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分组内合并同类项（NS2-02-XT1）

分组内合并同类项（NS2-02-XT1）
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2020-11-25 10:07
多边形函数不等式函数图像
① 本范例通过三个水果篮子（苹果、香蕉、橙子）的交互式分组，演示如何在代数表达式中识别并合并同类项。② 核心数学概念是代数式的化简，特别是同类项（具有相同变量和指数的项）的合并，以及多项式的基本运算。③ 作图要点：使用GeoGebra的Zip、LaTeX、Polygon、PointIn、Textfield、Join、TableText等命令，创建了多个数值输入框（numBasket*）、文本显示（textBasket*）、正确性判断（basket*correctness）以及图形元素（如水果图片imgBasket*、四边形basket*quad），通过动态反馈（对勾cmark、叉号xmark）帮助学生验证答案。④ 适合初中数学代数入门阶段，用于课堂互动练习或学生自主探索，强化对同类项概念的理解和合并技巧。

GeoGebra 命令及参数

  1. Zip(A ≟ Text[B], A, {textBasket3apples, textBasket3oranges, textBasket3bananas}, B, {numBasket3apples, numBasket3oranges, numBasket3bananas}) → basket3correctness
  2. Zip(A ≟ Text[B], A, {textBasket2apples, textBasket2oranges, textBasket2bananas}, B, {numBasket2apples, numBasket2oranges, numBasket2bananas}) → basket2correctness
  3. Zip(A ≟ Text[B], A, {textBasket1apples, textBasket1oranges, textBasket1bananas}, B, {numBasket1apples, numBasket1oranges, numBasket1bananas}) → basket1correctness
  4. LaTeX(UnicodeToLetter[10003]) → cmark
  5. LaTeX(UnicodeToLetter[10007]) → xmark
  6. Polygon({(-8, 2), (-8, 6.5), (1.5, 6.5), (1.5, 2)}) → basket1quad
  7. PointIn(basket1quad) → basket1apple1
  8. PointIn(basket1quad) → basket1apple2
  9. PointIn(basket1quad) → basket1apple3
  10. PointIn(basket1quad) → basket1apple4
  11. PointIn(basket1quad) → basket1apple5
  12. PointIn(basket1quad) → basket1orange1
  13. PointIn(basket1quad) → basket1orange2
  14. PointIn(basket1quad) → basket1orange3
  15. PointIn(basket1quad) → basket1banana1
  16. PointIn(basket1quad) → basket1banana2
  17. PointIn(basket1quad) → basket1banana3
  18. PointIn(basket1quad) → basket1banana4
  19. Polygon({(22, 2), (22, 6.5), (31.5, 6.5), (31.5, 2)}) → basket3quad
  20. PointIn(basket3quad) → basket3apple1
  21. PointIn(basket3quad) → basket3apple2
  22. PointIn(basket3quad) → basket3apple3
  23. PointIn(basket3quad) → basket3apple4
  24. PointIn(basket3quad) → basket3banana1
  25. PointIn(basket3quad) → basket3banana2
  26. PointIn(basket3quad) → basket3banana3
  27. PointIn(basket3quad) → basket3orange1
  28. Textfield(textBasket1apples) → ansBoxBasket1apples
  29. Textfield(textBasket1oranges) → ansBoxBasket1oranges
  30. Textfield(textBasket1bananas) → ansBoxBasket1bananas
  31. Textfield(textBasket2apples) → ansBoxBasket2apples
  32. Textfield(textBasket2oranges) → ansBoxBasket2oranges
  33. Textfield(textBasket2bananas) → ansBoxBasket2bananas
  34. Textfield(textBasket3apples) → ansBoxBasket3apples
  35. Textfield(textBasket3oranges) → ansBoxBasket3oranges
  36. Textfield(textBasket3bananas) → ansBoxBasket3bananas
  37. 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
  38. 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
  39. 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
  40. Polygon({(7, 2), (7, 6.5), (16.5, 6.5), (16.5, 2)}) → basket2quad
  41. PointIn(basket2quad) → basket2apple1
  42. PointIn(basket2quad) → basket2apple2
  43. PointIn(basket2quad) → basket2banana1
  44. PointIn(basket2quad) → basket2banana2
  45. PointIn(basket2quad) → basket2orange1
  46. PointIn(basket2quad) → basket2orange2
  47. PointIn(basket2quad) → basket2orange3
  48. PointIn(basket2quad) → basket2orange4
  49. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  50. LaTeX("\textbf{Basket 1 contains:}") → basket1Header
  51. LaTeX("\textbf{Basket 2 contains:}") → basket2Header
  52. LaTeX("\textbf{Basket 3 contains:}") → basket3Header
  53. TableText({numBasket1apples, numBasket1oranges, numBasket1bananas}, {"\text{\vphantom{\dfrac{1}{2}}apple(s)}", "\text{\vphantom{\dfrac{1}{2}}orange(s)}", "\text{\vphantom{\dfrac{1}{2}}banana(s)}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, basket1correctness], {}], "v") → basket1Table
  54. TableText({numBasket2apples, numBasket2oranges, numBasket2bananas}, {"\text{\vphantom{\dfrac{1}{2}}apple(s)}", "\text{\vphantom{\dfrac{1}{2}}orange(s)}", "\text{\vphantom{\dfrac{1}{2}}banana(s)}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, basket2correctness], {}], "v") → basket2Table
  55. TableText({numBasket3apples, numBasket3oranges, numBasket3bananas}, {"\text{\vphantom{\dfrac{1}{2}}apple(s)}", "\text{\vphantom{\dfrac{1}{2}}orange(s)}", "\text{\vphantom{\dfrac{1}{2}}banana(s)}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, basket3correctness], {}], "v") → basket3Table

AI 绘图提示语参考

画三个篮子，每个篮子装有苹果、香蕉和橙子。第一个篮子有5个苹果、3个橙子和4个香蕉，第二个篮子有4个苹果、2个橙子和3个香蕉，第三个篮子有6个苹果、4个橙子和5个香蕉。每个篮子都是一个四边形，篮子内每个水果的位置可以自由放置，但必须在篮子区域内。在每个篮子旁边输入框中输入水果数量，正确时显示勾号，错误时显示叉号。
以上提示语为根据原始绘图命令整理而来，仅供参考。