This lesson for sure won't live everyone's loving cup of tea, but I enjoyed planning it so much I wanted to portion it here. Tessellation is no longer on the GCSE specification but I think it helps students railroad train their cognition of angles inward polygons, summation it's interesting, so is worth looking at.
I started amongst a quick Don Steward inquiry aimed at refreshing my students' memories on how to calculate angles inward polygons, which I'd taught them the 24-hour interval before.
I too then asked the class, "What is tessellation too where do nosotros run into it?". One or 2 students described it inward price of tiling, too 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, too nosotros talked most the important of the discussion plane in this context.
I told them most the etymology of the discussion tessellated. In planning this lesson I was interested to regain that the discussion derives from the discussion 'four', referring to 4 corners.
I spoke of The Alhambra. H5N1 pupil set upwards his mitt too told me he'd been there. I told him I was real jealous - I long to visit.
I also talked most Escher. Having of late been to the Escher exhibition at Dulwich Picture Gallery I could accept happily talked most 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 travel was loved past times both hippies too mathematicians. H5N1 pupil set upwards his mitt too said he had a mass total of Escher's artwork at home. This made me happy.
I showed some examples too non-examples of tessellation (when planning lessons I oftentimes do a quick trawl of google images for the pictures I demand to illustrate a point).
I showed an instance of a semi-regular tessellation, which tin forcefulness out live created past times using 2 or to a greater extent than regular polygons repeatedly to tile the bird (for instance an octagon too a square).
I too then showed them a serial of animations from a Tumblr draw of piece of work organisation human relationship called Skunk Bear. They were 'wowed' past times these animations (one man child asked, "where do yous larn all this cool stuff, Miss?". "Mostly through Twitter" I replied.). I think these gifs volition assist my students recollect what tessellation is. If not, the animations for sure assist foster an enthusiasm for the beauty too complexity of mathematics.
When I told them most the recent uncovering of a novel type of tessellating pentagon ("It's a actually large deal", I said) - they laughed. "Miss, are at that topographic point actually people who pass their life looking for tessellating pentagons? Shouldn't they live trying to regain the cure for cancer or something?".
During this practise some students asked most the names of a 20-sided too 15-sided polygon, too thankfully I had a listing to mitt (borrowed from a Don Steward slide) too nosotros chatted most the words. I overheard some students trying to pause the words downward too 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 too Pentagon Angle Compilation) which were pretty challenging. These activities developed their fluency inward calculating angles inward polygons. Towards the destination of the lesson I invited a duad of students to come upwards up to the board too verbalize through their approaches to these problems.
In the concluding infinitesimal of the lesson I decided to pick out everyone dorsum together to state them most platonic solids. One pupil kept referring to a dodecagon equally a dodecahedron during the lesson so I wanted to alternative upwards on the departure betwixt gon too hedron. So I ended upwards amongst an unplanned tangential plenary...
This lesson may accept been relatively lite inward 'exam content' but it was rich inward mathematics. It mightiness non accept 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 chip of structure. Here's my slides for this lesson, experience gratis to borrow whatsoever bits that yous like.
Do I sometimes pass likewise long planning lessons? Absolutely! Are my lessons the 'best possible agency of instruction that topic'? Absolutely not. I accept non perfected the fine art of instruction mathematics. This tessellation lesson is real 'me', too I doubtfulness anyone would desire to learn it inward the same agency I did.
I savour lesson planning. It allows me to explore my subject. It allows me to live creative. I wholly concur 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 dear to hear all most a lesson you've taught of late that yous peculiarly enjoyed planning too delivering.
tessellated (adj.)I showed them some pictures of tessellations.
1690s, from Late Latin tessellatus "made of pocket-sized 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," perchance from Greek tessera, neuter of tesseres, Ionic variant of tessares "four", inward reference to 4 corners.
I also talked most Escher. Having of late been to the Escher exhibition at Dulwich Picture Gallery I could accept happily talked most 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 travel was loved past times both hippies too mathematicians. H5N1 pupil set upwards his mitt too said he had a mass total of Escher's artwork at home. This made me happy.
I showed some examples too non-examples of tessellation (when planning lessons I oftentimes do a quick trawl of google images for the pictures I demand to illustrate a point).
They noticed that the angles only about the betoken accept to total to 360o if the polygons are to tessellate.
I showed an instance of a semi-regular tessellation, which tin forcefulness out live created past times using 2 or to a greater extent than regular polygons repeatedly to tile the bird (for instance an octagon too a square).
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| Tessallating equilateral triangles |
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| Non-tessellating pentagons |
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| Tessellating pentagons - equally discovered inward 2015 |
All of this chat most tessellation took a expert 25 minutes. It was a chip longer than I usually talk, but that's ok. They listened intently, too their reactions suggested that they were interested. I could accept gone on for longer - exercise.
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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 chip of structure. Here's my slides for this lesson, experience gratis to borrow whatsoever bits that yous like.
Do I sometimes pass likewise long planning lessons? Absolutely! Are my lessons the 'best possible agency of instruction that topic'? Absolutely not. I accept non perfected the fine art of instruction mathematics. This tessellation lesson is real 'me', too I doubtfulness anyone would desire to learn it inward the same agency I did.
I savour lesson planning. It allows me to explore my subject. It allows me to live creative. I wholly concur 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 dear to hear all most a lesson you've taught of late that yous peculiarly enjoyed planning too delivering.
