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....?

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

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

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?

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

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Here is a chance to play a version of the classic Countdown Game.

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?

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

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

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

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?

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

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

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

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

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?

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?

An environment which simulates working with Cuisenaire rods.

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

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?

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

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

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

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?

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?

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

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

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

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!

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?

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

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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

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

Can you complete this jigsaw of the multiplication square?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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.

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