三位朋友骑车速度比较的随机化应用题
几何画板及绘图内容加载中,请稍等……
该范例通过一个关于三位朋友骑车距离与时间的实际应用题,演示了如何利用GeoGebra的随机化功能生成不同数据并自动计算速度。核心数学概念是比例与速度(距离÷时间),涉及单位换算和比较大小。作图要点包括使用LaTeX文本显示公式、TableText制作数据表格、滑块(stepper)控制步骤、按钮(button1)触发随机化,以及多个文本对象(如SummerDist、NatashaTime等)存储变量并动态更新。适合初中阶段学习比例、速度或应用题建模,也可用于教师制作随机练习题,帮助学生理解变量关系与计算过程。
GeoGebra 命令及参数
LaTeX(steps) → counterLaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → RandomizationTextCorner(1) → ACorner(3) → BLaTeX("\text{Determine the unit rate for each rider.}") → text1LaTeX((((((((("\text{Summer rides " * SummerDist) * " miles in ") * SummerTime) * " minutes, or }\textcolor{#000099}{\frac{") * SummerTime) * "\text{ minutes}}{") * SummerDist) * "\text{ miles}}}.")) → text4LaTeX((((((((((((("\text{Summer rides " * SummerDist) * " miles in ") * SummerTime) * " minutes.}\cr\text{Natasha rides ") * NatashaDist) * " miles in ") * NatashaTime) * " minutes.}\cr\text{Robin rides ") * RobinDist) * " miles in ") * RobinTime) * " minutes.}")) → ProblemLaTeX((((((((("\text{Natasha rides " * NatashaDist) * " miles in ") * NatashaTime) * " minutes, or }\textcolor{#000099}{\frac{") * NatashaTime) * "\text{ minutes}}{") * NatashaDist) * "\text{ miles}}}.")) → text6LaTeX((((((((("\text{Robin rides " * RobinDist) * " miles in ") * RobinTime) * " minutes, or }\textcolor{#000099}{\frac{") * RobinTime) * "\text{ minutes}}{") * RobinDist) * "\text{ miles}}}.")) → text8LaTeX((((((("\text{Summer's rate is " * SummerRtime) * " minutes per mile.} \cr\text{Natasha's rate is ") * NatashaRtime) * " minutes per mile.} \cr\text{Robin's rate is ") * RobinRtime) * " minutes per mile.}")) → text10aLaTeX((("\text{" * conclusions) * "}")) → text11LaTeX("\text{Use the unit rates to state two conclusions that can be made about the rates each person rides.}") → text10LaTeX("\text{First set up a ratio for each rider. }\cr\text{Then determine the unit rate by reducing the fraction.}") → text2TableText({{LaTeX[(((("\textcolor{#000099}{\frac{" * SummerTime) * "\text{ minutes}}{") * SummerDist) * "\text{ miles}}}")], LaTeX["\text{Summer's rate}"]}, {LaTeX[(((("\textcolor{#000099}{=\frac{" * SummerRtime) * "\text{ minutes}}{") * SummerRdist) * "\text{ mile}}}")], LaTeX["\text{Reduce the fraction.}"]}}, "l") → text5TableText({{LaTeX[(((("\textcolor{#000099}{\frac{" * NatashaTime) * "\text{ minutes}}{") * NatashaDist) * "\text{ miles}}}")], LaTeX["\text{Natasha's rate}"]}, {LaTeX[(((("\textcolor{#000099}{=\frac{" * NatashaRtime) * "\text{ minutes}}{") * NatashaRdist) * "\text{ mile}}}")], LaTeX["\text{Reduce the fraction.}"]}}, "l") → text7TableText({{LaTeX[(((("\textcolor{#000099}{\frac{" * RobinTime) * "\text{ minutes}}{") * RobinDist) * "\text{ miles}}}")], LaTeX["\text{Robin's rate}"]}, {LaTeX[(((("\textcolor{#000099}{=\frac{" * RobinRtime) * "\text{ minutes}}{") * RobinRdist) * "\text{ mile}}}")], LaTeX["\text{Reduce the fraction.}"]}}, "l") → text9LaTeX("\text{Move the slider to solve the problem.}") → text0LaTeX("\text{The ratio compares the number of minutes per mile or, written as a fraction, }\textcolor{#000099}{\frac{\text{minutes}}{\text{miles}}}.") → text3
AI 绘图提示语参考
绘制一个数学练习界面,用于展示三个朋友骑自行车速度比较的随机化问题。界面顶部包含说明文本,引导用户计算每位骑车人的单位速率。中间部分分为三个区域,分别对应Summer、Natasha和Robin,每个区域用文本框动态显示他们骑行的距离和时间,例如Summer骑行25英里用时75分钟。下方是一个表格,每行对应一位骑车人,展示原始比率(分钟每英里)的分数形式及简化后的单位速率。底部设有结论区域,列出基于单位速率的两个比较结论。界面还包括一个滑块用于控制解题步骤,以及一个按钮用于随机生成新数据。整体布局应清晰,文本和表格排列整齐,便于教学互动。
以上提示语为根据原始绘图命令整理而来,仅供参考。