Delight your friends with this cunning trick! Can you explain how it works?

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Can you explain the strategy for winning this game with any target?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

This challenge extends the Plants investigation so now four or more children are involved.

Choose any three by three square of dates on a calendar page...

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Find out about Magic Squares in this article written for students. Why are they magic?!

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?

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?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

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

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

There are nasty versions of this dice game but we'll start with the nice ones...

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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.

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

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!

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?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?