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

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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

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

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?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

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

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

A Sudoku with clues given as sums of entries.

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?

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

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

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

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

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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?

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....?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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 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?

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

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

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

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?

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

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