Working systematically

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
Who's who?

Age

11 to 16

Challenge level

Can you solve the clues to find out who's who on the friendship graph?
problem
Dice stairs

Age

7 to 11

Challenge level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
problem
Centred squares

Age

7 to 11

Challenge level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
problem
An equilateral triangular problem

Age

11 to 14

Challenge level

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
problem
Open boxes

Age

7 to 11

Challenge level

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
$Build it \Up more$

problem
Build it up more

Age

7 to 11

Challenge level

This task follows on from Build it Up and takes the ideas into three dimensions!