\documentclass[12pt]{article}
\usepackage[Aymar]{ammaths}

\begin{document}\en

\module{Repetitive throws of a fair die}{01}{10}{1 period}

\prereq{Statistics main measures}

\object{\begin{itemize}
        \item Study an example of statistical data.
	\item Introduce the difference between probabilities and statistics.
	\end{itemize}}

\mater{\begin{itemize}
	\item Dice.
	\item Graph paper.
	\item Slideshow.
	\end{itemize}}

\modpart{Throwing the dice}{30 mins}

The class is divided in groups of four or five. Each group is given a set of dice. 

\begin{description}
\item[Step 1 :] Each student throws a die ten times, builds a frequency table and draws a relative frequency polygon, with scale 2 cm for 1 on the $x$-axis and 10 cm for 1 on the $y$-axis.
\item[Step 2 :] Each student throws a die a hundred times, builds a second frequency table and draws a relative frequency polygon on the same graph as step 1, with a different color.
\item[Step 3 :] Inside each group, results are gathered to build a third frequency table and draw a third relative frequency polygon, still on the same but using a third color.
\item[Step 4 :] In the whole class, results are gathered to build a fourth frequency table and draw a fourth relative frequency polygon, still on the same but using a third color.
\end{description}

\modpart{More throws}{15 mins}

Results are given for samples of 10 000 throws and 50 000 throws. Each student must then draw two new frequency polygons on the same graph.

\modpart{Discussion}{10 mins}

One possible set of graphs is shown and discussed. What's going on ? What are the theoretical values.



\end{document}
