How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

In how many ways can you stack these rods, following the rules?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

These practical challenges are all about making a 'tray' and covering it with paper.

An investigation that gives you the opportunity to make and justify predictions.

Can you draw a square in which the perimeter is numerically equal to the area?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Can you find all the different ways of lining up these Cuisenaire rods?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Number problems at primary level that require careful consideration.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

An activity making various patterns with 2 x 1 rectangular tiles.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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.

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?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

How many different triangles can you make on a circular pegboard that has nine pegs?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?