A task which depends on members of the group noticing the needs of others and responding.
Can you deduce the perimeters of the shapes from the information given?
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?
We started drawing some quadrilaterals - can you complete them?
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.
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Use the information on these cards to draw the shape that is being described.
Are these statements always true, sometimes true or never true?
An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
Measure problems at primary level that may require resilience.
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Measure problems at primary level that require careful consideration.
A follow-up activity to Tiles in the Garden.
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
Explore one of these five pictures.
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?
I cut this square into two different shapes. What can you say about the relationship between them?
Measure problems for inquiring primary learners.
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.
How many tiles do we need to tile these patios?
Measure problems for primary learners to work on with others.
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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. . . .
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 rectangles have been torn. How many squares did each one have inside it before it was ripped?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
This article for teachers gives some food for thought when teaching ideas about area.
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?
How would you move the bands on the pegboard to alter these shapes?
A simple visual exploration into halving and doubling.
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
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?
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
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?
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 rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These practical challenges are all about making a 'tray' and covering it with paper.
What do these two triangles have in common? How are they related?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
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?