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.

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?

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.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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?

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

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?

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

Try this matching game which will help you recognise different ways of saying the same time interval.

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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.

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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?

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

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

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.

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?

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

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

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Can you find all the different triangles on these peg boards, and find their angles?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

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

What could the half time scores have been in these Olympic hockey matches?

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?