Working systematically

Design an arrangement of display boards in the school hall which fits the requirements of different people.

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

In the café, your ice cream selection can't include a combination that someone else has chosen. What could these seven children have chosen?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?