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!

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?

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.

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

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?

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

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

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?

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?

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

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

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

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

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

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

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

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?

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.

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.

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?

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.

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?

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

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.

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

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

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

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

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?

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

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

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?

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?

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 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.

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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

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