Exploring and noticing

problem
Taking a die for a walk

Age

5 to 11

Challenge level

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
problem
Month mania

Age

5 to 11

Challenge level

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
problem
Making squares

Age

7 to 11

Challenge level

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?
problem
Presents

Age

7 to 11

Challenge level

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
problem
Sending cards

Age

7 to 11

Challenge level

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
problem
I'm eight

Age

5 to 11

Challenge level

Find a great variety of ways of asking questions which make 8.
problem
Roll these dice

Age

7 to 11

Challenge level

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
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?
problem
Pebbles

Age

7 to 11

Challenge level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
problem
Stairs

Age

5 to 11

Challenge level

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.