# Middle school math games for the parking lot

I'm looking for math games that a group of students in grades 5 to 10 (ages 11 to 15, say) could play in a gym or parking lot. My school has a STEM Day each year and I get tasked with cooking up some sort of math activity. (It's hard to compete with the science people, who get to build catapults and blow things up.)

Here's two examples of what I've done in the past:

1. I drew four different graphs (easy, medium, hard, impossible) with sidewalk chalk in the parking lot. Students get sent in waves of about 10, once per hour. I had some small traffic/agility cones and the students were to walk the graph, trying to find an Euler tour (trace out each line exactly once.) If they used a line, they marked it with the traffic cone. This was fairly successful. Most groups made it through easy, medium, hard in a few minutes. So the group of 10 would end up at the impossible graph and start arguing and debating about how to find the Euler tour. (I couched this as a snowplow needing to plow all the streets of this little town but having exactly enough gas to do all the streets once.) So it got exciting and I got good feedback.

2. There's a game called "Gale" described here:

https://en.wikipedia.org/wiki/Shannon_switching_game#Gale

I had 30 orange and 30 blue traffic cones and some 3-foot green bamboo sticks (sold for staking garden plants) and some 3-foot natural-color bamboo sticks. I set up a grid for Gale with the cones 3-feet apart. When the wave of 10 students came, I had them pick teams of 3-ish and compete. This also worked pretty well. There was much yelling and excitement (which we don't get much of in math.) We had to make a "no sword fighting" rule right away, however.

So I'm looking for other similar ideas. My criteria are: 1. Real math involved and 2. Needs a parking lot or gym to implement (that is, the activity should be physical.) 3. Is competitive.

After the Snowplow problem, I could talk in my classes about the Königsburg Bridge Problem and the theorem that tells us when an Euler tour exists. (The upperclass students act as assistants for STEM Day, so the 11th and 12th graders also know about the exercise.) So there's some "real math" going on that we get to talk about later. Likewise, with Gale, we spent some time in regular class analyzing the game. For STEM day, the grids were 5 x 6. So in class we looked at smaller and smaller grids. 4 x 5 is still complicated. 3 x 4 is simple enough that "whoever moves first is probably going to win." 2 x 3 we can analyze completely. 1 x 2 gets a laugh.

So I'm looking for other ideas with the same sort of flavor. (And if someone uses one of my ideas above, all the better.)

• Which age means grades five to ten? You might want to specify this in the question, as it varies from country to country. Mar 16, 2022 at 16:27
• @AdamRubinson 5th graders can understand the proof to Euler's Theorem. And after they tried so hard to do my "impossible" problem, they were definitely interested. Now they know just how to tell whether an Euler tour exists for a given graph. One 11th grader came to talk to me about it over a year later. And there are no fat kids in our school. We're "Charlotte Mason." Mar 16, 2022 at 17:59
• After reading the OP properly, I retract much of my previous statements. +1, good question. Mar 16, 2022 at 19:42

Nim? Draw chalk circles and put some beanbags on each one. On your turn, you go over to one circle, put some beanbags into a pail, and carry them away. Admittedly, the winning condition isn't as well motivated as the snow plowing story, but competition can be its own motivation.

Ehrenfeucht-Fraisse Games, maybe?

Draw two (small-ish) graphs on the sidewalk

• Player 1 colors in a new color one vertex on either graph

• Player 2 colors with the same color a vertex on the other graph to match them together

This repeats. The game ends when both graphs have been fully colored in, or when matched vertices are connected in one graph and not connected in the other graph. (for instance, if the red and blue vertices are connected in one graph but not in the other)

It's a bit more complicated than finding Euler tours and it'll be hard to explain why they should care about first order logic, but your students might be able to come up with some strategies to identify similarities/differences between graphs.

You can try out EF games in the browser here: https://trkern.github.io/efg

The human knot game is certainly mathematical but also fun. And definitely suitable for a parking lot.