Exploring and noticing

problem

1, 2, 3, 4, 5

Age

7 to 11

Challenge level

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
problem

Magic Triangle

Age

7 to 11

Challenge level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
problem

The Pied Piper of Hamelin

Age

7 to 11

Challenge level

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
problem

Beads

Age

7 to 11

Challenge level

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
problem

A Numbered Route

Age

7 to 11

Challenge level

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
problem

Magic Matrix

Age

7 to 11

Challenge level

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
game

Daisy

Age

7 to 11

Challenge level

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?
problem

Bundles of Cubes

Age

7 to 11

Challenge level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
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

Lost Books

Age

7 to 11

Challenge level

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?