Being resourceful

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

What's the largest volume of box you can make from a square of paper?

Can you do a little mathematical detective work to figure out which number has been wiped out?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

Can you make sense of these three proofs of Pythagoras' Theorem?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?