Four Corners

5th grade games are delayed for a week, so that gives me a chance to write up our last game that was a pretty good success.

The commission from Mr. Schiller was a game to introduce graphing in the first quadrant.

Yes! Graphing! So game like already, thanks to Battleship and Connect Four. A lot of ideas came to me - too many, to be honest. And too complicated. My first thought was to put points in a line. The choosing dice mechanic has been so good, I was thinking about that...

On your turn, roll four dice. Use those numbers to make up the two coordinates of a point, but you don’t have to use them all. For example, if you roll 2, 2, 3, 5, you could make (2+2,3+5)=(4,8), (2+3,2+5)=(5,7), (2, 2+3+5)=(2,10), or even just (2,2+5)=(2,7) (don’t use the 3) or (2,2).

On the graph put your point using your initial or symbol.

Each player makes 5 points.

Then draw 1 line through as many points as you can. The winner is the player with the most points on their line.

original image source

Great game for beginners, right? I thought there'd be lots of vertical and horizontal lines. Filed that away for a future algebra game, though. Maybe.

What about a chase? I went through lots of variations of trying to get to an escape point and the other team hunting you down... like a Battleship where you could move your ship. I couldn't figure out the hunt mechanic, though, and it didn't emphasize the placement of the points. Felt more vectory. That's a word. File that away for linear algebra.

If they're going to make vertical and horizontals anyway, why not go with that? Maybe the game could be about making rectangles. An early attempt:

On your turn, roll four dice. Use those numbers to make up the two coordinates of a point, but you don’t have to use them all. For example, if you roll 2, 2, 3, 5, you could make (2+2,3+5)=(4,8), (2+3,2+5)=(5,7), (2, 2+3+5)=(2,10), or even just (2,2+5)=(2,7) (don’t use the 3) or (2,2).

On the graph put your point using your initial or symbol.

The first team makes one point and then each turn after you make two points. A game is 12 points for each team.
Team 1 – one point; Team 2 – two points; Team 1 – two points; Team 2 – two points;
Team 1 – two points; Team 2 – two points; Team 1 – two points; Team 2 – two points;
Team 1 – two points; Team 2 – two points; Team 1 – two points; Team 2 – two points;
Team 1 – one point.

The goal is to make rectangles up to 12 squares in area. When your points make the corners of a rectangle, draw in the rectangle, add the area to your score.

Still the dice choice. You can see me struggling with the advantage of going first. It still felt too complicated. Variations on capturing opponents' points were even more complex. But as I was testing this, I started to notice. It was pretty hard to make a rectangle. I didn't have to worry about multiples... it was hard to make one! That was the key. I also stopped worrying about getting rid of the going first advantage. The randomness of the rolling really reduced the impact. So...


And of course you'll need some graph paper. (Here's the 12x12 labeled axes I used, 2 to a page.)

I launched the game by playing vs the whole class. Students made connections to other games, especially Minecraft. (Engagement +2 immediately. "This stuff is in Minecraft?")

We've settled into a routine for the whole class play. Pick someone who is ready to contribute to make the class move, then they pick someone of the other gender to make the next move. I intentionally picked some hard rectangles to complete by picking x or y coordinates to be low or high, and they won by actually making two rectangles at once. The whole class play provided opportunity for the instruction on placing points, and they got to be self-correcting pretty quickly. As well as developing some strategy. We debated whether you could use zero or not, and after resolving how you'd even plot those points, everyone agreed that would make a better game.

As usual, they played mostly in teams of two, though this game was direct enough that some felt comfortable playing one on one.

At the close, they had lots of things to suggest for strategy, some conflicting. The blocking aspect was brought up by one team and there were a lot of "Oooooh"s. Some conflict over whether you were better off towards the middle. Some agreement on putting them in lines if you can. Engagement was very high, and some people felt this was the best game all year.  There were variation ideas from the students, some of which they had already tried. Three people competing on one board, for example.

Overall, Mr. Schiller and I were both very happy with the game, for engagement and mathematically. This offers lots of advantages over Battleship. The making rectangles aspect helped a lot with getting the idea of the coordinates, and almost all students knew about common x or y-coordinates making a line, and several were finding new points from old instead of plotting from the axes. More strategy and thinking in terms of the coordinates you want and how to make the best use of your dice roll. Deeper strategies available for students ready to think about it. Lots of practice placing points with another team to monitor you. (I was impressed how few students were doing the x-y reversal by the end of the game.) It just has the good feel of simple rules and reasonable depth.

Of course, if you have ideas or get to try it, I'd love to hear back.