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从混合数到假分数的转换：几何作图与分数概念

从混合数到假分数的转换：几何作图与分数概念
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2021-07-19 16:01
所属专题 Wiederholung I: Brüche - Begriffe & Arten
这个范例演示了如何将混合数转换为假分数，并通过几何图形直观展示分数概念。核心数学概念包括混合数、假分数、分数运算以及几何作图。作图要点包括使用GeoGebra命令如Sequence、Element、Shuffle、Textfield、Polygon、Circle、Segment、CircleSector、Translate、Take等对象，以及随机生成数字和颜色设置。适合小学五年级到六年级学生，用于学习分数运算和几何作图。

GeoGebra 命令及参数

  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