Tuesday, August 12, 2014

Dots and Boxes (and adding and multiplying)

who: J1 and J2
when: while waiting for lunch during a Chinese religious holiday
what material did we use: paper and pencil

Games, Games, Games!

So, I've been (binge) reading the posts over at Talking Math with Your Kids. I suggest you go over there an do the same (binge reading).  Try to absorb as much as you can, then go back from time to time in order to reinforce the new habits.

Here, I want to offer you a cheat: games. One key objective of TMWYK is to achieve the moment of reflective wonder ("I wonder why/what/if/etc") and games have the wonder built in: ("I wonder what I need to do to win?")

To provoke a rich conversation, the games can have pretty simple rules.  We've written about others in past posts; recently we've played several rounds recently of dots-and-boxes.

On a piece of paper, you start with an array of dots. Each player takes turns drawing a horizontal or vertical line connecting adjacent dots. If one player completes a box by drawing the fourth boundary line, they take possession of that box and get to take another turn. Here's the wikipedia page, from which I'm borrowing this helpful illustration of a simple 3(dot)x 3(dot) game:

Sample topics we've discussed:

  • How many dots are there?
  • How many boxes will there be? 
  • Is there a relationship between the number of dots and boxes?
  • Can this game (for a particular grid) end in a tie?
  • Simple strategy: filling or avoiding long chains.
  • More advanced strategy: double cross
  • Symmetrical play: what happens if the 2nd player copies the moves of the first player (reflected through a line or point of symmetry)? This is interesting for other games as well.
Other than the mathematical content, these games have been a welcome distraction during the dead time waiting around family obligations.

Oh, and for the other Thai readers here, Happy Mother's Day!

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