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?

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?

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.

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

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?

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?

How can we help students make sense of addition and subtraction of negative numbers?

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?

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

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

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?

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

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

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

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

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.

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

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

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

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

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?

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

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?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

These two group activities use mathematical reasoning - one is numerical, one geometric.

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

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

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

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?

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?

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

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.

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

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.

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

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.

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?