In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

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?

Can you find all the different ways of lining up these Cuisenaire rods?

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?

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

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

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?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

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.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Can you draw a square in which the perimeter is numerically equal to the area?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

What is the best way to shunt these carriages so that each train can continue its journey?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.