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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Can you complete this jigsaw of the multiplication square?

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

Sort the houses in my street into different groups. Can you do it in any other ways?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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?

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

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

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

Can you hang weights in the right place to make the equaliser balance?

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

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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

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

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

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

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

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....?

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

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

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

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

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?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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?

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?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

Move just three of the circles so that the triangle faces in the opposite direction.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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

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?

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?