Area and Volume

Every maths department should own a giant tennis ball! Walk into the classroom with a large fluorescent ball under your arm and you've instantly got the attention of the class.

Students stand in a circle and are told they're only allowed to speak if they're holding the ball. Ask "how could we work out the surface area of this ball?" and throw it to a random student. Students throw the ball around the circle as they share their thoughts and suggest ideas. At some point a teacher prompt may be necessary, along the lines of, "why did I bring a tennis ball? Why not a football or netball or golf ball?". In my experience this prompt may lead some students to 'eureka' moments as they start thinking about the markings on the surface of the tennis ball. Eventually someone will spot that the surface is made up of 4 circles wrapped around each other, and they can then deduce that the formula for the surface area is 4πr². If they need convincing, show them this slide.

This is a very engaging activity. As pupils can't talk unless they're holding the ball, you'll see them wildly waving their arms about, silently begging their friends to pass them the ball so they can share their ideas!

Try it - I'd love to hear how it goes.

Area and volume is a wide ranging topic, from areas of triangles in Year 7 to volumes of hemispheres and frustums in Year 11. Here's a handful of my favourite resources:

• I hand out these rhymes for the area and circumference of a circle in Year 7, tell them to pick their favourite or come up with their own. Love this silly song too.
• Also for Year 7, these matching cards from the Nuffield Foundation involve calculating the area and perimeter of compound shapes.
• As always, plenty of great activities on teachitmaths.com. 
• At GCSE I use this problem solving challenge with questions from Median Don Steward. Pupils work on A3 paper in pairs. They need their brains switched on for this one. There's loads of brilliant activities on Don Steward's blog that could be used in a similar way.
• The Chalk Face has some lovely activities, including: cornflakes problem; Penny Farthing; fuel tank; golden balls and baby surface area. 
• There's a nice activity on finding the volume of different shaped glasses from Shell Centre. 
• Illustrativemathematics.org has fantastic geometry activities. I love the rich task Eight Circles which relates to finding the area of a circle.
• The Chalk Face also brings us this great interactive cuboid for teaching surface area. This could be followed up with harder surface area questions from Don Steward.
• Maths Sandpit has a fantastic resource for investigating the surface area of a cone.
• Challenging volume and area revision questions for Year 11. Some of these are quite tricky and demonstrate that this topic isn't just about substituting into formulae.

For related class discussion - why do we say hemisphere but semicircle? Why not semisphere or hemicircle? I believe it's because the word circle is from the Latin word circus (meaning ring), hence we use the Latin prefix semi, whereas sphere is from the Greek word sphaira (ball), hence we use the Greek prefix hemi. This article about semi/hemi/demi gives more examples. If you like this then you might also like these lovely maths vocabulary activities.

Finally, here's one for the teachers. It's not as obvious as it seems!

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