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

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 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?

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?

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?

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

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.

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?

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

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

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

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

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

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

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?

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?

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

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

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?

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?

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

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

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

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

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

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.

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?

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

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

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

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

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?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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....?

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

Find out what a "fault-free" rectangle is and try to make some of your own.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?