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

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?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

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

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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

An environment which simulates working with Cuisenaire rods.

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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

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

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 game in which players take it in turns to choose a number. Can you block your opponent?

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

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?

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

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Use the interactivities to complete these Venn diagrams.

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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

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

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

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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

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!