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

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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?

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

There were 22 legs creeping across the web. How many flies? How many spiders?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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?

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

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

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

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 clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

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?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

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?

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 each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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

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?

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

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.

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

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

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?

Generate large numbers then give the values of each digit.

Find a great variety of ways of asking questions which make 8.

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

Investigate the different distances of these car journeys and find out how long they take.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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?

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?