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

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

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?

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?

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

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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.

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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.

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?

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

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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 clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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?

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

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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?

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.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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?

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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