Here is what we do ... and it has been pretty successful.
One member creates a grid numbered from 1 through 10 on the left, initials or names
on the top, with a place for each person to fill in his/her responses. They typically
allow this to be created before the timer starts.
Each member is assigned problems from the start (these are actually assigned when
the team is formed and the same assignments are used at every practice). I give
my two faster problem-solvers 1-3 and 4-6, with the students who are better at hard
problems getting 7-8 and 9-10 (it is not always the case that these are harder, but
it is often the case, more so at the higher level competitions).
The goal for my teams at chapter competitions is for everyone to work every problem
to completion, at states everyone is trying to get 5-8 problems done (but specifically
they need to be sure they take time on their own problems, checking wording, avoiding
carelessness, answer the right question, etc.).
I ask them to work silently for the first 10 minutes or so ... they only communicate
to trade problems (for instance, if one student stinks at Geometry and gets a hard
Geometry problem, they are encouraged to trade early with someone who is stronger
at Geometry). Without this rule, they often end up talking way to much and arguing
... or sometimes they all end up trying the same problem because it seems like a
As a student gets an answer, they fill it in on the grid. If they are unsure, they
add a “?” to let others know ... if they are confident, they add a check mark to
let others know that they should look over other problems and come back to it last
once others are checked.
When each person finishes their assigned problems, they continue to the next problems
(the person assigned to 4-6 next checks 7 ... 8 ... 9 ... etc, and each member wraps
around after they do 10). After about 10 minutes they usually have a pretty good
idea of what problems need work/cooperation and which they can mark complete and
they work together on problems for the remaining time (or at least they redistribute
the work that remains).
If I have a "star", we invoke the "always trust ____" rule in the case of disputed
problems (last year this was the case, but my team is very balanced this year). Assigning
problems may go more like 1-2, 3-4, 5-6, 7-10 with the goal being that everyone finishes
their assigned problems in about the same amount of time