Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Use the information to work out how many gifts there are in each pile.

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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!

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

How could you put eight beanbags 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?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

A game for 2 players. Practises subtraction or other maths operations knowledge.

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

Investigate what happens when you add house numbers along a street in different ways.

Can you make square numbers by adding two prime numbers together?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

How would you count the number of fingers in these pictures?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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