Measure problems at primary level that require careful consideration.

Measure problems at primary level that may require resilience.

Measure problems for primary learners to work on with others.

Measure problems for inquiring primary learners.

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.

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?

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

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

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.

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

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

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

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

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

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

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

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?

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.

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

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?

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

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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. . . .

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

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

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

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

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

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.

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

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?

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

A simple visual exploration into halving and doubling.

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?

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

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

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?

A follow-up activity to Tiles in the Garden.

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

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?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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.