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

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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

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

Here is a chance to play a version of the classic Countdown Game.

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.

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

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

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?

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?

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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

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

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

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

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

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

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?

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

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.

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?

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

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?

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

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

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

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?

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.

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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

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

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

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

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....?

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?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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