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?

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?

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

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

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

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

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....?

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

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

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

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?

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

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

What happens when you try and fit the triomino pieces into these two grids?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

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.

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?

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

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

How many right angles can you make using two sticks?

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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.

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

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

This activity challenges you to make collections of shapes. Can you give your collection a name?

Use the interactivity or play this dice game yourself. How could you make it fair?

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

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

A train building game for two players. Can you be the one to complete the train?

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

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

These interactive dominoes can be dragged around the screen.

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