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

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

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

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

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

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.

Complete the squares - but be warned some are trickier than they look!

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

Can you fit the tangram pieces into the outline of Little Ming?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

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

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.

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

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?

Use the interactivities to complete these Venn diagrams.

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

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?

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?

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.

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?

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?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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!

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

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

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

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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.

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.

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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.

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?

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

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?