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?

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?

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?

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

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

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?

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?

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.

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

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

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?

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

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

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?

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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

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

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

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

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?

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

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?

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?

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

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.

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

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

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?

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?

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?

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.

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

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

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.

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

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?

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

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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

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

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

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