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分数与几何作图：探索分数表示与图形变换

分数与几何作图：探索分数表示与图形变换
几何画板及绘图内容加载中，请稍等……
2021-07-28 15:58
所属专题 Wiederholung I: Brüche - Begriffe & Arten
本范例通过GeoGebra演示分数作为部分与整体的关系，并结合几何图形变换展示分数操作。核心数学概念包括分数表示、图形变换与比例关系。作图要点涉及使用Shuffle、Append、Polygon等GeoGebra命令创建动态图形，适用于小学5-6年级学生进行分数与几何结合的数学学习。

GeoGebra 命令及参数

  1. Shuffle(Sequence[Random[2, 5], i, 1, 100]) → randomNosCols, {5, 2, 4, 3, 4, 2, 4, 5, 3, 2, 2, 5, 2, 2, 2, 5, 5, 5, 3, 5, 4, 5, 2, 4, 2, 2, 3, 2, 4, 3, 3, 3, 2, 4, 2, 4, 3, 5, 5, 5, 4, 3, 4, 3, 3, 5, 3, 4, 3, 5, 5, 5, 4, 3, 3, 5, 3, 5, 4, 4, 5, 3, 4, 5, 4, 3, 3, 3, 3, 2, 4, 2, 4, 2, 4, 4, 4, 4, 5, 4, 2, 3, 4, 4, 2, 2, 5, 5, 5, 5, 2, 5, 5, 5, 3, 5, 5, 5, 5, 5}
  2. Shuffle(Sequence[Random[2, 5], i, 1, 100]) → randomNosRows, {5, 5, 5, 3, 4, 3, 2, 2, 4, 3, 5, 3, 2, 3, 5, 2, 3, 5, 4, 5, 3, 4, 4, 4, 3, 2, 3, 5, 4, 3, 5, 4, 5, 5, 4, 5, 5, 5, 4, 3, 2, 4, 3, 2, 4, 3, 4, 3, 4, 4, 5, 2, 4, 3, 4, 2, 3, 5, 4, 4, 2, 2, 2, 3, 5, 3, 4, 5, 4, 2, 2, 4, 5, 2, 5, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 5, 4, 4, 2, 4, 3, 5, 3, 3, 3, 2, 5, 5}
  3. Append(Random[1, (randomNosCols(1) * randomNosRows(1)) - 1], Sequence[Random[1, (randomNosCols(i) * randomNosRows(i))], i, 2, 100]) → randomNosNumColored
  4. Element(randomNosCols, Mod[count, 100] + 1) → cols
  5. Element(randomNosRows, Mod[count, 100] + 1) → rows
  6. Element(randomNosNumColored, Mod[count, 100] + 1) → numColored
  7. Textfield(aInput) → InputBox1
  8. Textfield(bInput) → InputBox2
  9. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  10. Flatten(Sequence[Sequence[Polygon[PtableTopLeft + ((r * heightCell) * (0, -1)) + ((c * widthCell) * (1, 0)), PtableTopLeft + ((r * heightCell) * (0, -1)) + (((c + 1) * widthCell) * (1, 0)), PtableTopLeft + (((r + 1) * heightCell) * (0, -1)) + (((c + 1) * widthCell) * (1, 0)), PtableTopLeft + (((r + 1) * heightCell) * (0, -1)) + ((c * widthCell) * (1, 0))], c, 0, cols - 1], r, 0, rows - 1]) → grid
  11. Segment(A_{1}, B) → bruchstrich
  12. Take(Shuffle[grid], 1, numColored) → coloredCells
  13. Flatten(Sequence[Sequence[Polygon[PtableTopLeft + ((r * heightCell) * (0, -1)) + ((c * widthCell) * (1, 0)), PtableTopLeft + ((r * heightCell) * (0, -1)) + (((c + 1) * widthCell) * (1, 0)), PtableTopLeft + (((r + 1) * heightCell) * (0, -1)) + (((c + 1) * widthCell) * (1, 0)), PtableTopLeft + (((r + 1) * heightCell) * (0, -1)) + ((c * widthCell) * (1, 0))], c, 0, cols - 1], r, 0, rows - 1]) → grid2
  14. OrthogonalLine(C, xAxis) → f
  15. Point(f) → C1
  16. Point(f) → A
  17. Point(f) → C3
  18. Defined((aInput * bInput)) → fixed