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.

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?

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

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

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

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

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

A follow-up activity to Tiles in the Garden.

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

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

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?

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

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal 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?

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

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?

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

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

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?

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. . . .

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

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

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

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. . . .

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

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

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

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?

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?

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

Measure problems for inquiring primary learners.

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?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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

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

Measure problems at primary level that may require resilience.

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

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

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

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

Measure problems at primary level that require careful consideration.

Measure problems for primary learners to work on with others.

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?

A simple visual exploration into halving and doubling.

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