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

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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?

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

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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

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?

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.

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

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

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

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

Surprise your friends with this magic square trick.

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.

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?

By selecting digits for an addition grid, what targets can you make?

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

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

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?

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

This Sudoku requires you to do some working backwards before working forwards.

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

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Try out some calculations. Are you surprised by the results?

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

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

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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

Play this game to learn about adding and subtracting positive and negative 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?

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.

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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

This article suggests some ways of making sense of calculations involving positive and negative numbers.

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

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. . . .

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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

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?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?