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

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?

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.

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.

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

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

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

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. . . .

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?

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.

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.

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?

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?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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.

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

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

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?

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

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.

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?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

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?

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

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?

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

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

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

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.

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

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?

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?

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?

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

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!

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

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!

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?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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

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

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

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

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?