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

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

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

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....?

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?

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

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

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?

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

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

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?

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

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

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.

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

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

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

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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.

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

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

The 2012 primary advent calendar features twenty-four of our posters, one for each day in the run-up to Christmas.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping 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?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

An interactive activity for one to experiment with a tricky tessellation

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.

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Use the interactivity or play this dice game yourself. How could you make it fair?

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

Can you explain the strategy for winning this game with any target?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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

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

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