Math Circles at Home: Take 1

By March 18, 2020Uncategorized

I know parents and caregivers are struggling to find activities for their children to engage in as we wait to see when school will relaunch. I thought MC2 could provide some ‘curated’ suggestions for giving your child a math circle like activity that you can try at home. Rather than providing a laundry list of links, I feel concise and specific suggestions might be most helpful. So here’s a list…of two ideas:

Idea #1 1d Tic-tac-toe

The words in italics describe the progression of a typical math circle. Initially, engage in a game that is accessible. Next, try to ‘solve’ the game, describing a strategy that works for the initial version of the game. Then generalize and create!

The initial rules of the game:ย Draw seven blank spaces in a row. Take turns putting x’s (and only x’s; no o’s!) in open spaces. The person who gets three or more x’s in a row wins. It’s important to understand that no one ‘owns’ an x–what matters is who was the person who added that last x that led to at least three x’s being consecutive.

Play a few times and start to ask questions:

  • Are there particular moves for player 1 or player 2 that are ‘bad’?
  • Can player 1 or player 2 always win?
  • Can you describe what moves will ensure that victory? Is there more than one choice of moves that will lead to victory no matter what?


  • How can you change the rules of the game? The first, perhaps most obvious generalization is to change the number of spaces. I encourage you to explore that first.
  • What’s the fewest number of spaces that a game can have? [3] Who wins in that case?
  • Who can always win with games of 4, 5, and 6 spaces? Organize your thinking in a table, and continue to explore bigger numbers. Is there a fundamental difference between games with an even and an odd number of spaces?
  • At some point, jump to a big number, like 171. Can you give a winning strategy for player 1 or player 2 there?
  • What big mathematical ideas are at play? How does symmetry support your thinking?

Invent & QED

Now it’s time to make up your own variation and explore. Here’s an old post that can help support your brainstorming if you need it, but I believe there is something particularly valuable about kids generating and exploring their own ideas. That’s what QED is all about.

Idea #2 Tangrams

My initial love of mathematics was seeded by toys like soma cubes, rubik’s cubes, and, plain old cubes. I also have early memories of playing with tangrams.

Tangrams are a collection of seven shapes–5 isosceles triangles, a square, and a parallelogram. Play with tangrams generally involves arranging these shapes into a figure shown as a silhouette–the number of possible tangram puzzles is limitless.

  • You can find instructions here for creating your own tangrams if you don’t have any on hand.
  • There are any number of websites that give tangram challenges–here’s one that has links to a few 100 at a variety ofย  difficulty levels.

I believe that many children will be given school work to do at home in the upcoming weeks to continue their academic studies. I hope you’ll help them continue their enrichment studies too–we’ll keep the posts coming. ๐Ÿ™‚