The Joy Of Planning

I had corking fun planning a lesson on tessellation lastly week. Planning lessons is 1 of my favourite parts of the job.

This lesson for sure won't live everyone's loving cup of tea, but I enjoyed planning it so much I wanted to percentage it here. Tessellation is no longer on the GCSE specification but I think it helps students prepare their cognition of angles inward polygons, addition it's interesting, so is worth looking at.

I started amongst a quick Don Steward interrogation aimed at refreshing my students' memories on how to calculate angles inward polygons, which I'd taught them the twenty-four hours before.

I so asked the class, "What is tessellation together with where do nosotros encounter it?". One or 2 students described it inward damage of tiling, together with some pointed out examples of tessellation only about the room (the painted bricks on the wall, the foursquare vinyl tiles on the floor). I gave them a definition, which they noted down, together with nosotros talked virtually the pregnant of the discussion plane in this context.

I told them virtually the etymology of the discussion tessellated. In planning this lesson I was interested to abide by that the discussion derives from the discussion 'four', referring to iv corners.

tessellated (adj.)
1690s, from Late Latin tessellatus "made of modest foursquare stones or tiles," past times participle of tesselare, from tessella "small foursquare rock or tile," diminutive of tessera "a cube or foursquare of rock or wood," possibly from Greek tessera, neuter of tesseres, Ionic variant of tessares "four", inward reference to iv corners.

I showed them some pictures of tessellations.

I spoke of The Alhambra. Influenza A virus subtype H5N1 pupil position upwards his mitt together with told me he'd been there. I told him I was really jealous - I long to visit.

I also talked virtually Escher. Having of late been to the Escher exhibition at Dulwich Picture Gallery I could select happily talked virtually Escher for the total hour, but alas - fourth dimension is limited. My Year 10s were amused when I told them that inward the 60s Escher's run was loved past times both hippies together with mathematicians. Influenza A virus subtype H5N1 pupil position upwards his mitt together with said he had a majority total of Escher's artwork at home. This made me happy.

I showed some examples together with non-examples of tessellation (when planning lessons I oft do a quick trawl of google images for the pictures I demand to illustrate a point).

They noticed that the angles only about the request select to amount to 360^o if the polygons are to tessellate. 

I showed an instance of a semi-regular tessellation, which tin live created past times using 2 or to a greater extent than regular polygons repeatedly to tile the bird (for instance an octagon together with a square).

I so showed them a serial of animations from a Tumblr occupation concern human relationship called Skunk Bear. They were 'wowed' past times these animations (one man child asked, "where do you lot larn all this cool stuff, Miss?". "Mostly through Twitter" I replied.). I think these gifs volition assist my students retrieve what tessellation is. If not, the animations for sure assist foster an enthusiasm for the beauty together with complexity of mathematics.

Tessallating equilateral triangles

Non-tessellating pentagons

When I told them virtually the recent uncovering of a novel type of tessellating pentagon ("It's a actually large deal", I said) - they laughed. "Miss, are in that place actually people who pass their life looking for tessellating pentagons? Shouldn't they live trying to abide by the cure for cancer or something?".

Tessellating pentagons - every bit discovered inward 2015

All of this chat virtually tessellation took a proficient 25 minutes. It was a flake longer than I usually talk, but that's ok. They listened intently, together with their reactions suggested that they were interested. I could select gone on for longer - exercise.

During this practise some students asked virtually the names of a 20-sided together with 15-sided polygon, together with thankfully I had a listing to mitt (borrowed from a Don Steward slide) together with nosotros chatted virtually the words. I overheard some students trying to interruption the words downwards together with brand feel of them.

Some of my students completed the tessellation activity actually speedily - others took a lot longer. I followed it upwards amongst 2 Don Steward activities (Regular Polygon Angle Compilation together with Pentagon Angle Compilation) which were pretty challenging. These activities developed their fluency inward calculating angles inward polygons. Towards the halt of the lesson I invited a brace of students to come upwards up to the board together with utter through their approaches to these problems.

In the lastly infinitesimal of the lesson I decided to convey everyone dorsum together to say them virtually platonic solids. One pupil kept referring to a dodecagon every bit a dodecahedron during the lesson so I wanted to alternative upwards on the divergence betwixt gon together with hedron. So I ended upwards amongst an unplanned tangential plenary...

This lesson may select been relatively lite inward 'exam content' but it was rich inward mathematics. It mightiness non select ticked all the 'good lesson' boxes, but I felt that it went well.

I don't write formal lesson plans. I do minimalist PowerPoints instead. I brand no apologies for using slides - this is non 'death past times PowerPoint' - it's only a flake of structure. Here's my slides for this lesson, experience complimentary to borrow whatever bits that you lot like.

Do I sometimes pass besides long planning lessons? Absolutely! Are my lessons the 'best possible agency of educational activity that topic'? Absolutely not. I select non perfected the fine art of educational activity mathematics. This tessellation lesson is really 'me', together with I incertitude anyone would desire to learn it inward the same agency I did.

I relish lesson planning. It allows me to explore my subject. It allows me to live creative. I wholly handle with Megan Guinan's recent tweet, "Planning lessons is my 2d favourite business office of the job, after delivering a lesson I've planned well."

I'd beloved to hear all virtually a lesson you've taught of late that you lot especially enjoyed planning together with delivering.

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