Are these statements always true, sometimes true or never true?

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

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.

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?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

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. . . .

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

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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!

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

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

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?

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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

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?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

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

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.

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

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.

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!

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?

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.

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

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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 challenge focuses on finding the sum and difference of pairs of two-digit 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?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

This challenge combines addition, multiplication, perseverance and even proof.

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

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

This task combines spatial awareness with addition and multiplication.

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

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?