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

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

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.

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

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?

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

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.

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?

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

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?

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

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.

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

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!

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

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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?

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

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

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.

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

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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.

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.

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

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?

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

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?

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?

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

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

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