Exploring and noticing

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?