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

\begin{document}

\module{Solve a system by elimination}{01}{AP11}{1 period}

%\prereq{}

\object{\begin{itemize}
        \item Discover the elimination method for solving a system.
	\end{itemize}}

\mater{\begin{itemize}
	\item Task sheets.
	\item 10 cut-out coloured card sheets.
	\item Slideshow.
	\end{itemize}}

\modpart{Example}{5 mins}

There are three type of coloured cards : green, yellow and blue. 

Each blue card has a value of 1, but the values of the green and yellow cards are unknown.

The following system has to be solved to find out the values of the green and yellow cards.

$$\left\{
\begin{array}{l}
\textrm{Two green cards and two yellow cards make four.}\\
\textrm{Three green cards and one yellow card make four.}
\end{array}\right.$$

The steps of the method are shown below.

\begin{multicols}{2}

\begin{enumerate}
\item Set up the two equations. 
\begin{center}
\includegraphics[scale=0.75]{images/step0.eps}
\end{center}
\item Multiply one equation so that the number of yellow (or green) cards are equal.
\begin{center}
\includegraphics[scale=0.75]{images/step1.eps}
\end{center}\smallskip
\item Take from each equation the number of green, yellow and blue cards there are in one of the equations.
\begin{center}
\includegraphics[scale=0.75]{images/step2.eps}
\end{center}
\item Deduce the value of the green card.
\begin{center}
\includegraphics[scale=0.75]{images/step3.eps}
\end{center}
\item Go back to the first equation.
\begin{center}
\includegraphics[scale=0.75]{images/step4.eps}
\end{center}\pagebreak
\item Replace each green card by the appropriate number of blue cards.
\begin{center}
\includegraphics[scale=0.75]{images/step5.eps}
\end{center}
\item Subtract the same number of blue cards from both sides.
\begin{center}
\includegraphics[scale=0.75]{images/step6.eps}
\end{center}
\item Deduce the value of the yellow card.
\begin{center}
\includegraphics[scale=0.75]{images/step7.eps}
\end{center}
\item Conclude : the values of the green and yellow cards are both equal to 1.
\end{enumerate}

\end{multicols}




\modpart{Solve systems with tokens}{Remaining time}

Students work in pairs. Each pair has to solve 10 systems with this method (the teacher should check that no other method is used). Every good answer earns two points to the team.

\pagebreak

\moddocdis{Solve a system by elimination}{01}{AP11}{Task sheet}

There are three type of coloured cards : green, yellow and blue. 

Each blue card has a value of 1, but the values of the green and yellow cards are unknown.

Use the cards to find out the values of the green and yellow cards in the following situations.

\begin{enumerate}
\item $\left\{
\begin{array}{l}
\textrm{One green card and two yellow cards make eight.}\\
\textrm{Three green cards and three yellow cards make fifteen.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Four green cards and three yellow cards make fifteen.}\\
\textrm{Three green cards and two yellow cards make eleven.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Three green cards and two yellow cards make two.}\\
\textrm{Six green cards and four yellow cards make two.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Two green cards and three yellow cards make seven.}\\
\textrm{Four green cards and two yellow cards make six.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Three green cards and three yellow cards make seven.}\\
\textrm{Four green cards and six yellow cards make ten.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Two green cards and three yellow cards make one.}\\
\textrm{Four green cards and six yellow cards make two.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Three green cards and eight yellow cards make four.}\\
\textrm{Six green cards and four yellow cards make five.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Three green cards and two yellow cards make one.}\\
\textrm{Two green cards and three yellow cards make minus one.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Two green cards and one yellow card make zero.}\\
\textrm{Three green cards and two yellow cards make one.}
\end{array}\right.$\smallskip
\item $\left\{
\begin{array}{l}
\textrm{Three green cards and four yellow cards make minus one.}\\
\textrm{Four green cards and five yellow cards make minus two.}
\end{array}\right.$

\end{enumerate}


\pagebreak

\moddoc{Cut-out coloured card sheets}

{\Huge

\begin{center}
\begin{tabular}{|p{1cm}cp{1cm}|p{1cm}cp{1cm}|p{1cm}cp{1cm}|p{1cm}cp{1cm}|}
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
\end{tabular}
\end{center}

\pagebreak

\begin{center}
\begin{tabular}{|p{1cm}cp{1cm}|p{1cm}cp{1cm}|p{1cm}cp{1cm}|p{1cm}cp{1cm}|}
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
& ? &&& ? &&& ? &&& ? & \rule{0cm}{1.5cm}\\[0.2cm]
\hline
\end{tabular}
\end{center}

\pagebreak

\begin{center}
\begin{tabular}{|p{0.2cm}cp{0.2cm}|p{0.2cm}cp{0.2cm}|p{0.2cm}cp{0.2cm}|p{0.2cm}cp{0.2cm}|p{0.2cm}cp{0.2cm}|p{0.2cm}cp{0.2cm}|}
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& 1 &&& 1 &&& 1 &&& 1 &&& 1 &&& 1 & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& $-1$ &&& $-1$ &&& $-1$ &&& $-1$ &&& $-1$ &&& $-1$ & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
& $-1$ &&& $-1$ &&& $-1$ &&& $-1$ &&& $-1$ &&& $-1$ & \rule{0cm}{1.2cm}\\[0.2cm]
\hline
\end{tabular}
\end{center}

}


\end{document}
