Snowball fight with a twist, using lightweight ball-pond balls
Lightweight coloured ball-pond balls, paper and pen, whistle
Secretly assign a value to each colour ball pond ball, giving some positive and some negative values (eg: red = +5, yellow = -10 and so on). Don't tell the Beavers about the values.
Divide the Beavers into any number of teams and mark boundaries (using chalk, tape or benches for example). Each team must stay behind their boundary.
Explain the object is to pick up any "snowballs" which land in their area and throw them into another team's area. They're not aiming for the other Beavers, just their team areas.
On the first whistle they can start throwing. The balls are so light they don't travel far. On the second whistle they must stop immediately and stand still.
Ask the Beavers to count up how many of each ball they have in their area, suggesting the lowest number will win. Then introduce the twist - each ball is worth a different value. Calculate what each team's score is now and decide who wins that way.