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四则运算与分数结合的几何作图示例

四则运算与分数结合的几何作图示例
几何画板及绘图内容加载中，请稍等……
2024-02-26 23:35
解析几何几何作图
所属专题 Bruchzahlen - Verbindung der Grundrechnungsarten
该范例演示了如何将四则运算与分数结合进行几何作图。核心数学概念包括运算顺序、分数运算和几何构造。作图要点涉及使用GeoGebra命令如Point、Translate、Midpoint等进行图形绘制。适合小学5-6年级学生，用于学习运算规则和几何作图技能。

GeoGebra 命令及参数

  1. Point(Line[P0, xAxis]) → P1
  2. Point(Line[P0, xAxis]) → P2
  3. Translate(Polygon[(0, 0), (tablesizex2, 0), (tablesizex2, tablesizey), (0, tablesizey)], P2 - ((0.2 * tablespace), (-2 * tablesizey) - (2 * tablespace))) → vrechts3
  4. Translate(Polygon[(0, 0), (tablesizex2, 0), (tablesizex2, tablesizey), (0, tablesizey)], P2 - ((0.2 * tablespace), (-tablesizey) - tablespace)) → vrechts2
  5. Translate(Polygon[(0, 0), (tablesizex3, 0), (tablesizex3, tablesizey), (0, tablesizey)], P1 - (0, (-3 * tablesizey) - (3 * tablespace))) → vlinks4
  6. Translate(Polygon[(0, 0), (tablesizex3, 0), (tablesizex3, tablesizey), (0, tablesizey)], P1 - (0, (-5 * tablesizey) - (5 * tablespace))) → vlinks6
  7. Translate(Polygon[(0, 0), (tablesizex2, 0), (tablesizex2, tablesizey), (0, tablesizey)], P2 - ((0.2 * tablespace), (-3 * tablesizey) - (3 * tablespace))) → vrechts4
  8. Translate(Polygon[(0, 0), (tablesizex2, 0), (tablesizex2, tablesizey), (0, tablesizey)], P2 - ((0.2 * tablespace), (-5 * tablesizey) - (5 * tablespace))) → vrechts6
  9. Translate(Polygon[(0, 0), (tablesizex2, 0), (tablesizex2, tablesizey), (0, tablesizey)], P2 - ((0.2 * tablespace), (-4 * tablesizey) - (4 * tablespace))) → vrechts5
  10. Translate(Polygon[(0, 0), (tablesizex3, 0), (tablesizex3, tablesizey), (0, tablesizey)], P1 - (0, 0)) → vlinks1
  11. Midpoint(Corner[TextLinks1, 1], Corner[TextLinks1, 3]) → M1
  12. Midpoint(Corner[TextRechts2, 1], Corner[TextRechts2, 3]) → M2
  13. Midpoint(Corner[TextRechts4, 1], Corner[TextRechts4, 3]) → M41
  14. Midpoint(Corner[TextRechts5, 1], Corner[TextRechts5, 3]) → M5
  15. Midpoint(Corner[TextRechts6, 1], Corner[TextRechts6, 3]) → M61
  16. Midpoint(Corner[TextLinks6, 1], Corner[TextLinks6, 3]) → M62
  17. Midpoint(Corner[TextLinks4, 1], Corner[TextLinks4, 3]) → M42
  18. Midpoint(Corner[TextRechts3, 1], Corner[TextRechts3, 3]) → M3
  19. Textfield(input1) → Eingabefeld1
  20. Textfield(input2) → Eingabefeld2
  21. CountIf(m ∈ vrechts2, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count2
  22. CountIf(m ∈ vrechts4, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count41
  23. CountIf(m ∈ vlinks4, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count42
  24. CountIf(m ∈ vrechts6, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count61
  25. CountIf(m ∈ vrechts5, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count5
  26. CountIf(m ∈ vlinks6, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count62
  27. CountIf(m ∈ vlinks1, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count1
  28. Sequence(P1 + ((-0.3 * tablespace) + textposx, (m * tablesizey) + (m * tablespace) - 0.2), m, 0, 5) → listPosA
  29. Point(Line[A, xAxis]) → B
  30. SpeechBubbleLeft(C, 8.4, 1.1) → Vieleck1
  31. Point(Line[D, xAxis]) → E
  32. Point(Line[F, xAxis]) → G
  33. SpeechBubbleRight(H, 12, 3.97) → Vieleck2
  34. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{\frac{20}{12} -- \frac{9}{12} = \frac{11}{12}"), -25°) → TextStartRechts6
  35. RotateText("\textsf{Rechenschritt}", 90°) → Text28
  36. Zip(Segment[P + (tablespace, (-tablespace)), P + (tablespace, tablesizey - tablespace)], P, listPosA) → listLines
  37. Translate(Polygon[(0, 0), (tablesizex3, 0), (tablesizex3, tablesizey), (0, tablesizey)], P1 - (0, (-tablesizey) - tablespace)) → vlinks2
  38. Translate(Polygon[(0, 0), (tablesizex3, 0), (tablesizex3, tablesizey), (0, tablesizey)], P1 - (0, (-4 * tablesizey) - (4 * tablespace))) → vlinks5
  39. Translate(Polygon[(0, 0), (tablesizex3, 0), (tablesizex3, tablesizey), (0, tablesizey)], P1 - (0, (-2 * tablesizey) - (2 * tablespace))) → vlinks3
  40. CountIf(m ∈ vrechts3, m, {M1, M2, M3, M41, M42, M5, M61, M62}) → count3
  41. Sequence(P2 + (0, (m * tablesizey) + (m * tablespace) - (0.5 * textposx)), m, 0, 5) → listPosB
  42. Translate(Polygon[(0, 0), (tablesizex2, 0), (tablesizex2, tablesizey), (0, tablesizey)], P2 - ((0.2 * tablespace), 0)) → vrechts1
  43. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{Gemischte Zahlen werden in unechte Brüche umgerechnet.}"), 45°) → TextStartLinks1
  44. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{Punktrechnungen werden vor Strichrechnungen ausgeführt."), -15°) → TextStartLinks4
  45. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{Die Differenz wird ermittelt.\vphantom{g}\\Ungleichnamige Brüche werden auf gleichen Nenner gebracht."), 30°) → TextStartLinks6
  46. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{\frac{4}{3} \cdot \Big(\frac{4}{8} + \frac{6}{8}\Big) -- \frac{3}{4} ="), -10°) → TextStartRechts2
  47. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{\frac{4}{3} \cdot \frac{10}{8} -- \frac{3}{4} ="), -20°) → TextStartRechts3
  48. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{\frac{4 \cdot 10}{3 \cdot 8} -- \frac{3}{4} ="), 20°) → TextStartRechts4
  49. RotateText((("\textsf{\small\fcolorbox{000000}{" * colour) * "}{\frac{20}{12} -- \frac{3}{4} ="), 10°) → TextStartRechts5
  50. Point(Line[J, yAxis]) → L

AI 绘图提示语参考

绘制一个用于分数运算教学的几何构造图。左侧和右侧各有一列矩形框，分别表示不同的运算步骤。左侧框内显示带分数转换为假分数、乘除优先于加减、通分与求差等文字说明，右侧框内显示具体分数算式，如三分之四乘以（八分之四加八分之六）减四分之三，并逐步化简。每个矩形框中央有标记点，用于统计各步骤。底部有输入框和提示气泡。整体布局整齐，矩形框按垂直方向排列，间距均匀。
以上提示语为根据原始绘图命令整理而来，仅供参考。