This month, Lindsey Bowkett (@MissBowkett) and I have been challenging ourselves to draw a mandala a day in May. We both wanted to get back into the swing of making art regularly, and when Lindsey coined the hashtag #Maydala, we were off!

We have been delighted to have been joined on the journey by many other maths teachers across Twitter – here are some of their wonderful designs. For even more marvellous mandala mayhem, do check out the #Maydala hashtag!

Mandalas are rich in mathematics (circle geometry, reflective and rotational symmetry), and provide useful practice with geometry tools including rulers, compasses and protractors. Several teachers have asked how to introduce the activity to their students, so I have decided to collate the ideas and resources from my original twitter thread here.

The word ‘mandala’ means ‘circle’ in Sanskrit, and mandalas have a deep spiritual or cosmic meaning in many cultures and traditions. For our #Maydala purposes, a mandala is any circular design exhibiting pattern and symmetry.

Mandala making is accessible to all. The repetitive nature of these designs means that drawing them can be a wonderfully absorbing and meditative process, and it's a process that results in stunning geometrical patterns - bonus!

Designs can be drawn entirely freehand, or using a mixture of freehand and compass/ruler construction, or solely compass and ruler construction. Anything goes! Some participants are even using technology or origami to make their mandalas, with stunning results:

So, how do you get started? These Wikihow instructions are really clear and easy to follow:

And this set of video tutorials from Kathryn Costa (@100mandalas) are very useful too.

Lindsey (@MissBowkett) has made a series of lovely timelapse videos showing her process, such as this one:

And Miss Konstantine (@giftedHKO) made this set of instructions for a fabulous cube mandala, which Becky Warren (@becky_k_warren) followed to make her version, coloured in with colouring pencils, below.

But there are lots of other things you can do too!

How about making a mandala from objects around the house, or from things found on a walk outside? The artist James Brunt (@RFJamesUK) makes fabulous designs from found objects, or from the contents of his junk drawer!

Or if you have a pebble collection you could get creative and add some dotty colour. Check out this totally scrumptious work by the artist Elspeth McLean!

If you’ve got a Spirograph set gathering dust in a cupboard somewhere then this is the perfect excuse to dust it off and get spiralling. Metallic pens add that extra bling!

Fancy giving your compasses a workout? Islamic geometric patterns begin with a single circle, and are some of the most beautifully proportioned patterns in the world. Check out Samira Mian's (@samira_mian) Youtube channel for some clear and easy-to-follow tutorials. Here is a lovely circular pattern perfect for a mandala!

So, a plethora of resources and ideas to help you get started! If you post your finished artwork on Twitter, be sure to use the #Maydala hashtag. You can use it any time of the year - why not?!

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!