Exploring and noticing

problem

Centred Squares

Age

7 to 11

Challenge level

2 out of 3

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

Dice Stairs

Age

7 to 11

Challenge level

2 out of 3

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

Diagonal in a Spiral

Age

7 to 11

Challenge level

2 out of 3

Investigate the totals you get when adding numbers in threes on the diagonal of this pattern.
problem

Tiles on a Patio

Age

7 to 11

Challenge level

2 out of 3

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

Magazines

Age

7 to 11

Challenge level

2 out of 3

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

Pebbles

Age

7 to 11

Challenge level

2 out of 3

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

My New Patio

Age

7 to 11

Challenge level

2 out of 3

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

Presents

Age

7 to 11

Challenge level

2 out of 3

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

Bean Bags for Bernard's Bag

Age

7 to 11

Challenge level

2 out of 3

How could you put eight bean bags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
problem

Special 24

Age

7 to 11

Challenge level

2 out of 3

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.