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.

A Sudoku with clues given as sums of entries.

This challenge extends the Plants investigation so now four or more children are involved.

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

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

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?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

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?

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.

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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

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. . . .

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

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?

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

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?

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?

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

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

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

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?

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.

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

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

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

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?

An activity making various patterns with 2 x 1 rectangular tiles.

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

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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

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

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?

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?

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

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.

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