Asilomar #5: Michael Serra

Session Title

Games And Puzzles That Develop Sequential Reasoning

Better Title





A structure not dissimilar to Megan Taylor’s yesterday, where Serra debuted games and puzzles and gave us time to tease them out.

I sat with two former colleagues in the back – all of us now at different schools. One teacher enthused over Sudoku puzzles. They challenge kids. Kids like them. It gets them comfortable with numbers. The other enjoys Serra’s games and puzzles, like Lunar Lockout. Both cite improved student disposition toward math and improved deductive reasoning.

I disagreed with them. In general, I find it dangerous to put too much distance between “fun time” and “math time” preferring, instead, to have that cake and eat it too, creating as many challenges as I can that are both fun and mathematically rigorous. (Which Sudoko, to put it plainly, isn’t.) My task is harder, I think, and I know I fail at it more, but I’m more satisfied on balance.

It was a good conversation. Feel free to interrupt us.

Serra’s best offering for my money was Racetrack Math:

It’s like this:

  1. Draw a racetrack on graph paper, however crude.
  2. You and your opponent start anywhere on the starting line.
  3. You travel along vectors. You may increase or decrease either the x-value, the y-value, or both, but only by one unit per turn.
  4. First person to the finish line wins.
  5. (P.S. No crashing.)

This gets very interesting very quickly. You start out with tiny vectors which lengthen by one unit every turn. If you fail to notice the side of the track off in the distance, though, and fail to slow down in time, you crash. (Which I did in the example above.)

I hereby toss all of my battleship exercises in the recycling bin. This is a much more straightforward introduction to positive/negative coordinates since each new turn is relative to the last turn rather than relative to this strange coordinate axis thing.

Plus, your students can create racetracks of their own, of infinite complexity, within seconds. Serra cited some kids who created a pit lane, which you had to enter on your second lap, and oil slicks, on which you could not adjust your vector at all. I’m impressed.


PowerPoint. Which is tough when you’re asking people to solve a puzzle. If someone suggests an alternative route to the one you have programmed into your slide, you have to dodge their answer a bit.


Blank puzzles and games to draw on. Again, paper is not dead. How do you do this digitally? Load each picture one at a time into Skitch and pass a stylus back and forth? Moderation, please.


  • “There is no research that demonstrates these games improve outcomes in other mathematical procedures like two-column proofs,” Serra admitted reluctantly. “It has to be there. I know it is.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. I don’t see why you need to throw out battleship. The racetrack is good for positive & negative, and two dimensions, and, I dunno, head to toe vectors in later courses, but don’t you need them to learn about that strange coordinate axis thing sometime?

  2. I was thinking the same as Mark – indeed, if I did this in a class then I would demonstrate it on a whiteboard, and once I’d got everyone going, I’d have one pair of kids playing on the whiteboard at all times (they love that).

    Still, *the rest of them would be using paper.*

  3. I was independently thinking about racetrack math this week. Given that I haven’t played it in about 25 years, that’s a good sign that it’s a winner.

  4. I wish I’d had this trick when I was teaching basic GUI programming to students (students were, in fact, making a race car move around a screen).

    This game is exactly what (I quickly learned) I was taking for granted students could do in their head. Turns out many of them couldn’t.

    Next time I find myself doing this, I’ll make sure kids have played on graph paper before I introduce the concept of pixels on a screen… :)

  5. Hi Dan,
    Thanks for the kind words. I would not abandon Battleship. However, I’d suggest changing the name to Buried Treasure.
    Perhaps next years talk at Asilomar will explore some of the variations I’ve created with Buried Treasure (Battleship without the war and killing inference).

    How about Buried Treasure with Equations?
    Or Polar graphing Buried Treasure?
    How about on the sphere?
    Or 3D Buried Treasure?
    Again the kids will offer up a variety of rule changes for each.