**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.
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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!

# Activity Notes

## Supplies needed

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.

- Activity sheet whiteboard: four square problem sheet in sheet protectors.
- Whiteboard markers.
- Erasers or rags.

**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.
- Triangulation.
- 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?

## Additional Resources

- Criss Cross worksheet (pdf).
- Julia Robinson Math Festival Criss-Cross worksheet (pdf).
- Sam Vandervelde’s Circle in a Box Criss-Cross chapter (pdf).