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?

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?

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!

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

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

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?

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

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

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?

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

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

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

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?

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

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.

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

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

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.

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 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.

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.

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?

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

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

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

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

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

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?

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

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

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

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!

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?

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

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

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

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!

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.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

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