When I left my first teaching school (the one I’m back working at again now) I decided to make a piece of art as a leaving gift for my colleagues in the maths team. I’d seen an image on Pinterest of a mural made from different coloured paper tetrahedra, and wanted to try it for myself. However, being a maths teacher, I was intrigued by the possibilities of tessellating smaller tetrahedra within the gaps left by bigger tetrahedra....

Now I know that A-sized paper has some pretty cool properties, so, using the photocopier I reduced an A4 tetrahedron net down through the various A-sizes - and, yes, I made some lovely discoveries (which made perfect sense once I started thinking about it)!

Each iteration of A-sized paper decreases in area by half, (so the side lengths decrease by a factor of 1/(sqrt2)): A5 is half the area of A4, A6 half the area of A5, and so on. So the base of an A6 tetrahedron is a quarter the area of an A4 base, meaning that four A6 tetrahedron bases can be packaged in the gap left by an A4 tetrahedron. I played around and found some other combinations (see some examples below).

I printed and cut out all my nets, assembled my different sized tetrahedra (step-by-step instructions to follow below) and played around with lots of different arrangements. When finally happy, I stuck them down onto a ready-made canvas.

A week ago my ex-colleague Ali got in touch because she wanted to try the activity with her class. I talked her through the instructions and her students went on to produce the wonderful artwork below :)

Here are the step-by-step instructions if you would like to try this activity with your students.

I've come across a few mathsy-arty Halloween-themed ideas over the last week or two, and include here three that would make lovely classroom activities.

An Origami Bat

Geometric Halloween masks

These geometric paper masks by @Wintercroft (below), available from www.wintercroft.com, have often caught my eye on Twitter, and when I found out that there was a sixth form Halloween Fancy Dress Day coming up on the 31st, I finally had an excuse to try them out!  I treated my Y12 Further Maths group to a mask-making session after their end of term assessment.  No photos of their handiwork yet, as students have taken them home to finish - I'm very much looking forward to seeing their end results on Monday.

These masks are not strictly-speaking origami, but are instead constructed from printable 'nets' or templates.  Although the masks are sold for personal use only, Wintercroft are keen to promote craft in educational settings, and will allow the printing of class sets for one-off projects, so long as the digital files are not saved or stored on shared computers, or otherwise shared or distributed.

The masks can be made from cereal boxes or other recycled card, but I printed the templates directly onto white 160 gsm card, which was just about sturdy enough.  We used the slightly more time-consuming, but more robust, tabbed assembly method and stuck the pieces together using a glue stick.  I made the bat half-mask (above, top left) and found it very straight-forward to assemble.  I shall spray paint it black, and swoop around campus on Monday :)

The templates come with full instructions, but there is also a video guide.  And the maths?  As well as encouraging patience, perseverance and attention to detail, this would be a good activity to link to polygons, nets and polyhedra - how many different polygonal faces can your students spot and name?  And what about the challenge of designing their own geometric mask?!

Tessellated Halloween skulls

Chris Watson (@tessellationART), a digital tessellation artist, has produced a wonderful short video that shows the design process behind one of his recent pieces, a skulls triptych inspired by Mexican 'Day of the Dead' imagery.  As well as incorporating tessellations, the skulls also include a repeating fractal element where the skull appears again in the eye socket, and again, disappearing off into infinity.  This is a really nice resource for stimulating class discussion on lots of levels.

Do feedback in the comments below, or on Twitter, if you try any of the activities.  I'd love to see photos of your students' work.  And Happy Halloween!

This year I have started an exciting new role as STEM Faculty Lead Practitioner and KS5 teacher of maths at a stand-alone sixth form campus.  This has meant a whole new classroom to decorate (and how I love a display challenge!).  However, it being an A Level only classroom, I have had to completely rethink what displays might be suitable, and ditch some old favourites - alas, 'squares and cubes' is no more!

