Fraction Extension Practice

Fraction Extension Practice
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2022-08-10 19:27
This example demonstrates the concept of fraction extension, involving core mathematical concepts such as the basic properties and methods of fractions. Using GeoGebra commands like Join, Sequence, Point, etc., students can visually understand the process of fraction extension. Suitable for students in grades 5-6, it helps them master the methods of extending and simplifying fractions.

GeoGebra Commands & Parameters

  1. Join({{"$\textsf{\vphantom{Äg}\phantom{=}}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1
  2. Sequence(Random[2, 12], i, 1, 100) → randomNenner, {5, 2, 12, 2, 12, 10, 11, 12, 7, 4, 2, 8, 10, 6, 10, 12, 7, 9, 10, 6, 3, 10, 5, 12, 3, 2, 3, 5, 2, 8, 5, 12, 8, 5, 7, 7, 9, 7, 5, 11, 4, 11, 2, 2, 6, 2, 11, 6, 7, 4, 8, 9, 12, 11, 7, 8, 12, 2, 3, 7, 7, 2, 11, 11, 6, 12, 2, 6, 7, 7, 7, 5, 6, 6, 12, 5, 8, 3, 3, 8, 10, 12, 3, 7, 9, 4, 6, 3, 4, 8, 3, 8, 5, 10, 6, 10, 9, 2, 7, 7}
  3. Sequence(Random[2, nenner2 - 1], i, 1, 100) → randomZaehler, {7, 3, 5, 7, 2, 6, 6, 2, 3, 4, 6, 7, 4, 3, 3, 5, 7, 4, 3, 5, 5, 6, 4, 6, 7, 3, 6, 4, 2, 2, 5, 3, 6, 5, 2, 7, 3, 2, 7, 3, 5, 4, 7, 2, 5, 3, 7, 3, 6, 5, 6, 2, 7, 5, 6, 7, 5, 2, 2, 6, 7, 7, 5, 6, 5, 5, 6, 5, 4, 6, 2, 3, 2, 6, 4, 4, 3, 5, 4, 5, 7, 5, 7, 6, 6, 4, 5, 4, 7, 3, 7, 6, 3, 2, 4, 4, 2, 2, 2, 4}
  4. Sequence(I + ((i * widthNennerBar / 12) * (1, 0)), i, 1, 12) → allowedPositionsNennerBar
  5. Point(allowedPositionsNennerBar) → PNenner
  6. Circle(M, B) → c
  7. Segment(M, M + (Radius[c] * (0, 1))) → f
  8. Vector(F, G) → u
  9. Segment(H, H + (widthZaehlerBar * (1, 0))) → g
  10. Segment(I, I + (widthNennerBar * (1, 0))) → h
  11. Sequence(H + ((i * widthZaehlerBar / 12) * (1, 0)), i, 0, nenner2) → allowedPositionsZaehlerBar
  12. Point(allowedPositionsZaehlerBar) → PZaehler
  13. Sequence(Rotate[f, ((i * 2) * pi / nenner2), M], i, 0, nenner2 - 1) → l1
  14. Sequence(CircleSector[M, Rotate[KreisOben, (((-(i + 1)) * 2) * pi / nenner2), M], Rotate[KreisOben, (((-i) * 2) * pi / nenner2) - 0.0001, M]], i, 0, zaehler2 - 1) → l2
  15. Sequence(Random[1, zaehler2 - 1], i, 1, 100) → randomSubtrahend, {4, 1, 4, 3, 2, 2, 4, 3, 4, 1, 2, 4, 3, 2, 2, 2, 4, 4, 1, 3, 2, 2, 3, 2, 1, 2, 2, 4, 2, 3, 2, 1, 3, 4, 3, 1, 3, 1, 2, 2, 3, 2, 3, 4, 1, 4, 1, 1, 3, 4, 3, 4, 4, 1, 1, 4, 1, 4, 3, 1, 3, 4, 2, 1, 1, 3, 1, 1, 3, 1, 3, 3, 1, 3, 4, 2, 1, 1, 3, 4, 3, 3, 4, 4, 3, 4, 3, 4, 2, 3, 2, 4, 1, 2, 1, 2, 2, 4, 4, 1}
  16. Center(sektor12v1) → M12v1
  17. Center(sektor12v2) → M12v2
  18. Center(sektor12v3) → M12v3
  19. Center(sektor12v4) → M12v4
  20. Center(sektor12v5) → M12v5
  21. Center(sektor12v6) → M12v6
  22. Center(sektor12v7) → M12v7
  23. Center(sektor12v8) → M12v8
  24. Center(sektor12v9) → M12v9
  25. Center(sektor12v10) → M12v10
  26. Center(sektor12v11) → M12v11
  27. Center(sektor12v12) → M12v12
  28. Textfield(input1) → Eingabefeld1
  29. Textfield(input2) → Eingabefeld2
  30. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1_{1}
  31. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP2
  32. Point(xAxis) → J
  33. OrthogonalLine(J, xAxis) → i
  34. Point(xAxis) → K
  35. LineBisector(K, J) → j
  36. Translate({l2}, (dxBruch2, 0)) → showBruch201
  37. Sequence(Rotate[f, ((i * 2) * pi / ((verfeinerung * nenner2))), M], i, 0, (verfeinerung * nenner2) - 1) → l3
  38. Translate({l3}, (dxBruch2, 0)) → showBruch202
  39. Translate({c, l1}, (dxBruch2, 0)) → showBruch203
  40. LaTeX(step, true, true) → Text5
  41. CircleArc(O, N, PosBogerl) → bogerl11
  42. Point(bogerl11) → P
  43. Vector(P, N + (0.1 * Vector[P, N])) → bogerl1pfeil
  44. Translate({bogerl11, bogerl1pfeil}, (0, 0)) → bogen1
  45. OrthogonalLine(Q, yAxis) → k
  46. Mirror(bogen1(1), k) → bogen1'
  47. Point(bogen1') → R
  48. Point(bogen1') → S
  49. Vector(R, S + (0.1 * Vector[R, S])) → v
  50. Point(bogen1') → T
  51. If(step ≟ 3, SelectedIndex[LDP1] ≠ 1, false) → fixedSectors
  52. If(step ≟ 3, SelectedIndex[LDP1] ≟ 1, step ≟ 4, false, true) → showpart2

AI Drawing Prompt Reference

Create a visual representation of fraction extension, illustrating the basic properties and methods of fractions. Include a coordinate axis, a circle, and multiple sectors. The sectors are arranged through rotation and translation, forming a geometric representation of a fraction. There is a center point on the circle, with points and line segments on its circumference, having specific positional relationships. The sectors overlap and are spaced apart, forming the overall fraction representation. Start by drawing the coordinate axis and circle, then add points and line segments on the circle, rotate and move the sectors, and finally adjust their positional relationships.
The prompt above was compiled from the original drawing commands and is for reference only.