Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Number problems at primary level that require careful consideration.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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!

Try this matching game which will help you recognise different ways of saying the same time interval.

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.

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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?

Can you substitute numbers for the letters in these sums?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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?

In this matching game, you have to decide how long different events take.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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.

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

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?

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

Ben has five coins in his pocket. How much money might he have?

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?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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?

These two group activities use mathematical reasoning - one is numerical, one geometric.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.