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

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

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.

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.

Measure problems for inquiring primary learners.

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

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

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

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

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

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?

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

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

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.

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.

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

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 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?

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?

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

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

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?

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?

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?

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?

Here are many ideas for you to investigate - all linked with the number 2000.

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

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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

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

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

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

What fractions of the largest circle are the two shaded regions?

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

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. . . .

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

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

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

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?

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Can you work out the area of the inner square and give an explanation of how you did it?