邮票购买情境的分步代数表达式交互演示

邮票购买情境的分步代数表达式交互演示
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2015-09-25 23:54
该范例以 Easton 购买 49 美分邮票和 34 美分明信片邮票的情境为线索,演示如何用变量 f 表示已使用邮票数量,并分步推导剩余数量或总花费的代数关系。核心概念包括代数表达式、同类项、有理数运算、线性组合与分步解题逻辑。构造上利用 LaTeX 命令渲染公式,通过 SelectedElement 与 SelectedIndex 读取选择状态,并借助 step、progress、hint、data 以及 prev1、next1、prev2、next2、Refresh 等按钮和文本对象实现提示切换、进度更新与重置。适合初中代数入门、应用题建模和 GeoGebra 交互课件制作。

GeoGebra 命令及参数

  1. LaTeX("\text{Write an expression with parentheses that represents the value of all the stamps Easton has left.}") → text3
  2. LaTeX("\text{We need to find the total value of all of Easton’s remaining stamps, so add these two expressions:}") → text8
  3. LaTeX("\text{Easton has left.}") → text11
  4. LaTeX("\text{Distribute as needed.}") → text13
  5. LaTeX("\text{Original expression}") → text17
  6. LaTeX("\text{Rewritten expression}") → text23
  7. LaTeX("\text{Combine like terms.}") → text29
  8. LaTeX("\text{Rearrange to group like terms.}") → text33
  9. LaTeX("\text{Expression from the previous step}") → text34
  10. SelectedElement(NOS1) → st1
  11. SelectedElement(NOS2) → st2
  12. SelectedElement(ROS1) → sr1
  13. SelectedElement(ROS2) → sr2
  14. LaTeX((((("\text{Multiply \textcolor{#000099}{" * st1) * "} by \textcolor{#000099}{") * sr1) * "}, and}")) → text19
  15. LaTeX((("\text{multiply \textcolor{#000099}{\textendash\;f} by \textcolor{#000099}{" * sr1) * "}.}")) → text20
  16. LaTeX((((((((("\text{\textcolor{#000099}{= " * stsr1) * "\;\textendash\; ") * sr1) * "f + \mathbf{") * stsr2) * "\; \textendash\; ") * sr2) * "p}} }")) → text24
  17. LaTeX((((("\text{Multiply \textcolor{#000099}{" * st2) * "} by \textcolor{#000099}{") * sr2) * "}, and}")) → text25
  18. LaTeX((("\text{multiply \textcolor{#000099}{\textendash\;p} by \textcolor{#000099}{" * sr2) * "}.}")) → text26
  19. LaTeX((((((((((((("\text{In the expression \textcolor{#000099}{" * stsr1) * " \;\textendash\; ") * sr1) * "f + ") * stsr2) * "\; \textendash\; ") * sr2) * "p}, the terms \textcolor{#000099}{") * stsr1) * "} and \textcolor{#000099}{") * stsr2) * "} are like terms.}")) → text30
  20. LaTeX((((((((("\text{\textcolor{#000099}{" * stsr1) * "\;\textendash\; ") * sr1) * "f + ") * stsr2) * "\; \textendash\; ") * sr2) * "p} }")) → text31
  21. LaTeX((((((((("\text{\textcolor{#000099}{= " * stsr1) * "\;+ ") * stsr2) * "\;\textendash\; ") * sr1) * "f \; \textendash\; ") * sr2) * "p} }")) → text32
  22. LaTeX((((((("\text{\textcolor{#000099}{=" * stsr12) * "\; \textendash\;") * sr1) * "f \; \textendash\; ") * sr2) * "p }}")) → text35
  23. LaTeX((((("\text{Add \textcolor{#000099}{" * stsr1) * "} and \textcolor{#000099}{") * stsr2) * "}.}")) → text36
  24. SelectedIndex(NOS1) → Nos_1
  25. SelectedIndex(NOS2) → Nos_2
  26. SelectedIndex(ROS1) → Ros_1
  27. SelectedIndex(ROS2) → Ros_2
  28. LaTeX((((((("\text{A simplified expression for the total value in cents of the stamps Easton has left is \textcolor{#000099}{" * stsr12) * "\; \textendash\;") * sr1) * "f \; \textendash\; ") * sr2) * "p }.}")) → text37
  29. LaTeX((((("\text{\textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)}}")) → text5
  30. LaTeX((((("\text{\textcolor{#000099}{" * sr2) * "(") * st2) * "\; \textendash\; p)}}")) → text7
