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

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

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.

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?

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

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

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

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.?

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.

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

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

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?

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

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?

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

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

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?

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

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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.

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

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

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?

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.

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

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

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

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

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?

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

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?

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

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

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?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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?

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

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

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?