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?

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

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!

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

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?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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?

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?

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

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. . . .

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?

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

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

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

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

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

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

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

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

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.

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, 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.

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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?

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

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.

Can you find all the ways to get 15 at the top of this triangle of numbers?

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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

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

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 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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?

In this game for two players, the aim is to make a row of four coins which total one dollar.

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.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

Got It game for an adult and child. How can you play so that you know you will always win?

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.