I'm delighted to have been asked to take part in Emily Grosvenor's blog tour for her new children's book, 'Tessalation!'. Emily (@emilygrosvenor) has always had a particular interest in tessellations and was instrumental in organising the first World Tessellation Day on 17th June this year (a wonderful celebration; check out the hashtag #WorldTessellationDay). Her book, funded via a successful Kickstarter campaign, describes the adventures of girl named Tessa, who enjoys hiding herself in the tessellating patterns she finds in the world around her. The illustrations by Maima Widya Adiputri are exquisite, and the book provides the perfect way to introduce young children to the mathematics of pattern-making by tapping into their inherent curiosity about the natural world.
Emily's work got me thinking about the many ways we can use the appealing aesthetics of tessellations to engage the students in our mathematics classrooms. The book itself contains clear step-by-step instructions for making tessellating tiles or 'tesserae' from a starting square. These instructions would be suitable for use with students of all ages (see the central image below) and the method is explained in more detail in this post on the Kids Math Teacher blog.
Many other bloggers on the tour have contributed their ideas for exploring tessellations with children. For secondary students, Brent Yorgey's post presents a clear introduction to the geometrical reasoning behind the mathematics of tessellations. And the post by John Golden (@mathhombre) contains links to his comprehensive resources page covering many aspects of this rich topic.
One of the lesser known ways of working with tessellations is through the medium of paper folding (a favourite pursuit of mine) and I have come across two great resources to support teachers in working with this technique in the classroom.
The first is this fascinating publication from Liz Meenan, which explains how to create various Islamic-influenced tiling patterns (see below) from squares, equilateral triangles, kites and hexagons folded from A-sized paper. Liz has kindly allowed me to use her instructions on this presentation and handout.
The second is this fantastic resource from mathematical origamist David Mitchell, found on his website origamiheaven.com. The whole website is worth exploring, especially if you are interested in mathematical or modular origami. The instructions for folding origami tiles from 'silver rectangles' (A-sized paper is a good approximation) are of particularly high quality, and the easiest ones to fold would be accessible to students from early primary upwards. For example, it would never have crossed my mind that the trapezia created from a simple, single fold would tessellate in such a variety of ways!
David's detailed instructions also discuss the angles, geometry and symmetries of the various tiles, along with investigations of area and perimeter (including work with surds), which make this activity suitable for students across the full age range. Truly worth a look.
I do hope you've been inspired to explore some of these tessellation resources in your classroom. As always, please do share your experiences on Twitter, or in the comments below.