A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

What is the greatest number of squares you can make by overlapping three squares?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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

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?

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

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.

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.

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

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?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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....?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Train game for an adult and child. Who will be the first to make the train?

A train building game for two players. Can you be the one to complete the train?

These interactive dominoes can be dragged around the screen.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?