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Proportional Relationships and Geometric Construction: Visualizing Direct and In

Proportional Relationships and Geometric Construction: Visualizing Direct and In
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2023-07-20 14:12
In collections Wiederholung: Direkte und Indirekte Proportionalität Direkte Proportionalität
This example demonstrates proportional relationships through geometric construction. Key mathematical concepts include proportionality, graphical representation, and geometric construction. Construction involves GeoGebra commands such as If, Rotate, CircleArc, etc. Suitable for elementary students (grades 5-6) to understand proportionality and geometric construction skills.

GeoGebra Commands & Parameters

  1. If(step ≤ 5, 0.4, 0.65) → sizecoord
  2. Rotate(O2 + ((15 * sizecoord) + 0.2, 0), 45°, O2) → Ccorrect
  3. CircleArc(O2, Cstart, Ccorrect) → c
  4. Point(c) → C
  5. If(step ≤ 5, O1, O2) → O
  6. Flatten(Sequence[Sequence[O + (m * (sizecoord, 0)) + (j * (0, sizecoord)), m, 0, widthcoord], j, 0, heightcoord + 1]) → pointsCoords
  7. Point(pointsCoords) → X9
  8. Point(pointsCoords) → X7
  9. Point(pointsCoords) → X6
  10. Point(pointsCoords) → X4
  11. Point(pointsCoords) → X3
  12. Sort({X3, X4, X6, X7, X9}) → points2
  13. Flatten(Sequence[Sequence[O + (m * (sizecoord, 0)) + (j * (0, sizecoord)), m, 0, widthcoord - 1], j, 0, heightcoord]) → pointsGoal
  14. Flatten(Sequence[Sequence[PTabularLeft + (m * (0.7, 0)) + (j * (0, (-sizetabular))) + (-2, -1.65), m, 0, 2], j, 0, 4]) → pointsStart
  15. Point(Join[{pointsGoal, pointsStart}]) → X0
  16. Point(Join[{pointsGoal, pointsStart}]) → X8
  17. Point(Join[{pointsGoal, pointsStart}]) → X5
  18. Point(Join[{pointsGoal, pointsStart}]) → X2
  19. Flatten(Sequence[Sequence[Z + (m * (sizetabular, 0)) + (j * (0, (-sizetabular))), m, 0, 2], j, 0, 7]) → l3
  20. Segment(pointsCoords(1), pointsCoords(((widthcoord + 1) * (heightcoord + 1)) - widthcoord)) → yline
  21. Sequence(O + (m * (0, sizecoord)), m, 1, heightcoord - 1) → pointsy
  22. Zip(Segment[A + ((-heightlines), 0), A + (heightlines, 0)], A, pointsy) → linesy
  23. Sequence(Text["\textsf{" + (m) + "}", ((m * sizecoord) + x(O), y(O) - 0.9), true, true, -0, 1], m, 0, widthcoord - 2) → textx
  24. Join({Sequence[Segment[pointsCoords((widthcoord * m) + m + 1), pointsCoords(((m + 1) * widthcoord) + m)], m, 0, heightcoord], Sequence[Segment[pointsCoords(m), pointsCoords(((widthcoord + 1) * heightcoord) + m)], m, 1, widthcoord]}) → linescoord
  25. Segment(pointsCoords(1), pointsCoords(widthcoord)) → xline
  26. Polygon(Corner[lineal, 1], Corner[lineal, 2], Corner[lineal, 3], Corner[lineal, 4]) → v2, f, h, i, j
  27. SpeechBubbleLeft(N, 6.1, 1.7) → Vieleck1
  28. If(step ≟ 3.5, correcttab, If[step ≟ 3.75, true, listfixed(step)]) → fixed
  29. Point(Line[S, xAxis]) → T
  30. Textfield(input1) → Eingabefeld1
  31. Textfield(input2) → Eingabefeld2
  32. Textfield(input3) → Eingabefeld3
  33. Textfield(input4) → Eingabefeld4
  34. Textfield(input5) → Eingabefeld5
  35. Textfield(input6) → Eingabefeld6
  36. Textfield(input7) → Eingabefeld7
  37. Textfield(input8) → Eingabefeld8
  38. Point(Line[A_1, xAxis]) → B_1
  39. Point(Line[A_1, xAxis]) → C_1
  40. Point(Line[L, xAxis]) → M
  41. SpeechBubbleLeft(G_1, 9.2, 1.1) → Vieleck2
  42. Point(Line[I_1, xAxis]) → H_1
  43. Point(Line[C_1, xAxis]) → D_1
  44. Segment(O, O + ((1.07 * heightcoord) * (sizecoord, sizecoord))) → g
  45. Sequence(Text["\textsf\small{" + (m) + "}", ((m * sizecoord) + x(O), y(O) - 0.9), true, true, -0, 1], m, 0, widthcoord - 2) → textxsmall
  46. Sequence(Text[(("\textsf\small{" * ReplaceAll["" + ((m * 0.5)) + "", ".", ","]) * "}"), (x(O) - 0.6, (m * sizecoord) + y(O) - 0.4), true, true, -0, 1], m, 1, heightcoord - 1) → textysmall
  47. SpeechBubbleLeft(N, 7.2, 1.1) → Vieleck3
  48. Sequence(PTabularLeft + (m * (0, aby)) + (abx, 0), m, 0, 5) → listPTabular
  49. Zip(CountIf[m ≟ Ö, m, {X3, X4, X6, X7, X9}], Ö, {X3, X4, X6, X7, X9}) → pointsSame
  50. Max(pointsSame) → numPointsSame
  51. Sequence(Text[(("\textsf{" * ReplaceAll["" + ((m * 0.5)) + "", ".", ","]) * "}"), (x(O) - 0.6, (m * sizecoord) + y(O) - 0.4), true, true, -0, 1], m, 1, heightcoord - 1) → texty
  52. Sequence(O + (m * (sizecoord, 0)), m, 1, widthcoord - 2) → pointsx
  53. Zip(Segment[A + (0, (-heightlines)), A + (0, heightlines)], A, pointsx) → linesx
  54. KeepIf(Y ∈ pointsx, Y, {X3, X4, X6, X7, X9}) → pointsonXaxis
  55. If(pointsonXaxis ≟ {}, {}, Sort[Zip[(x(Y) - x(O2)) / sizecoord, Y, pointsonXaxis]]) → xonXaxis
  56. Length(pointsonXaxis) → lengthonXaxis
  57. Point(Line[GB1, xAxis]) → GB2