Working systematically

problem
Pocket money

Age

11 to 14

Challenge level

Which of these pocket money systems would you rather have?
problem
Price match

Age

7 to 11

Challenge level

Can you find pairs of differently sized windows that cost the same?
problem
Almost one

Age

11 to 14

Challenge level

Choose some fractions and add them together. Can you get close to 1?
problem
Jigsaw pieces

Age

7 to 11

Challenge level

How will you go about finding all the jigsaw pieces that have one peg and one hole?
problem
Linked chains

Age

7 to 11

Challenge level

Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.
problem
Fraction lengths

Age

7 to 11

Challenge level

Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?
problem
Open squares

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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.
problem
Dart target

Age

7 to 11

Challenge level

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.
problem
How fast does it grow?

Age

16 to 18

Challenge level

Exponential functions grow pretty quickly...