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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Find out what a "fault-free" rectangle is and try to make some of your own.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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

In this matching game, you have to decide how long different events take.

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.

Investigate the different ways you could split up these rooms so that you have double the number.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

What happens when you try and fit the triomino pieces into these two grids?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

How many different rhythms can you make by putting two drums on the wheel?

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?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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?

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?

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?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?