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

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

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

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

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

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

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

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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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?

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

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

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?

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

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?

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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.?

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

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

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

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

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

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

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

An activity making various patterns with 2 x 1 rectangular tiles.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

This task challenges you to create symmetrical U shapes out of rods and find their areas.

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?

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

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

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

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 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?

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?

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.

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?

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?

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?

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 shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?