If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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?

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 over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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?

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

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.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

This task follows on from Build it Up and takes the ideas into three dimensions!

Investigate the different distances of these car journeys and find out how long they take.

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

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?

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!

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

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.

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?

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

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

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?

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.

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

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.

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?

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?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

There were 22 legs creeping across the web. How many flies? How many spiders?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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

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

Find the next number in this pattern: 3, 7, 19, 55 ...

Number problems at primary level that may require resilience.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

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

This dice train has been made using specific rules. How many different trains can you make?

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?