Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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.

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.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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....?

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?

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!

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

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

An environment which simulates working with Cuisenaire rods.

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.

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

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?

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

Can you complete this jigsaw of the multiplication square?

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

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

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

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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?

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

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

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

Train game for an adult and child. Who will be the first to make the train?

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?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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

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?

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 can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

An interactive activity for one to experiment with a tricky tessellation

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Use the interactivities to complete these Venn diagrams.

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?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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?

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