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

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

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?

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?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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

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

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

This activity investigates how you might make squares and pentominoes from Polydron.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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

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

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?

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?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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 involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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.

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!

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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!

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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

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

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?

In this matching game, you have to decide how long different events take.

The pages of my calendar have got mixed up. Can you sort them out?

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!

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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.