Working systematically

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?
problem

Centred Squares

Age

7 to 11

Challenge level

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

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
Favourite

Price Match

Age

7 to 11

Challenge level

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

Tiles on a Patio

Age

7 to 11

Challenge level

How many ways can you find of tiling the square patio, using square tiles of different sizes?
problem

Worms

Age

7 to 11

Challenge level

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
problem

Newspapers

Age

7 to 11

Challenge level

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
problem

Magazines

Age

7 to 11

Challenge level

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
problem

My New Patio

Age

7 to 11

Challenge level

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?