A colleague of mine recently stumbled across the website of Peter Bland, a maths tutor. It contains some excellent GCSE revision resources in the form on booklets of exam questions on particular topic. They are all available form his website here, but for your convenience I have also linked to his hosted resources by topic below:

# Category Archives: Shape, Space and Measure

# GCSE exam questions by topic- bland.in

# Hexaflexagons…

Vi Hart has produced an engaging pair of videos about hexaflexagons, the hexagons with 3 faces! The videos are below, and here is a link to a page with instructions and a template for building them…

Have fun!

# Swirlflakes

Another classic video from Vi Hart…

How to make snowflakes with rotational symmetry… swirlflakes!

# TES Maths Podcast 3 goes live

This time Craig Barton and his guests from King’s College, London discuss falling standards in maths, advice on running discussion based lessons, and some festive maths ideas. In the attached Word document you will find links to all the resources, ideas and activities discussed, and a link to the Forum discussion as well.

# Flash Maths doesn’t disappoint

@StudyMaths shared an excellent website with me via Twitter recently: FlashMaths.co.uk

This site adds to the growing number of websites providing interactive games and learning applets based on Adobe Flash. Other favourites of mine include FlashyMaths.co.uk and TeacherLed.com. Flash Maths is a worthy addition and well worth bookmarking. They have numerous applets that are well designed and add a little bit of a zing to your lessons. Get on over to Flash Maths to sample their offerings. Top tip… Shape Shoot is very good!

# Surface area of spheres- an apeeling lesson…

How do you give pupils a beautiful visual picture of why the surface area of a sphere is 4 pi r squared? A super lesson idea I heard recently involved an orange!

Give pupils an orange and a blank sheet of paper. They have to draw circles around the orange onto the paper. The idea is that the circles on the paper should have the same radius as the orange. They draw as many circles on the paper as possible.

Then get the pupils to peel the orange and arrange the peel so that it fills the circles they drew on the paper. Some careful ‘sculpting’ of the peel will be required to get it to fill the circles with no gaps or overlaps. Pupils should fully fill one circle with peel before moving onto the next circle and so on.

A beautiful image should arise whereby the peel completely fills four of the circles proving the surface area of the sphere is 4 pi r squared!

If you give this a go with your class please take some pictures and email them to us at info@greatmathsteachingideas.com so we can feature them on this post!

Finally, time for an orange joke:

What did the little chic say when it’s mother laid an orange?

Look at the orange marmalade

# Angles in parallel lines colouring fun

I want to give my current GCSE year 10 class more practice on identifying angles in parallel lines; alternate, corresponding and co-interior. I have put together the following worksheet that gets them to colour each type of angle a particular colour. Please feel free to use it with your own classes if you like it!

# The first TES Maths Podcast goes live!

The TES Maths Panel are delighted to announce the arrival of The TES Maths Podcast! This is a brand new series hosted by Craig Barton, featuring recommended resources, discussions of best practice, conversations with leading educational professionals and more.

You can listen to the first episode by clicking here. TES are working on putting the series on iTunes shortly so they can be downloaded onto your iPhone, iPod, computer etc.

Highly recommended.

# The Math Factor

The other day, a friend of mine brought an excellent little podcast to my attention called * The Math Factor*. Suitable for pupils and teachers alike, the 10 minute episodes feature interesting problems and concepts within mathematics. Hilbert’s Infinity Hotel, Algebra on the Radio and Space Walkers; there is something here to engage any mathematically minded person. The show is pitched beautifully, making it accessible to people of all mathematical abilities. Highly recommended.

# A watertight demonstration of Pythagoras’ Theorem

Thanks to +Jerry Smith for bringing this to my attention. Lovely!

# Angle fact flashcards (including circle theorems)

How often do your pupils calculate the answer to an angle fact question correctly, but then don’t get the mark for the ‘*give a reason for your answer*‘ question? Rather than ‘*alternate angles are equal*‘ they write any manner of things such as ‘*it is a z shape and so the angles are the same*‘. Since ‘*z angles*‘ is no longer accepted on the GCSE exam, they stand no chance of getting the mark, even though they do know the concept.

Pupils must know the appropriate angle fact language and use it. Repetition is the key and so I have created a set of flashcards that you can use with your classes on a regular basis as a quick starter to revise the angle facts. The idea is you print them out, laminate them and then shuffle them. You hold them up one at a time and the class have to say the angle fact using the correct language. You could project them on the board instead or even turn it into a mini-test. They are levelled from 3 to 8 and include types of angle, angle facts (basic and in parallel lines), the 3 rules of bearings and all the circle theorems so you can use whichever ones are appropriate for your class.

# Sunflowers are applied mathematicians at heart

I have known about the beauty of the pattern of seeds in the heads of sunflowers for a long time now, but still stare in wonder just as I did when I saw it the first time. You count the number of spirals in each direction and find that they are two consecutive numbers in the Fibonacci Sequence.

I recently heard that the pattern also includes the Golden Angle. This is when you divide up 360 degrees into two angles in the Golden Ratio. The smaller angle is the Golden Angle which is irrational and measures 137.508… degrees. The seed pattern is formed by seeds being ‘fired’ from the centre of the flower head outwards one at a time. The angle that each seed heads off from the centre when measured from the last one is the Golden Angle.

For a bit of fun I thought I’d write a computer simulation of this procedure to see if I could replicate the pattern. I then also changed the angle of consecutive seeds to plus and minus one degree from the Golden Angle to see how sensitive the pattern is to the angle. The results are surprising!

It seems as though the seed pattern is extremely sensitive to the angle that the seeds are released! Therefore we must conclude that sunflowers are great admirers of the beauty of mathematics! They are applied mathematicians at heart, putting their knowledge into a wonderful real world application!

# Geogebra for iPad…

I looked into the feasibility of using iPads in the maths classroom last year and concluded that the time wasn’t quite right. The ‘planets were moving into alignment’, with the direction of technological development leading towards the iPad being a brilliant learning tool in the maths classroom, but they weren’t there yet.

The lack of Flash compatibility was a big issue as sites like MyMaths and Manga High use it. Also, QuickGraph is an excellent free graph plotting app but I couldn’t find an app that also handles dynamic geometry. If only Geogebra had an app for the iPad…

There is a Kickstarter project to develop the Geogebra app for the iPad. They need to raise $10 000 to develop it which will then be a free download from the App Store.

You can read more about the project on the superb Math and Multimedia blog here.

# The Chaos Game- a very surprising result

Created by Michael Barnsley, The Chaos Game is a deceptively simple idea, but the results are astonishing.

Start with an equilateral triangle, a pencil, a ruler and a die. Label one vertex of the triangle “1 and 2″, the next “3 and 4″ and the final one “5 and 6″. Mark a dot on one of the vertices of the equilateral triangle. Now roll the die. This tells you which corner of the triangle to move towards. Mark your next dot half way between your last dot and the corner of the triangle your die identified. Then roll the die again and mark your next dot half way between your last dot and the corner of the triangle your die identified. Repeat this until you discover the beautiful result!

You may like to write a spreadsheet to do this for you rather than constructing it by hand. I wrote a spreadsheet that did 10 000 trials and look at the result:

You get the famous fractal, Sierpinski’s Triangle!

If you extend the idea into three-dimensions, adding a fourth vertex directly above the centre of the equilateral triangle, the points form a Sierpinski Tetrahedron!