Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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

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

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

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?

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

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....?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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

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.

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

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?

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?

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

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

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

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

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.

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

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 shaped overlaps can you make with two circles which are the same size?

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?

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?

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

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.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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?

Use Excel to explore multiplication of fractions.

Can you beat the computer in the challenging strategy game?

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?

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

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

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