Being collaborative

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Can you find a way of counting the spheres in these arrangements?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Can you place the blocks so that you see the reflection in the picture?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.