Other alternative games are as follows:

- Place differently colored blocks randomly on four or five of the ponds. Two players start at alternative ends of the “rainbow.” (So if your using four blocks, one person might start at whatever color is closest to the top of the rainbow and another at whichever color is closest to the bottom.) The players choose or are assigned a how many steps they are allowed per turn. I recommend using 2, 3, 4, or 5 although we did experiment as well with 8. Each player has to then try to move through, stopping at each of the colored blocks in order going either up or down the rainbow. (We start at alternative sides so that no one can just copy the other person’s path.)
- Play tag. Whomever is it can move three spaces. Everyone else moves just two. A person is tagged only if It can end his turn on the same space that person is on. Alternate It taking a turn and everyone else taking a turn. After a while, switch it up. Whomever is it can only move two spaces and everyone else moves three. How does that change the game?
- Play guessing games. Place an assortment of colored blocks on every pond. Have someone call out a hint, and everyone has to run to land on a pond that matches the clues. In this game people don’t have to follow the paths to move but the hints should be related to the paths. Hints can be things like: Find a pond with a blue cube. Or find a pond that is two steps away from a pond with a blue cube. Or find a pond that is not a neighbour to a pond with a red block.
- Stand on a pond and challenge everyone to move to a different pond as far away as possible. (Distance is measured by the number of edges connecting them, not by physical size.)

I presented the logic to my oldest by asking him how many times he’s gone through the closet door. He hides there frequently, but of course he hasn’t counted. Then I asked if he’s been through the door an even or an odd number of times. The smile grew on his face as he understood that it must have been an even number of times, because if it was an odd number then he’d still be inside the closet! So we talked about the lines of an Euler’s path being like doors that can only be gone through once. If you go through it, your going to be stuck in that room, unless there’s another door/line. If there is, then you can go through. You keep following the open doors around and around. The only ways to “lose” on a Euler’s path is to start at the wrong location or go to the ending location too soon, and the only way to “lose” on a Euler’s cycle is to return to your starting place too soon.

After using the Euler’s cycles and the Land of Many Ponds, I asked my oldest son to compare the Land of Ponds with an Euler’s cycle, and explain how we could turn the one into an Euler’s cycle.

## 2 Comments

## Lisa Nelson

What fantabulous math game ideas, Cristy. They are actually brilliant. I love how you waited until the kids were calmer to play. Sometimes there is just too much excitement to sit down and think about things.

I love the way you encourage math.

I’m sharing this post! Thanks so much for sharing with us at the #homeschoollinkup!

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