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

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?

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

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

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

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

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

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

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

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

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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.

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

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?

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

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?

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?

What is the best way to shunt these carriages so that each train can continue its journey?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

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

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?

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!

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

What happens when you try and fit the triomino pieces into these two grids?

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

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?

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?

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

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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