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

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

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

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

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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

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

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

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.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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?

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?

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....?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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?

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

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

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 quadrilaterals can be made by joining the dots on the 8-point circle?

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

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

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

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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?

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Investigate the different ways you could split up these rooms so that you have double the number.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?