children how the game of Taxman is played. The script for such a videotape is given below. (If a tape is not available, the classroom teacher can use the script as a guide to introducing the game.)

The scene opens in a classroom setting, with a teacher and a group of six students. There is a chalkboard on one wall.

Teacher: Today I'm going to show you how to play a new number game, called Taxman. The game is played with a list of numbers starting with the number one. For example, the Taxman game with six numbers would start with this list: [Teacher writes list on chalkboard]

There are two players, You and the Taxman. Every time it is your turn, you can take any number in the list, as long as at least some factors of that number are also in the list. You get your number, and the Taxman gets all of the factors of that number that are in the list. For example, if you take 4, …

Student A: … then the Taxman would get 2!

Teacher: Why?

Student A: Because 2 is a factor of 4.

Student B: The Taxman'd get 1, too.

Student C: Oh, yeah, because 1's a factor of 4.

Teacher: So if you took 4, then the list would look like this: [writes]

Now you have 4 points …

Student D: … and the Taxman has 3 points. [Teacher writes]