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

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?

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?

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

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?

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?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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

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

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

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.

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?

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

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

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

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

This challenge is about finding the difference between numbers which have the same tens digit.

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

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?

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.

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?

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.

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.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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.

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.

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!

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?

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

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

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

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

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?

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

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?

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

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?

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

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

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.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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!