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

\module{Opposite and collinear vectors}{01}{15}{1 period}

\prereq{Notions of vector. Basic notions about grids.}

\object{\begin{itemize}
        \item Understand the concepts of opposite and collinear vectors.
	\end{itemize}}

\mater{\begin{itemize}
	\item Five groups of 4 cards with vectors on a grid.
	\item Cards with non-collinear vectors for the bingo.
	\item Cards with vector coordinates.
	\end{itemize}}

\modpart{Matching games}{25 mins}

Each student is given a card with a vector on a grid.

{\bf Part 1 :} Each student has to find who in the class has a vector opposite to his own vector, then find a precise definition of ``opposite vectors''.

Cards are shuffled then handed out back to the students.

{\bf Part 2 :} Each student has to find those in the class with a vector collinear to his own vector, then find a precise definition of ``collinear vectors''.

\modpart{Bingo}{30 mins}

Each student is handed out a card with a vector, with no two vectors collinear in the class. The teacher randomly picks a card a vector. The student who has a vector collinear to it gets one point.

\pagebreak

\moddoc{Five groups of 4 cards with vectors on a grid}

\begin{center}
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\end{center}

\pagebreak

\moddoc{Cards with non-collinear vectors for the bingo}

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\end{center}

\pagebreak

\moddoc{Coordinates for the bingo}

{\large

\begin{center}
\begin{tabular}{|p{0.1cm}cp{0.1cm}|p{0.1cm}cp{0.1cm}|p{0.1cm}cp{0.1cm}|p{0.1cm}cp{0.1cm}|p{0.1cm}cp{0.1cm}|}
\hline
&$(0,4)$&&&$(1,4)$&&&$(1,3)$&&&$(1,2)$&&&$(2,3)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(2,2)$&&&$(3,2)$&&&$(2,1)$&&&$(3,1)$&&&$(3,0)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(4,-1)$&&&$(3,-1)$&&&$(2,-1)$&&&$(3,-2)$&&&$(2,-2)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(2,-3)$&&&$(1,-2)$&&&$(1,-3)$&&&$(1,-4)$&&&$(4,1)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(0,8)$&&&$(2,8)$&&&$(2,6)$&&&$(2,4)$&&&$(4,6)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(4,4)$&&&$(6,4)$&&&$(4,2)$&&&$(6,2)$&&&$(6,0)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(8,-2)$&&&$(6,-2)$&&&$(4,-2)$&&&$(6,-4)$&&&$(4,-4)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(4,-6)$&&&$(2,-4)$&&&$(2,-6)$&&&$(2,-8)$&&&$(8,2)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(0,-4)$&&&$(-1,-4)$&&&$(-1,-3)$&&&$(-1,-2)$&&&$(-2,-3)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(-2,-2)$&&&$(-3,-2)$&&&$(-2,-1)$&&&$(-3,-1)$&&&$(-3,0)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(-4,1)$&&&$(-3,1)$&&&$(-2,1)$&&&$(-3,2)$&&&$(-2,2)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(-2,3)$&&&$(-1,2)$&&&$(-1,3)$&&&$(-1,4)$&&&$(-4,-1)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(0,2)$&&&$(0.5,2)$&&&$(0.5,1.5)$&&&$(0.5,1)$&&&$(1,1.5)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(1,1)$&&&$(1.5,1)$&&&$(1,0.5)$&&&$(1.5,0.5)$&&&$(1.5,0)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(2,-0.5)$&&&$(1.5,-0.5)$&&&$(1,-0.5)$&&&$(1.5,-1)$&&&$(1,-1)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(1,-1.5)$&&&$(0.5,-1)$&&&$(0.5,-1.5)$&&&$(0.5,-2)$&&&$(2,0.5)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(0,-8)$&&&$(-2,-8)$&&&$(-2,-6)$&&&$(-2,-4)$&&&$(-4,-6)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(-4,-4)$&&&$(-6,-4)$&&&$(-4,-2)$&&&$(-6,-2)$&&&$(-6,0)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(-8,2)$&&&$(-6,2)$&&&$(-4,2)$&&&$(-6,4)$&&&$(-4,4)$&\rule{0pt}{20pt}\\[5pt]\hline
&$(-4,6)$&&&$(-2,4)$&&&$(-2,6)$&&&$(-2,8)$&&&$(-8,-2)$&\rule{0pt}{20pt}\\[5pt]\hline
\end{tabular}
\end{center}}




\end{document}
