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

Use two dice to generate two numbers with one decimal place. 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?

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

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

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.

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

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?

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

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

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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.

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

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

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

An investigation that gives you the opportunity to make and justify predictions.

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 shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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

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

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

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

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

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

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

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

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

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

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

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?

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

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

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.

Can you substitute numbers for the letters in these sums?

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?

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

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.

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?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?