another graph paper game

I love math games and I'm loving as my second child advances to the stage where he can join in more and more of the games.

One of the games we played recently is played with a die and graph paper. Before we started I did a little warm-up exercise getting him to draw rectangles. Could he draw a rectangle that had only one square in it? Two? Three? How many different rectangles could he draw with only four squares? We talked about the rectangles that could be made from two rows of squares. He could make a rectangle like that with six or eight squares, but not with seven. For seven the squares would have to be lined up in one long line.

After the warm-up exercise we started a game. I marked off a rectangle for our playing board. Then we took turns rolling the dice. If we rolled an odd number, then we had to draw a long-thin rectangle with that number of squares. If we rolled an even number the rectangle was made out of the appropriate number of pairs of two squares side-by-side. The goal was to be the last person able to draw the rectangle dictated by the dice.

 

We started with four colors of pencil crayon, switching colors whenever we wanted but trying to make sure each shape we drew was distinguishable not blending it with its neighbour. I wondered slightly if we would be able to continue with just the four colors, in accordance with the four color theorem, but my son wasn't strategizing with the colors, we didn't manage to fill the whole space with four colors. Another time I'll make it part of the challenge.