What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Can you find pairs of differently sized windows that cost the same?
Can you draw a square in which the perimeter is numerically equal to the area?
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
This article for teachers gives some food for thought when teaching ideas about area.
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?
How could you find out the area of a circle? Take a look at these ways.
A simple visual exploration into halving and doubling.
How would you move the bands on the pegboard to alter these shapes?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Measure problems for you to work on with others.
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.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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.
Investigate the successive areas of light blue in these diagrams.
Measure problems for primary learners to work on with others.
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?
An investigation that gives you the opportunity to make and justify predictions.
These resources introduce and explore the concepts of area and perimeter.
These articles, written for primary teachers, offer guidance on the teaching and learning of geometry.
In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .
Explore one of these five pictures.
Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.
These resources are based around measuring in a variety of different ways.
These upper primary activities all make use of a geoboard or pegboard.
Have a go at this 3D extension to the Pebbles problem.
Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.
We hope the new ideas and situations in these activities will make you curious to know more.
These activities offer novel situations which will help provoke learners' sense of awe and wonder.
Here are many ideas for you to investigate - all linked with the number 2000.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Are you resilient enough to solve these measure problems?
These upper primary activities are all about measuring in different contexts from money to mass.
These upper primary challenges will help deepen your understanding of area and perimeter.
Measure problems for upper primary that will get you thinking.
Measure problems at primary level that may require resilience.
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?
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?
A collection of 5 investigations.
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.