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

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?

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

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

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

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?

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?

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 the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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

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

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

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.

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 if you work in a systematic way, you won't leave any out.

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?

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

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 to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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.

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

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

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?

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

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?

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

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

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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

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?

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

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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

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