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

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

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

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....?

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?

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 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?

Can you complete this jigsaw of the multiplication square?

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

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

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?

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

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

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 ways of lining up these Cuisenaire rods?

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.

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?

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

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?

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?

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!

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

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.

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

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?

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

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?

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

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

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

Use the interactivities to complete these Venn diagrams.

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.

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

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

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.

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.

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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

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

An interactive activity for one to experiment with a tricky tessellation