Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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?

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

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

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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?

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 find out in which order the children are standing in this line?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

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?

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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....?

How many different shapes can you make by putting four right- angled isosceles triangles together?

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

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?

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.

My coat has three buttons. How many ways can you find to do up all the buttons?

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?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Can you fill in the empty boxes in the grid with the right shape and colour?

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

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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

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

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?