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

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

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

What happens when you round these numbers to the nearest whole number?

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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?

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

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

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?

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?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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

Can you work out some different ways to balance this equation?

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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.

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?

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?

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?

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

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

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?

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

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

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?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

This challenge extends the Plants investigation so now four or more children are involved.

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

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?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

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

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

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

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.