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

fractions.

Start by lightly drawing an n-by-n grid on paper, or better yet, use

graph paper.

(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

lattice-point).

He then connects one of the grid's corners to this dot with a straight

line-segment.

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

same slope.)

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

perfectly.

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.

thanks,

Leroy Quet

## Friday, September 19, 2008

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