If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Can you fill in the empty boxes in the grid with the right shape and colour?

Find all the numbers that can be made by adding the dots on two dice.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

My coat has three buttons. How many ways can you find to do up all the buttons?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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

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

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.

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?

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

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

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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

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

This challenge is about finding the difference between numbers which have the same tens digit.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

How many possible necklaces can you find? And how do you know you've found them all?

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?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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....?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

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?

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?