PRIME NUMBER SORTING GAME
The team is given a bunch of sealed envelopes, each with a number printed
on it. In each prime numbered envelope is a golden ticket. In each
composite numbered envelope is a red ticket. Your job is to open all
the prime numbered envelopes but not the composite numbered envelopes,
which you must instead give to the Ticket Taker, unopened. For each
prime numbered envelope you open, you get the golden ticket inside.
If by mistake you give a prime numbered envelope to the Ticket Taker,
he keeps the golden ticket. For each composite numbered envelope you turn
in unopened, he'll take out the red ticket and give you the golden ticket.
If by mistake you open it, you're stuck with the red ticket. Your final
prize/rank is determined by how many golden tickets you collect.
Students should play as a single team. If playing for prizes, a list
can be posted ahead of time. For example, if all 99 numbers from 2 to 100
are used, the prizes might be as follows:
80 tickets -- smalest prize
90 tickets -- a little better prize
95 tickets -- medium prize
98 tickets -- good prize
99 tickets -- something really worth playing for
Or they can play for "prime number hunter" ranks, or military ranks or
aristocratic titles or whatever.
If you want to do this activity, I'll supply the envelopes. The idea
is for them to understand in elementary terms what a prime number is,
e.g., a number is prime if it can't be shared equally among any number
of people greater than 1, and for them to find effective strategies for
sorting into primes and composites. Also, it is a good activity for
getting students to talk to each other and compare ideas, since if they
are to make few mistakes, they will need to form a consensus before
opening or hading over each envelope.