  31. LaTeX((((((((("\text{The expression \textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\;\textendash\; p)} represents the total value in cents of the stamps}")) → text10
  32. LaTeX((((((((("\text{The expression \textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\;\textendash\; p)} contains two sets of parentheses where distribution can be applied.}")) → text14
  33. LaTeX((((((((("\text{\textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\; \textendash\; p)}}")) → text16
  34. LaTeX("\text{-cent}") → text2_2
  35. LaTeX("\text{-cent}") → text2_3
  36. LaTeX((((((((("\text{\textcolor{#000099}{\mathbf{= " * stsr1) * "\; \textendash\; ") * sr1) * "f} + ") * sr2) * "(") * st2) * " \;\textendash\;p)} }")) → text18
  37. LaTeX((((((((("\text{\textcolor{#000099}{" * stsr1) * " \;\textendash\; ") * sr1) * "f + ") * sr2) * "(") * st2) * "\; \textendash\; p)} }")) → text22
  38. LaTeX((((("\text{Next, distribute \textcolor{#000099}{" * sr2) * "} to \textcolor{#000099}{") * st2) * "} and \textendash\textcolor{#000099}{p}.}")) → text21
  39. LaTeX((((((((("\text{\textcolor{#000099}{" * sr1) * "(") * st1) * "\;\textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\; \textendash\; p)}}")) → text9
  40. LaTeX((((((((((((((((("\text{Once distributed, the expression \textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\; \textendash\; p)\;}is \textcolor{#000099}{") * stsr1) * "\;\textendash\; ") * sr1) * "f + ") * stsr2) * "\; \textendash\; ") * sr2) * "p.}}")) → text27
  41. LaTeX((((("\text{First, distribute \textcolor{#000099}{" * sr1) * "} to \textcolor{#000099}{") * st1) * "} and \;\textcolor{#000099}{\textendash\;f}.}")) → text15
  42. LaTeX((((("\text{\textcolor{#000099}{" * sr1) * "}-cent stamps: Easton bought \textcolor{#000099}{") * st1) * "} and used \textcolor{#000099}{f} of them.")) → text1
  43. LaTeX((((("\text{ \textcolor{#000099}{" * sr2) * "}-cent stamps: Easton bought \textcolor{#000099}{") * st2) * "} and used \textcolor{#000099}{p} of them.}")) → text40
  44. LaTeX("\text{quantities that are not equivalent}") → text38
  45. LaTeX("\text{quantities are equal}") → text28
  46. LaTeX("\text{individual}") → text2_4
  47. LaTeX("\text{stamps}") → text39
  48. LaTeX("\text{individual}") → text2_5
  49. LaTeX("\text{stamps}") → text39_1
  50. LaTeX((((("\text{Easton had \textcolor{#000099}{" * st1) * "} individual \textcolor{#000099}{") * sr1) * "}-cent stamps and used \textcolor{#000099}{f} of them. This is represented as:}")) → text4
  51. LaTeX((((("\text{Easton had \textcolor{#000099}{" * st2) * "} individual \textcolor{#000099}{") * sr2) * "}-cent stamps and used \textcolor{#000099}{p} of them. This is represented as:}")) → text6
  52. LaTeX("\text{\mathbf{equation} a mathematical sentence that uses an equal sign (=) to show that two}") → text42
  53. LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between }") → text49

AI 绘图提示语参考

绘制一个代数邮票问题的分步讲解图。画面中央展示一个邮票购买场景:某人买了若干枚49分邮票和若干枚34分邮票,分别用变量f和p表示已使用的数量。图中用彩色文本和公式逐步展示原始表达式、分配律展开、合并同类项、简化结果等步骤,每一步配有说明文字,并用箭头或高亮标记当前操作。整体布局为从上到下的流程,包含多个文本框和公式,强调代数表达式的变形过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。