2) Each team of 4 (or 5) should pick a name for itself and sit at a table cluster. Write the team names on the board.
3) Each team will start with 6 stones + 2 for each person on that team that satisfactorily completed the bonus problem(s) given in the previous session. Each team will also get a paper cup.
4) For each of the problems, the teachers do the following:
a) Hand out the problem and give them 5 minutes to collectively come up with their best answer.
Answers that are shouted out during this five minutes will be ignored.
b) At the end of the five minutes they need to do 2 things.
- Agree on a single answer for their team, and
- put some number of their stones in the paper cup according to how
confident that their answer is correct (sort of like betting that they are right).
They can put 0 stones or all their stones. However, if they put in all their stones and lose,
it will be difficult to recover. If they cannot agree on an answer or a number of stones,
their team forfeits the round.
c) After the stones are in the cups, the teacher will write each team's answer
below the respective team's name on the board. Then the teacher will reveal the correct answer.
If a team got the wrong answer, all the tokens in their cup are collected.
If they got it right, they get additional tokens equal to the number placed in the cup + 1.
(The +1 makes it is possible for a team with 0 tokens to continue playing)
5) At the end, the team with the most tokens wins.
6) Finally, discuss the last week's challenge problem and give another challenge problem for them to take home to think about for the next practice.
We can also take away tokens for talking out of turn if needed. We should state up front that if a student speaks after we have asked for quiet, then their team will lose one token for each infraction.
At the end of the session give a very hard "bonus" problem that will be worth an additional two or three tokens for their team if they can find a solution by the next meeting. To win the tokens, however, they must clearly explain how they solved the problem in their own words and in their own handwriting. So if they were to get help from other kids, adults, or books - that is ok - because at least they thought about it and took time to write out a solution. The problem should be hard enough that only a few will do it and have acceptable solutions. In addition we could give tokens for solving in a similar manner any problem that they got wrong on a previous math league test.
I thought about giving a prize to the winning team, but I'm not sure it is a good idea. Introducing an extrinsic motivator might hinder development of a natural desire to solve the problems for their own sake.
Some challenge problems given so far:
- If a brick weighs 9 pounds + 1/2 a brick. How much does a brick and a half weigh?
- Can you tell me 2 numbers, neither of which ends in 0, that when multiplied together equal 1000?
- You have some Amoebas in a dish. Every minute their number doubles. After one year, the amoebas cover the earth. When did they cover half the earth?