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

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

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

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 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?

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

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

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?

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?

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.

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

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

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

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

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

Can you put these shapes in order of size? Start with the smallest.

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

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

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

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

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

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?

How would you move the bands on the pegboard to alter these shapes?

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

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

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?

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

Measure problems at primary level that may require resilience.

Measure problems at primary level that require careful consideration.

Measure problems for primary learners to work on with others.

Measure problems for inquiring primary learners.

We started drawing some quadrilaterals - can you complete them?

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

A follow-up activity to Tiles in the Garden.

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

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

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

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

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

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

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?

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.