This was a fun activity from Moebius Noodles for our PK-1st grade Homeschool Math in the Park group. The children take turns making a maze and setting a dinosaur inside. Then the other dinosaurs (parents or siblings) try to guess whether their friend is on the land or in the water.
Player #1
(1) First, draw a big circle on the white board. This is your lake.
(2) With a finger or a bit of cloth, erase a small section of the circle to create the opening for your maze.
(3) Starting at one edge of the opening, draw a random squiggle inside the circle. Make your squiggle end at the other edge of the opening.
(4) Set your dinosaur anywhere inside the maze.
Player #2
(1) Now it’s your turn to guess. Is the dinosaur standing on the land? Is it swimming in the water?
(2) How will you figure out if you guessed right?
(3) Check by jumping across the lines of the maze. Each jump takes you across a boundary: Splash! (Into the water.) Thump! (Back on the land.) Splash! Thump! … Until you reach the dinosaur inside.
(4) Or go to the maze entrance and walk your dinosaur along the path. Can you find your way?
Denise Gaskins' Let's Play Math 
My kids and I have been playing this game for a few days and they’re loving it, coming up with more and more complicated mazes in order to stump each other. But today someone asked the question I was dreading: “How is this math?”
I told them I really didn’t know — problem-solving, maybe?
So I thought I’d ask you.
(From your faithful math-dunce reader who is trying to remediate herself and her family of math-dunces.)
Hi, Kelly. I’m glad your kids are enjoying the game!
For mathematics, mazes fit into the category of topology, which studies the geometry of how things are connected. Topology began with the Bridges of Konigsberg problem, which was like a town-size maze puzzle: “Can we find a path to walk across all the bridges without doubling back over our path?”
The puzzle of the “land or water” maze game also connects to even and odd numbers, because there are just two options: You are on land and could walk out of the maze, or you are in the water (trapped in the maze). Every time you cross a boundary, you move from one condition to the other. In our summer math circle, we played with a variety of puzzles based on binary systems, such as deciding which directions a chain of gears will spin.
If you’d like to investigate the math of mazes and topology, here are a few places to start:
* Drawing the Cretan maze as a game
* Exploring Labyrinths
* What does mathematics have to do with mazes?
* More Topology Activities for Children
Thanks, that was helpful. The Bridges of Konigsberg made for interesting conversation at supper tonight. I showed my oldest son your answer here and he told me that the directions a chain of gears will spin was on the ASVAB test when he took it last year.