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PR2-07-ET2：跨组同类项合并练习

PR2-07-ET2：跨组同类项合并练习
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2021-07-21 03:25
多边形函数概率统计滑块动画函数图像
① 本范例通过三个水果篮子（苹果、橙子、香蕉）的视觉化分组，演示代数中“同类项”的识别与合并，特别是跨组（不同篮子）的同类项如何汇总。② 核心数学概念是代数式的化简，涉及同类项（相同变量与指数）的合并，以及随机变量、标准差等统计概念作为背景延伸，但主体是代数运算。③ 作图要点：使用GeoGebra的Polygon绘制篮子轮廓，PointIn与Join用于放置水果图片，Zip与Textfield创建交互输入框，TableText展示合并结果；对象包括numBasket1/2/3bananas/oranges/apples等变量，以及imgBasket*等图像对象，通过LaTeX公式显示代数表达式。④ 适合初中至高中阶段学习代数式化简的学生，也可用于教师课堂演示或学生自主练习，通过直观的篮子分组理解抽象的同类型合并规则。

GeoGebra 命令及参数

  1. LaTeX(UnicodeToLetter[10003]) → cmark
  2. LaTeX(UnicodeToLetter[10007]) → xmark
  3. Polygon({(-8, 2), (-8, 6.5), (1.5, 6.5), (1.5, 2)}) → basket1quad
  4. PointIn(basket1quad) → basket1apple1
  5. PointIn(basket1quad) → basket1apple2
  6. PointIn(basket1quad) → basket1apple3
  7. PointIn(basket1quad) → basket1apple4
  8. PointIn(basket1quad) → basket1apple5
  9. PointIn(basket1quad) → basket1orange1
  10. PointIn(basket1quad) → basket1orange2
  11. PointIn(basket1quad) → basket1orange3
  12. PointIn(basket1quad) → basket1banana1
  13. PointIn(basket1quad) → basket1banana2
  14. PointIn(basket1quad) → basket1banana3
  15. PointIn(basket1quad) → basket1banana4
  16. Polygon({(22, 2), (22, 6.5), (31.5, 6.5), (31.5, 2)}) → basket3quad
  17. PointIn(basket3quad) → basket3apple1
  18. PointIn(basket3quad) → basket3apple2
  19. PointIn(basket3quad) → basket3apple3
  20. PointIn(basket3quad) → basket3apple4
  21. PointIn(basket3quad) → basket3banana1
  22. PointIn(basket3quad) → basket3banana2
  23. PointIn(basket3quad) → basket3banana3
  24. PointIn(basket3quad) → basket3orange1
  25. Join({Sequence[(("SetLayer(imgBasket1apple" * q) * ", 8)"), q, 1, numBasket1apples], Sequence[(("SetLayer(imgBasket1orange" * q) * ", 8)"), q, 1, numBasket1oranges], Sequence[(("SetLayer(imgBasket1banana" * q) * ", 8)"), q, 1, numBasket1bananas]}) → basket1LayerCommands
  26. Join({Sequence[(("SetLayer(imgBasket2apple" * q) * ", 8)"), q, 1, numBasket2apples], Sequence[(("SetLayer(imgBasket2orange" * q) * ", 8)"), q, 1, numBasket2oranges], Sequence[(("SetLayer(imgBasket2banana" * q) * ", 8)"), q, 1, numBasket2bananas]}) → basket2LayerCommands
  27. Join({Sequence[(("SetLayer(imgBasket3apple" * q) * ", 8)"), q, 1, numBasket3apples], Sequence[(("SetLayer(imgBasket3orange" * q) * ", 8)"), q, 1, numBasket3oranges], Sequence[(("SetLayer(imgBasket3banana" * q) * ", 8)"), q, 1, numBasket3bananas]}) → basket3LayerCommands
  28. Polygon({(7, 2), (7, 6.5), (16.5, 6.5), (16.5, 2)}) → basket2quad
  29. PointIn(basket2quad) → basket2apple1
  30. PointIn(basket2quad) → basket2apple2
  31. PointIn(basket2quad) → basket2banana1
  32. PointIn(basket2quad) → basket2banana2
  33. PointIn(basket2quad) → basket2orange1
  34. PointIn(basket2quad) → basket2orange2
  35. PointIn(basket2quad) → basket2orange3
  36. PointIn(basket2quad) → basket2orange4
  37. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  38. Zip(A ≟ Text[B], A, {textApples, textOranges, textBananas}, B, {totalApples, totalOranges, totalBananas}) → totalCorrectness
  39. LaTeX("\textbf{In total there are:}") → header
  40. Textfield(textApples) → ansBoxApples
  41. Textfield(textBananas) → ansBoxBananas
  42. Textfield(textOranges) → ansBoxOranges
  43. TableText({totalApples, totalOranges, totalBananas}, {"\text{\vphantom{\dfrac{1}{2}}apples}", "\text{\vphantom{\dfrac{1}{2}}oranges}", "\text{\vphantom{\dfrac{1}{2}}bananas}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, totalCorrectness]], "v") → table

AI 绘图提示语参考

画三个水果篮，每个篮子用四边形表示，分别装不同数量和种类的水果：苹果、橙子和香蕉。用点表示每种水果，随机分布在篮子内部。添加文字标签显示每种水果的总数，并用颜色区分正确和错误的计数。最后，用一个表格汇总所有篮子的水果总数，表格标题为“总共有：”。
以上提示语为根据原始绘图命令整理而来，仅供参考。