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

\module{Line equations}{01}{16}{55 mins}

\prereq{Basic algebra skills.}

\object{\begin{itemize}
        \item Understand how an equation defines a line but also regions of the plane.
	\item Practise some computations with line equations.
	\end{itemize}}

\mater{\begin{itemize}
	\item Slideshow.
	\item Equation and list of points for each team.
	\end{itemize}}


\modpart{Find the right points}{25 mins}

The group is divided into 4 teams. Each team is given a line equation and a list of 20 point coordinates (the same for every team).
One member of each team goes to the board. He or she will place points on a coordinate graph according to the instruction of the team.

\begin{itemize}
\item Turn by turn, each team picks a pair of coordinates in the list and says it out loud. These are the coordinates of a point in the coordinate graph.
\item Every team computes the result of its algebraic expression with the coordinates given. If the result is 
	\begin{itemize}
	\itemb equal to zero, the team places the point on the graph with a red cross ;
	\itemb negative, the team places the point on the graph with a blue cross ;
	\itemb positive, the team places on the graph with a green cross.
	\end{itemize}
\end{itemize}


The first team to have three points of each colour wins and the game stops. 

Scores are then computed in the following way :
\begin{itemize}
\item Three points for every red point.
\item Two points for every blue or green point.
\end{itemize}

\modpart{Speed contest}{25 mins}

Each team is given a list of equations. For each equation, they have to find :
\begin{itemize}
\item the coordinates of three points on the set defined by this equation ;
\item the shape of the set.
\end{itemize}

They can study the equations in the order they want. 

The first team to give the correct answers about one equation wins 5 points. 

\modpart{Grading}{End of session}

At the end of the session, the team with the most points gets an A$^\star$, the second team an A, the third team a B. 




\pagebreak

\moddocdis{Line equations}{01}{16}{Team 1}

{\Large

\begin{center}
\fbox{Your expression : $-2x+6y-6$.}
\end{center}

\begin{center}

Twenty pairs of coordinates. 
\begin{tabular}{ccccc}
$(-2,3)$ & $(1,1)$ & $(4,-1)$ & $(3,2)$ & $(0,1)$ \\
$(-3,0)$ & $(-4,-1)$ & $(-1,1)$ & $(2,3)$ & $(0,2)$ \\
$(1,4)$ & $(-2,-2)$ & $(-4,2)$ & $(2,-2)$ & $(-2,5)$ \\
$(5,4)$ & $(4,1)$ & $(1,-1)$ & $(-3,1)$ & $(0,-1)$ \\
\end{tabular}
\end{center}

}

\vspace{6cm}

\moddocdis{Line equations}{01}{16}{Team 2}

{\Large

\begin{center}
\fbox{Your expression : $4x-6y+10$.}
\end{center}

\begin{center}

Twenty pairs of coordinates. 
\begin{tabular}{ccccc}
$(-2,3)$ & $(1,1)$ & $(4,-1)$ & $(3,2)$ & $(0,1)$ \\
$(-3,0)$ & $(-4,-1)$ & $(-1,1)$ & $(2,3)$ & $(0,2)$ \\
$(1,4)$ & $(-2,-2)$ & $(-4,2)$ & $(2,-2)$ & $(-2,5)$ \\
$(5,4)$ & $(4,1)$ & $(1,-1)$ & $(-3,1)$ & $(0,-1)$ \\
\end{tabular}
\end{center}

}

\pagebreak

\moddocdis{Line equations}{01}{16}{Team 3}

{\Large

\begin{center}
\fbox{Your expression : $4x-2y+4$.}
\end{center}

\begin{center}

Twenty pairs of coordinates. 
\begin{tabular}{ccccc}
$(-2,3)$ & $(1,1)$ & $(4,-1)$ & $(3,2)$ & $(0,1)$ \\
$(-3,0)$ & $(-4,-1)$ & $(-1,1)$ & $(2,3)$ & $(0,2)$ \\
$(1,4)$ & $(-2,-2)$ & $(-4,2)$ & $(2,-2)$ & $(-2,5)$ \\
$(5,4)$ & $(4,1)$ & $(1,-1)$ & $(-3,1)$ & $(0,-1)$ \\
\end{tabular}
\end{center}

}

\vspace{6cm}

\moddocdis{Line equations}{01}{16}{Team 4}

{\Large

\begin{center}
\fbox{Your expression : $2x+3y-5$.}
\end{center}

\begin{center}

Twenty pairs of coordinates. 
\begin{tabular}{ccccc}
$(-2,3)$ & $(1,1)$ & $(4,-1)$ & $(3,2)$ & $(0,1)$ \\
$(-3,0)$ & $(-4,-1)$ & $(-1,1)$ & $(2,3)$ & $(0,2)$ \\
$(1,4)$ & $(-2,-2)$ & $(-4,2)$ & $(2,-2)$ & $(-2,5)$ \\
$(5,4)$ & $(4,1)$ & $(1,-1)$ & $(-3,1)$ & $(0,-1)$ \\
\end{tabular}
\end{center}

}

\pagebreak

\moddocdis{Line equations}{01}{16}{15 equations}

{\large

For each equation find out :
\begin{itemize}
\item the coordinates of three points on the set defined by this equation ;
\item the shape of the set.
\end{itemize}
You can study the equations in the order you want. 

Whenever you think you have a complete answer, call the teacher to check and win 5 points if it's right.

\begin{center}
\begin{tabular}{ccc}
$x^2+y^2-1=0$ & $3x-y+2=0$ & $2x^2+y=0$ \\
$xy=6$  & $-x+4y=0$ & $y-\sqrt{x}=2$ \\
$x+y=7$ & $\sqrt{x+2}=6$ & $-3x-y-7=0$ \\
$x^2-y^2=5$ & $-\frac{x}{2}-2y=0$ & $-\frac{4}{x}-2y=0$ \\
$-2x^2-y-7=0$ & $\frac{1}{x}+\frac{1}{y}=0$ & $-x-y+1=0$ \\
\end{tabular}
\end{center}

}

\vspace{4cm}

\moddocdis{Line equations}{01}{16}{15 equations}

{\large

For each equation find out :
\begin{itemize}
\item the coordinates of three points on the set defined by this equation ;
\item the shape of the set.
\end{itemize}
You can study the equations in the order you want. 

Whenever you think you have a complete answer, call the teacher to check and win 5 points if it's right.

\begin{center}
\begin{tabular}{ccc}
$x^2+y^2-1=0$ & $3x-y+2=0$ & $2x^2+y=0$ \\
$xy=6$  & $-x+4y=0$ & $y-\sqrt{x}=2$ \\
$x+y=7$ & $\sqrt{x+2}=6$ & $-3x-y-7=0$ \\
$x^2+y^2=5$ & $-\frac{x}{2}-2y=0$ & $-\frac{4}{x}-2y=0$ \\
$-2x^2-y-7=0$ & $\frac{1}{x}+\frac{1}{y}=0$ & $-x-y+1=0$ \\
\end{tabular}
\end{center}

}

\end{document}
