If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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

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

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

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

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?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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

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?

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?

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

What two-digit numbers can you make with these two dice? What can't you make?

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

These activities lend themselves to systematic working in the sense that it helps to 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?

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?

Find all the numbers that can be made by adding the dots on two dice.

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

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?

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?

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?

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?

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.

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

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

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

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

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?

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

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?

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

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

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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?

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

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.

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.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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?

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?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?