Rectangulation

Players: 2
Ages: 6 and up
Cost: Free! Print the worksheet here (Page 2)
Math Ideas: Spatial reasoning, square and rectangles
Questions to Ask
   Do you want to go first or second?
   Can you make your own game board?

Writing about games every week, I sometimes worry that I'll run out. 

After all, I've long since written about basically every game, free or commercial, that I knew about before beginning this newsletter back in 2017.

So I scour the internet, looking for ideas. And every once in a while, I stumble upon a cornucopia! 

A couple of weeks ago, I found this British site called Cleave Books. I don't know anything about it, other than the fact that it has a TON of great games, puzzles, and classroom activities buried inside its site (which looks like a time machine to 2002).

The first game I played is called Rectangulation.

How to Play

Rectangulation can be played on any sort of grid paper, but you can print off a bunch of pre-made boards at this site (print page 2)

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Each board is a grid with a frowny face inside one of its squares. Players taketurns shading in, or outlining, rectangles on the board. Yes, squares count as rectangles (more on that later).

The loser is the person who shades in the square containing the frowny face. So in the game at right, green went first, then orange, and then green again. Orange has no legal move other than to color in the frowny face, so orange loses and green is the winner.

The fun of this game, aside from its basic form, is that the game strategy can change based on the size and shape of the board, as well as the location of the frowny face. You can even start with a blank grid, have Player 1 draw the game board, then have Player 2 choose the location of the frowny face, and then Player 1 makes the first rectangular move!

Where's the Math?

I chose this game based on a conversation I had with my son recently: Are squares rectangles?

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My son's first grade teacher had brought up this question in class (way to go her, right?). My son had initially misinterpreted her, however. He insisted to me that squares could not be rectangles.

After playing with that idea, and with this game, we settled on an informal definition of a rectangle: A shape with four sides and four "straight corners." (This was his term for right angles, and I'm fine with an informal definition at that age.)

Based on that definition, a square is a rectangle! It has four sides and four straight corners. It also happens to have four sides that are all the same length. That makes it a rectangle, and also a valid move in Rectangulation.

Apart from that fun conversation, there is a ton of deeper math in the game. It reminds me of a geometric version of The 100 Game, where the last person tomove is the loser. In The 100 Game, there is a strategy that will lead to victory no matter what. Is there a similar strategy in Rectangulation? How would it change when you alter the location of the frowny face, or change the dimensions of the board? What if you use a board that isn't even a rectangle to begin with?

To be clear, I don't know the answers to these questions. But I believe the answers exist, and that is why I keep playing around with the game. I'm doing my own investigation along with my kids while we play.

Questions to Ask

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One question you can ask your child is "Do you want to go first or second?"

Once you've played the game a few times on the same board, they might have a sense as to the best choice, and the best first move for that board.

To make sure the game doesn't get boring, switch up the dimensions and play again! Ask your child "What will be different about playing on this board?" and see what they notice.

If your child really wants to get into the strategy, try to simplify the game down. Play on a 1x2 board, then a 2x2 board, then a 3x2 board. Ask your child "Is there always a way for Player 1 to make sure they win?"

It's usually much easier to see the strategy of the game on these smaller boards. Then your child can use those strategies on the bigger, more complex boards!