This task is on the NRICH website. Students have to find out an unknown number of marbles by using a known number on a balance beam and looking for a relationship between position and quantity. There are four numbers involved, three known and one unknown, and trials can be carried out until a balance is achieved. If the players do not know what the conditions for balancing are, they can find out first before using it to find the unknown number.
You may want to set up a real balance to enable them to explore balancing more generally. The task also includes an interactive Flash activity.