Here is another game of mine played on a grid drawn on paper.
It seems like it might be a fun way to teach slopes or how to reduce
Start by lightly drawing an n-by-n grid on paper, or better yet, use
(I suggest an n of about 8 for starters.)
Game is for any number of players >= 2.
First, player 1 draws a dot at any intersection of grid-lines (at a
He then connects one of the grid's corners to this dot with a straight
Players alternate moving. On each move, a player first draws a dot at a
lattice-point of the grid and then connects the last dot drawn by the
previous player to the newly drawn dot by a
*straight* line-segment (where the segment terminates at these 2 dots).
The new dot must be drawn so that no line-segments coincide. (The
segments may cross, but they cannot be on top of each other with the
Also, the dots cannot be drawn on previously drawn segments or dots.
A player drawing a line-segment gets a point for every previously drawn
dot his/her line-segment intersects, considering the *exact* slope of
the segment and *exact* positions of the intersected dots
*in theory*, as if the dots and line-segments and grid had been drawn
So, for instance, if we have a dot at (2,2), and the last drawn dot is
at (0,1), and the player makes a new dot at (6,4), no matter how poorly
the lines and dots and grid are drawn, the player still gets a point
for the "intersected" point (2,2) (which was theoretically intersected
by the line-segment of slope -1/2).
The game continues until either a predetermined score is reached by one
player, or until every lattice-point is intersected by a lines-segment
or has a dot drawn on it.