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

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

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?

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

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

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

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

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

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?

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?

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?

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?

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

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.

A follow-up activity to Tiles in the Garden.

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?

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

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?

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?

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.

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

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

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?

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. . . .

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

Measure problems for primary learners to work on with others.

Measure problems for inquiring primary learners.

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

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?

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

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

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?

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

Measure problems at primary level that may require resilience.

Measure problems at primary level that require careful consideration.

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?

A simple visual exploration into halving and doubling.

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

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