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

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Measure problems at primary level that require careful consideration.

Measure problems at primary level that may require determination.

Measure problems for primary learners to work on with others.

Measure problems for inquiring primary learners.

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.

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

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

How many centimetres of rope will I need to make another mat just like the one I have here?

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

What do these two triangles have in common? How are they related?

Look at the mathematics that is all around us - this circular window is a wonderful example.

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

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

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?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

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.

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

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

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

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

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

Determine the total shaded area of the 'kissing triangles'.

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

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

A simple visual exploration into halving and doubling.

A follow-up activity to Tiles in the Garden.

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?

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?

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

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

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

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?

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

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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

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