## Monday, June 30, 2014

### Traffic Lights

Something we did before we started this blog: play traffic lights from NRICH: nrich.maths.org/1181.

There is so much I enjoyed about this game, but I mostly want to encourage you to go play it and explore.
This list of ideas is just to get you started and to remind you to pay attention to the kids ideas along the way:

• what if we had 3 players? this is a natural question for us now as I play these games with the two boys.
• Jin: what if the traffic lights would cycle (so so yellow follows red, green follows yellow, and red follows green)?
• Jate: What if we added another color (in our case, purple)?
• Jin and Jate: what if we had 4 colors and let them cycle?

Some other prompts for an investigation of the game structure and strategy:
Tips
• draw pictures and diagrams
• try a smaller board,  say 2x2 to consider a simpler case
• try using 2 colors (or even just one) for a simpler case.

Questions about game structure
1. Does the game always end?
2. How many turns are possible?
3. How many pieces of each color do you need? This is one benefit of making a simple version with paper, it leads you to ask this type of question.
4. An ending board is where someone has made 3 in a row.How many ending boards are there?
5. Are there fully colored boards (each square has a light) where no one has won? If so, what is the farthest number of moves such a board can be from a win?
6. What questions do you have?

Make your own
As I mentioned, making a paper version helped suggest some ideas for investigation, both for me and the boys.  It made it a more fun hands-on activity for them as well (cutting out little pieces and coloring them).

Another route is to write a program to play the game. Here is a pencilcode version I wrote for the basic game: jgplay.pencilcode.net/home/inProgress/masterTL. You can play against another person or against the computer, but I hope you also try to make your own version, investigate the variants we mention above, and find your own.