Over the summer I kept an eye out on Twitter for ideas and resources, and spent a couple of enjoyable afternoons in the last week of the holiday putting it all together.  With a big thank you to those who share their wonderful resources and ideas for free, here are some photos of the end result:

I thought it might be useful to provide links to all the displays that I collated from Twitter.   I'll take it wall by wall, from left to right...

The side wall:

The Greek Alphabet display is by Sarah Carter (@mathequalslove) and is one of a host of fantastic display resources on her website.  I think it adds a note of historical interest and background to some of the new mathematical symbols my students will encounter over the course of their sixth form studies.

The A Level Notation Periodic Table is a lovely twist on the well-known original by Mel Muldowney (@Just_Maths) and is by Clare Mazurkiewicz (@MrsMazzy).  It's an absolute must in an A Level classroom!  I've referred to it so many times already, and love the fact that it whets the appetite of those students new to A Level: look at all that exciting stuff ahead!  I used pre-cut display lettering to make the title underneath.

The 'Wall of Death' is a set of those 'Everytime you do this: ... an ... dies' (insert horrific-yet-alarmingly-common misconception and cute animal of choice) posters that you will have come across before.  Helpfully, @MathCurmudgeon has collated the full set on his blog, and, I think, added a few of his own.  Unfortunately I seem to be referring to these posters rather a lot at the moment (those poor, poor kittens!)!

Finally, above the whiteboard there's my version of the 'How to Learn Maths' flow chart which is available for download on my Classroom Display Ideas page.

The back wall:

This wall is dominated by large whiteboards, a resource that's new to me, and which I'm really enjoying seeing the students use.  Great for on the spot assessment, discussion and feedback.  However, there's still space above and below them for some bright displays...

Above the whiteboards I've put up my quotes from famous mathematicians and thinkers, which are available for download on my Classroom Display Ideas page.

Along the bottom I've used the wonderfully creative 'Maths Mr. Men' from Ed Southall (@solvemymaths), a poster set that's clever, fun and informative - ideal for an A Level classroom.  There are two lots of posters available, downloadable from Ed's excellent website.

The window wall:

I haven't had a classroom with a view for a while, so I decided I needed to frame my beautiful new view with some maths bunting.  Most of the bunting out there is GCSE-focused (see the links on my display page) but this lovely bunting from K Pitchford (@Ms_Kmp) is perfect and lends a note of cultural and artistic interest.

And the windowsill provides the perfect surface on which to display all my modular origami (in an attempt to entice more students along to my club!)  If you are interested in finding out more about this highly geometric form of origami, see my earlier blog post on the subject.

The front, teaching wall:

On the far left is my version of @mathequalslove's Growth Mindset display, available for download on my Classroom Display Ideas page.  I felt the message of this display was just as relevant at A Level, and have already referred to it a few times this term.

In the centre, at the top, I've put up my old 'mistakes quotes', also still relevant and also available for download on my Classroom Display Ideas page.

Underneath these there's a number line.  I ummed and ahhed at first about whether or not to put this up; it felt a bit too 'lower school'.  But then I thought back to how often I'd referred to my number line in sixth form lessons previously, and realised it was still important for teaching at this level.  I use it when talking about limits to infinity, domains of functions, the modulus function, solution sets for inequalities and so on. 

On the right of the IWB is a giant graphics calculator poster which was already in the classroom when I arrived.  Billy Adamson, (@Billyads_47) my head of department, and major 'GC' fan, had these printed for the team a while ago.  If you're interested in where he got these done, do contact him on Twitter.  I have to confess I've never mastered my GC, but will be teaching Stats 1 for the first time this year, so it'll soon be time to face my fears!

Above the right hand whiteboard I've put the 1-9 number facts poster set by Ed Southall. These are very intriguing.  For example, why is the number 1 'narcissistic'?  Why on earth is 5 'hungry'?  And why is 7 'odious'?!

With all the great display resources out there, there's no reason at all why A Level maths classrooms can't be bright, colourful and informative learning environments.  Feedback from my students has been really positive.