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

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

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book 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?

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.

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?

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

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?

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.

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

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?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Here is a chance to play a fractions version of the classic Countdown Game.

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?

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

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?

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

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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?

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.

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?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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?

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

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

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 article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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?

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!

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.