Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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

Can you complete this jigsaw of the multiplication square?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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?

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

An environment which simulates working with Cuisenaire rods.

If you have only four weights, where could you place them in order to balance this equaliser?

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

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

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?

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

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?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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....?

Use the interactivities to complete these Venn diagrams.

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?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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?

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!

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

Use the number weights to find different ways of balancing the equaliser.

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

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

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

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?

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?

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?

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Exchange the positions of the two sets of counters in the least possible number of moves

An interactive activity for one to experiment with a tricky tessellation

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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

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?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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

Work out how to light up the single light. What's the rule?