There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
How many trapeziums, of various sizes, are hidden in this picture?
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
How many possible necklaces can you find? And how do you know you've found them all?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
This task follows on from Build it Up and takes the ideas into three dimensions!
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Can you find the chosen number from the grid using the clues?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Investigate the different ways you could split up these rooms so that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
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!
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
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.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?