Measure problems at primary level that may require resilience.

Measure problems at primary level that require careful consideration.

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

Measure problems for inquiring primary learners.

Measure problems for primary learners to work on with others.

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

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

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

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

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

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

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.

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

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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

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

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

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?

A follow-up activity to Tiles in the Garden.

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

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?

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

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

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

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

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

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?

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

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

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

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

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

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

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

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

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?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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

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

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.

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

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

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.

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?