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?
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.
This article for teachers gives some food for thought when teaching ideas about area.
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
Look at the mathematics that is all around us - this circular window is a wonderful example.
How would you move the bands on the pegboard to alter these shapes?
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.
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
Use the information on these cards to draw the shape that is being described.
How many centimetres of rope will I need to make another mat just like the one I have here?
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
I cut this square into two different shapes. What can you say about the relationship between them?
Explore one of these five pictures.
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?
Determine the total shaded area of the 'kissing triangles'.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
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?
A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
Measure problems for inquiring primary learners.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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 do these two triangles have in common? How are they related?
Can you draw a square in which the perimeter is numerically equal to the area?
A task which depends on members of the group noticing the needs of others and responding.
How many tiles do we need to tile these patios?
You have a 12 by 9 foot carpet with an 8 by 1 foot hole exactly in the middle. Cut the carpet into two pieces to make a 10 by 10 foot square carpet.
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Measure problems at primary level that may require resilience.
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?
Derive a formula for finding the area of any kite.
Can you work out the area of the inner square and give an explanation of how you did it?
Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).
Measure problems at primary level that require careful consideration.
A simple visual exploration into halving and doubling.
A follow-up activity to Tiles in the Garden.
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.
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?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Measure problems for primary learners to work on with others.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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 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?