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

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

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

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

Use the interactivities to complete these Venn diagrams.

Can you complete this jigsaw of the multiplication square?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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

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

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

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

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

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?

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

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?

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?

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?

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

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!

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

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?

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

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.

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

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. . . .

An interactive activity for one to experiment with a tricky tessellation

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

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?

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?

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

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

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

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

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

These interactive dominoes can be dragged around the screen.

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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