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?

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?

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

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?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

In this matching game, you have to decide how long different events take.

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

Can you find the chosen number from the grid using the clues?

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

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.

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

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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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

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

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

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?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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?

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

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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

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?

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

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

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?

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?

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

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

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?

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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....?

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?

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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 ...?

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