  12. PointIn(restrictPts) → Frac3PtSet2
  13. PointIn(restrictPts) → Frac3PtSet3
  14. PointIn(restrictPts) → Frac3PtSet4
  15. PointIn(restrictPts) → Frac3PtSet5
  16. PointIn(restrictPts) → Frac3PtSet6
  17. If(set ≟ 1, Frac3PtSet1, If[set ≟ 2, Frac3PtSet2, If[set ≟ 3, Frac3PtSet3, If[set ≟ 4, Frac3PtSet4, If[set ≟ 5, Frac3PtSet5, Frac3PtSet6]]]]) → frac3MasterPt
  18. 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
  19. PointIn(restrictPts) → Frac2PtSet1
  20. PointIn(restrictPts) → Frac2PtSet2
  21. PointIn(restrictPts) → Frac2PtSet3
  22. PointIn(restrictPts) → Frac2PtSet4
  23. PointIn(restrictPts) → Frac2PtSet5
  24. PointIn(restrictPts) → Frac2PtSet6
  25. If(set ≟ 1, Frac2PtSet1, If[set ≟ 2, Frac2PtSet2, If[set ≟ 3, Frac2PtSet3, If[set ≟ 4, Frac2PtSet4, If[set ≟ 5, Frac2PtSet5, Frac2PtSet6]]]]) → frac2MasterPt
  26. 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
  27. PointIn(restrictPts) → Frac1PtSet1
  28. PointIn(restrictPts) → Frac1PtSet6
  29. PointIn(restrictPts) → Frac1PtSet2
  30. PointIn(restrictPts) → Frac1PtSet3
  31. PointIn(restrictPts) → Frac1PtSet4
  32. PointIn(restrictPts) → Frac1PtSet5
  33. If(set ≟ 1, Frac1PtSet1, If[set ≟ 2, Frac1PtSet2, If[set ≟ 3, Frac1PtSet3, If[set ≟ 4, Frac1PtSet4, If[set ≟ 5, Frac1PtSet5, Frac1PtSet6]]]]) → frac1MasterPt
  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 - 0.02, -0.75), k, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → labelPtList
  38. If(x(Frac1PtLn) ≤ 2.2 ∧ x(Frac2PtLn) ≤ 2.2 ∧ x(Frac3PtLn) ≤ 2.2 ∧ x(Frac4PtLn) ≤ 2.2 ∧ x(Frac1PtLn) ≥ -0.2 ∧ x(Frac2PtLn) ≥ -0.2 ∧ x(Frac3PtLn) ≥ -0.2 ∧ x(Frac4PtLn) ≥ -0.2 ∧ y(Frac1PtLn) ≟ 0 ∧ y(Frac2PtLn) ≟ 0 ∧ y(Frac3PtLn) ≟ 0 ∧ y(Frac4PtLn) ≟ 0, 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. Sequence((0.26 + j, 3), j, 0, 1.5, 0.498) → fracAlignPts