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

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?

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 numbers to the nearest whole number?

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

Can you replace the letters with numbers? Is there only one solution in each case?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

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?

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

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.

Can you substitute numbers for the letters in these sums?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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

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.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

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

In how many ways can you stack these rods, following the rules?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

How many models can you find which obey these rules?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

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

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

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 coins needed to make up 12 dollars and 83 cents?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Investigate the different ways you could split up these rooms so that you have double the number.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?