Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

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?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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. . . .

Can you hang weights in the right place to make the equaliser balance?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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.

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

If you have only four weights, where could you place them in order to balance this equaliser?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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

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!

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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.

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

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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!

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?

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?

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?

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.

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Use the number weights to find different ways of balancing the equaliser.

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 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?

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?