Criss-Cross is a game presented by S. Vandervelde in his Circle in a Box book of Math Circle activities and planning documents. The game is approachable by students of various backgrounds and easily scaffolded up or down depending on students’ interests.
In addition to the description of the game this lesson plan includes activity notes of required supplies, discussion on the mathematics included in the activity, guiding questions, and a list of additional resources to support the lesson.
How to play the game
Starting with a game board of 4 dots, add as many additional dots as you like and slowly alternate between 2 students connecting the vertices. Whoever makes the last connection wins!
This activity can be done with just blank paper and pencils. You can also use a whiteboard setup described below and then have the students record results on blank paper.
Outreach pro tip: 1 box of sheet protectors is a great low-cost way to make a classroom set of individual whiteboards that can be used with different inserts and new problems
Outreach pro tip: Use blue tape or similar device on your whiteboard markers so you don’t steal any markers from the school or room you are visiting.
Where's the Math?
The level of student will determine the level of mathematics to be introduced. Possible topics include:
- Patterns and sequences.
- Advanced mathematical topics and connections including Euler characteristic.
A list of Guiding Questions
- Does it matter if you go first or second?
- What is the pattern of the vertices (V), edges (E), and faces (F)? As we add one more vertex, how do the other quantities change?
- What shape is most prominent on the game board at the end of the game?
- Who would win on a game of 100 vertices?
- What happens if you play this game on a donut?