A task which depends on members of the group noticing the needs of others and responding.

Can you deduce the perimeters of the shapes from the information given?

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

We started drawing some quadrilaterals - can you complete them?

Use the information on these cards to draw the shape that is being described.

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

I cut this square into two different shapes. What can you say about the relationship between them?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

This article for teachers gives some food for thought when teaching ideas about area.

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

This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.

How would you move the bands on the pegboard to alter these shapes?

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Are these statements always true, sometimes true or never true?

In how many ways can you halve a piece of A4 paper? How do you know they are halves?

Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

A follow-up activity to Tiles in the Garden.

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Measure problems for inquiring primary learners.

Measure problems for primary learners to work on with others.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Measure problems at primary level that may require resilience.

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

Measure problems at primary level that require careful consideration.

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

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this 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?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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?

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

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

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

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

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