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

\begin{document}

\module{Cross sections of a tetrahedron}{2}{15}{1 period}

%\prereq{}

\object{\begin{itemize}
        \item Discover the concept of cross section of a solid. 
	\item Review the conceptq of collinearity and coplanarity in 3D.
	\item Study the possible cross sections of a tetrahedron.
	\end{itemize}}

\mater{\begin{itemize}
	\item Six copies of six different problems.
	\item One answer sheet for each student.
	\item Beamer.
	\end{itemize}}


\modpart{Introduction}{5 mins}

The teacher introduces the concept of cross section, with a beamer. The examples given are the cross sections of a
sphere, that are always circles. Then, the plan of the chapter is given : tetrahedron, cube and cone.

\modpart{Individual work}{10 mins}

Each student is given a problem about how to cut a tetrahedron to get a certain cross section shape. 

\modpart{Group work}{Remaining time}

Students mingle to form six groups of six people with different problems. They explain and check each other's answer to
fill out an answer sheet with the answers to the six problems. At the end of the hour, each group has to hand out to
the teacher the six answer sheets. These six answer sheets are then marked and graded. If the 6 answer sheets of a
group are not exactly the same, the lowest mark is credited to every member of the team.



\pagebreak

\moddocdis{Cross sections of a tetrahedron}{2}{15}{Answer sheet}

\newcounter{prob}
\newcommand{\prob}{\stepcounter{prob}\arabic{prob}}


\begin{multicols}{2}
\begin{center}
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\rowcolor{black}\centering\bf \textsf{\white Problem \prob}\rule{0pt}{12pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\centering\textsf{The cross section is \dotfill}\rule{0pt}{15pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\hline
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\hline
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\begin{center}
\begin{tabularx}{7cm}{|X|}
\rowcolor{black}\centering\bf \textsf{\white Problem \prob}\rule{0pt}{12pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\centering\textsf{The cross section is \dotfill}\rule{0pt}{15pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\hline
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\begin{multicols}{2}
\begin{center}
\begin{tabularx}{7cm}{|X|}
\rowcolor{black}\centering\bf \textsf{\white Problem \prob}\rule{0pt}{12pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\centering\textsf{The cross section is \dotfill}\rule{0pt}{15pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\hline
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\uput[r](5,3){$D$}
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\hline
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\begin{center}
\begin{tabularx}{7cm}{|X|}
\rowcolor{black}\centering\bf \textsf{\white Problem \prob}\rule{0pt}{12pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\centering\textsf{The cross section is \dotfill}\rule{0pt}{15pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\hline
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\begin{multicols}{2}
\begin{center}
\begin{tabularx}{7cm}{|X|}
\rowcolor{black}\centering\bf \textsf{\white Problem \prob}\rule{0pt}{12pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\centering\textsf{The cross section is \dotfill}\rule{0pt}{15pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\hline
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\begin{center}
\begin{tabularx}{7cm}{|X|}
\rowcolor{black}\centering\bf \textsf{\white Problem \prob}\rule{0pt}{12pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\centering\textsf{The cross section is \dotfill}\rule{0pt}{15pt}
\end{tabularx}
\begin{tabularx}{7cm}{|X|}
\hline
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\pagebreak

\moddoc{Six cross section problems}

\setcounter{prob}{0}

\bigskip
\hrulefill
\bigskip

\begin{center}
\parbox{15cm}{\centering\Large {\bf Problem \prob :} Find a way to cut a regular tetrahedron so that the cross section
is \emph{an equilateral triangle}.\par}
\end{center}

\bigskip
\hrulefill
\bigskip

\begin{center}
\parbox{15cm}{\centering\Large {\bf Problem \prob :} Find a way to cut a regular tetrahedron so that the cross section
is \emph{an isosceles triangle}, but not an equilateral one.\par}
\end{center}

\bigskip
\hrulefill
\bigskip

\begin{center}
\parbox{15cm}{\centering\Large {\bf Problem \prob :} Find a way to cut a regular tetrahedron so that the cross section
is \emph{a scalene triangle}.\par}
\end{center}
\bigskip
\hrulefill
\bigskip

\begin{center}
\parbox{15cm}{\centering\Large {\bf Problem \prob :} Find a way to cut a regular tetrahedron so that the cross section
is \emph{a square}.\par}
\end{center}


\bigskip
\hrulefill
\bigskip

\begin{center}
\parbox{15cm}{\centering\Large {\bf Problem \prob :} Find a way to cut a regular tetrahedron so that the cross section
is \emph{a rectangle} and not a square.\par}
\end{center}


\bigskip
\hrulefill
\bigskip

\begin{center}
\parbox{15cm}{\centering\Large {\bf Problem \prob :} Find a way to cut a regular tetrahedron so that the cross section
is \emph{a trapezium} and not a rectangle.\par}
\end{center}


\bigskip
\hrulefill
\bigskip








\end{document}
