In how many ways can you halve a piece of A4 paper? How do you know they are halves?
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
What fractions of the largest circle are the two shaded regions?
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.
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?
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. . . .
How many centimetres of rope will I need to make another mat just like the one I have here?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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?
This article for teachers gives some food for thought when teaching ideas about 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 draw a square in which the perimeter is numerically equal to the area?
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.
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
Measure problems at primary level that require careful consideration.
Measure problems for primary learners to work on with others.
Use the information on these cards to draw the shape that is being described.
A simple visual exploration into halving and doubling.
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?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Are these statements always true, sometimes true or never true?
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 many tiles do we need to tile these patios?
Look at the mathematics that is all around us - this circular window is a wonderful example.
Measure problems for inquiring primary learners.
I cut this square into two different shapes. What can you say about the relationship between them?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
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?
Here are many ideas for you to investigate - all linked with the number 2000.
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?
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?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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.
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?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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. . . .
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?
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 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?