Sim
Players: 2
Ages: 6 and up
Cost: Free!
Math Ideas: shape recognition, spatial reasoning, logical deduction
Questions to Ask:
How many lines can you draw before you create a triangle?
How many different lines can you draw between six points? How many triangles would you form in that situation?
I was chatting recently with Molly Rawding (who previously suggested a great way to play Garbage with Tiny Polka Dot cards).
Molly mentioned offhand a game that sounded perfect for parents: quick to play, easy to learn, hard to master. And best of all - it's totally free!
All you need is paper and two colors of pen, pencil, or marker.
The game is called Sim.
How to Play
Sim is a two-player game. I found a great write-up of the game, as well as some useful diagrams, on the site What Do We Do All Day? which has a bunch of other fun game recommendations for parents. Check them out!
To play Sim, begin by placing six points on a piece of paper, arranged so that they could form a regular hexagon.
Each player takes turns drawing line segments to connect two of the points on the paper. The goal is to not form a triangle with three of your lines. The person who forms the first triangle, loses.
An important clarification: The only triangles that matter are those that are formed using the six original points. So in this example, Green has just drawn a line from E to B. Although that line seems to make a triangle with Green's other two lines, Green hasn't lost yet. However, if Green connects points C and D, then Green would lose, since they have formed a triangle that connects points A, C, and D.
That's the game! Like I said, easy to learn and quick to play. But that doesn't make it easy to win...
Where's the Math?
Sim is a fantastic math game, since it has meaningful math ideas for kids of all ages (as well as adults)!
For young kids, there is a real challenge to looking at the game board and finding valid moves, especially as the board gets more crowded.
Take a look at this game, for example. Ask yourself these questions:
Where can Blue draw a line?
How many options do they have?
Did you even notice that Yellow has already lost?
It's quite difficult to look at a complicated geometric figure and focus on specific attributes, but that skill is also vital to success in later geometry courses.
If the problem at left makes you break out in hives, don't worry! But notice that this problem, which is a real challenge, is also based on the idea of seeing many different triangles in a given figure. It might seem silly to think that this little pencil-and-paper game could help your child develop the skills to solve this complicated area problem, but it's true!
Older kids, especially those who play Sim repeatedly, might get interested in the strategy of the game. Sim is what's called a finite game, which means there are limited choices and, therefore, an ideal strategy. Some finite games, like chess, are so complicated that they can't be solved. Others, like tic-tac-toe, are simple enough for a first grader to solve.
Sim sits in that sweet spot, where the game is solvable but by no means easy. If your child is interested, they can wonder about whether it's better to go first or second, what the best opening move is, and whether the game can ever end in a tie.
I won't spoil the fun by giving away the answers to those questions. Honestly, I don't know all the answers myself! But maybe your kids will notice something interesting about the game after they've played it a few times.
Questions to Ask
Young kids might struggle to see which lines can still be drawn. You can always play a variation with the lines pre-drawn, where you and your child use highlighters or markers to color in existing lines.
If you're playing this variation, though, you can turn the creation of the game board into a game itself! Ask your child "How do we know when we've drawn every line?" Perhaps they'll figure out an approach to drawing the lines that is more systematic than simply drawing lines at will.
Once you've drawn the board, you can ask "How many lines did we just draw?" This question is really tough! All the segments overlap, and you are always in danger of double-counting lines by accident. Again, though, your child might find an interesting way to count the lines reliably.
(Ok, I'll give you one strategy, as long as you promise not to spoil it for your kids. Count the number of lines coming off each point. Five lines coming from each of the six points makes 30, right? But you've double-counted each line. Divide by two, and you have your answer: 15 lines total)
Another question you can ask your child is "How many triangles can you make using these lines?" You can restrict this question to the triangles that are made by the original six points, or you can include all triangles of any size.
If the last question was tough, this one is TOUGH. Just looking at that diagram makes me a little dizzy when I try to count all the triangles I see. But I do notice that once I see one type of triangle, I can see six of them as I rotate the image or the paper. Maybe there's a reliable way to count the triangles that way.
The last question you can ask is "Want to play this game with only five points? What about with seven?" These variations are interesting to see how the game changes when the initial conditions are different. I'll admit that I think six points is the sweet spot for this game, but experiment! Figure out what you like.
Even if you never explore these variations, though, you and your kid are doing valuable mathematical work, simply by looking at the six points and trying to find a winning move. Everything else is, well, just for fun!