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From Mixed Number to Improper Fraction: Geometric Construction and Fraction Conc

From Mixed Number to Improper Fraction: Geometric Construction and Fraction Conc
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2021-07-19 16:01
In collections Wiederholung I: Brüche - Begriffe & Arten
This example demonstrates how to convert a mixed number to an improper fraction and visually represents fraction concepts through geometric figures. The key mathematical concepts include mixed numbers, improper fractions, fraction operations, and geometric construction. The construction involves using GeoGebra commands such as Sequence, Element, Shuffle, Textfield, Polygon, Circle, Segment, Circle

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 3], i, 1, 100) → randomNosGanze, {2, 3, 3, 1, 2, 1, 2, 2, 3, 1, 3, 3, 1, 1, 2, 1, 3, 1, 1, 2, 3, 2, 1, 3, 1, 3, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 2, 2, 1, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 3, 2, 3, 1, 3, 3, 1, 3, 3, 3, 1, 2, 3, 1, 2, 3, 3, 3, 2, 1, 3, 2, 1, 3, 1, 1, 3, 2, 2, 3, 1, 1}
  2. Element(randomNosGanze, Mod[count, 100] + 1) → ganze
  3. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosNenner, {5, 4, 2, 6, 9, 10, 3, 3, 2, 4, 9, 10, 9, 5, 10, 6, 3, 7, 6, 4, 7, 9, 4, 6, 10, 2, 10, 10, 9, 3, 4, 7, 3, 2, 5, 3, 8, 5, 6, 5, 6, 5, 3, 10, 9, 2, 6, 9, 7, 6, 9, 2, 10, 6, 6, 7, 4, 3, 9, 3, 5, 5, 6, 6, 8, 4, 10, 8, 5, 8, 10, 9, 8, 4, 8, 3, 8, 7, 2, 3, 7, 2, 10, 2, 10, 9, 6, 4, 6, 7, 4, 4, 2, 4, 9, 8, 6, 7, 9, 2}
  4. Sequence(Random[1, randomNosNenner(i) - 1], i, 1, 100) → randomNosZaehler, {3, 1, 1, 5, 4, 1, 1, 2, 1, 3, 1, 9, 4, 3, 2, 2, 1, 1, 2, 3, 5, 6, 3, 4, 7, 1, 6, 7, 8, 2, 1, 4, 1, 1, 4, 1, 1, 3, 3, 1, 4, 2, 2, 4, 4, 1, 2, 8, 5, 4, 1, 1, 2, 5, 2, 6, 3, 2, 8, 2, 3, 1, 1, 2, 1, 3, 8, 5, 4, 4, 1, 6, 1, 2, 6, 2, 7, 5, 1, 1, 1, 1, 7, 1, 5, 6, 2, 3, 3, 4, 3, 3, 1, 1, 5, 5, 2, 1, 3, 1}
  5. Element(randomNosZaehler, Mod[count, 100] + 1) → zaehler
  6. Element(randomNosNenner, Mod[count, 100] + 1) → nenner
  7. Textfield(aInput) → InputBox1
  8. Textfield(bInput) → InputBox2
  9. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  10. Circle(PM1, radius) → c
  11. Sequence(Translate[c, ((((2 * radius) * 1.2) * i), 0)], i, 0, ganze) → circles
  12. Segment(PM1, PM1 + (radius * (0, 1))) → f
  13. Sequence(Rotate[f, ((i * 2) * pi / nenner), PM1], i, 0, nenner - 1) → l2
  14. Sequence(Translate[l2, ((((2 * radius) * 1.2) * i), 0)], i, 0, ganze) → circlesSectors
  15. CircleSector(PM1, Rotate[PM1 + (0, radius), ((-2 * pi / nenner) * zaehler), PM1], PM1 + (0, radius)) → d
  16. Translate(d, ((((2 * radius) * 1.2) * ganze), 0)) → d'
  17. Take(circles, 1, ganze) → circlesGanze
  18. Polygon(A, B, C, D) → q1, a, b, c_1, d_1
  19. Sequence(Random[1, 3], i, 1, 100) → randomNosGanze_{1}, {2, 3, 1, 3, 2, 3, 3, 1, 2, 3, 3, 2, 2, 2, 1, 1, 1, 2, 2, 3, 2, 1, 1, 1, 2, 3, 1, 1, 1, 3, 2, 3, 1, 3, 1, 2, 3, 2, 1, 1, 3, 2, 1, 3, 3, 2, 1, 3, 1, 1, 1, 3, 3, 2, 3, 1, 1, 3, 3, 2, 2, 2, 2, 1, 1, 2, 3, 1, 3, 1, 3, 1, 2, 2, 1, 3, 3, 1, 3, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 1, 2, 1, 2, 3}
  20. Element(randomNosGanze_{1}, Mod[count, 100] + 1) → ganze_{1}
  21. Circle(PM1_{1}, radius) → c_{2}
  22. Sequence(Random[1, 3], i, 1, 100) → randomNosGanze_{2}, {1, 2, 2, 3, 1, 1, 3, 1, 2, 1, 3, 2, 1, 2, 2, 3, 3, 2, 1, 3, 1, 2, 1, 3, 2, 1, 1, 1, 3, 3, 2, 2, 1, 3, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 2, 1, 2, 1, 2, 2, 2, 3, 1, 1, 3, 3, 3, 3, 1, 3, 2, 3, 1, 3, 3, 2, 2, 2, 1, 3, 2, 3, 1, 1, 3, 3, 3, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 2}
  23. Element(randomNosGanze_{2}, Mod[count, 100] + 1) → ganze_{2}
  24. Circle(PM1_{2}, radius) → c_{3}
  25. Sequence(Translate[c_{3}, ((((2 * radius) * 1.2) * i), 0)], i, 0, ganze_{2}) → circles_{1}
  26. Polygon(E, F, G, H) → v1, e, f_1, g_1, h
  27. Take(circles, 1, ganze) → circlesSolution