Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

This activity challenges you to make collections of shapes. Can you give your collection a name?

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?

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

Sort the houses in my street into different groups. Can you do it in any other ways?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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?

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

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

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Complete the squares - but be warned some are trickier than they look!

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

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

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?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

How many right angles can you make using two sticks?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

If you have only four weights, where could you place them in order to balance this equaliser?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

Move just three of the circles so that the triangle faces in the opposite direction.

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

Can you find all the different triangles on these peg boards, and find their angles?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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?

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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....?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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