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

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

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

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

Can you draw a square in which the perimeter is numerically equal to the area?

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!

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!

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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?

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

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?

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

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

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

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.

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?

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.

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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?

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?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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?

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?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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?

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.