Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

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

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

How many different rectangles can you make using this set of rods?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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.

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?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

This task follows on from Build it Up and takes the ideas into three dimensions!

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

How many possible necklaces can you find? And how do you know you've found them all?

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

This challenge is about finding the difference between numbers which have the same tens digit.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

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?

This article for primary teachers suggests ways in which to help children become better at working systematically.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?