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

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?

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.?

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

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.

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

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

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

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?

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?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Try this matching game which will help you recognise different ways of saying the same time interval.

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

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?

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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.

How many different triangles can you make on a circular pegboard that has nine pegs?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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.

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

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?

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

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

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

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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?

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Can you find all the different triangles on these peg boards, and find their angles?

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?

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

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?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?