5 Maths Gems #16

It's December! Time for students as well as teachers to outset getting overly excited almost the upcoming Christmas holidays. There's even thus 3 to a greater extent than weeks of teaching to larn through though, as well as most schools do mock GCSEs inward Dec or January, thus things are every bit busy every bit ever. Let's expect at roughly of the ideas that receive got been shared on Twitter this week. I've got lots of dainty geometry for you lot today.

1. Frozen Fractals

I'm non a fan of Disney princess films, merely I receive got daughters at nowadays thus I've been forced to scout Frozen many many times. I genuinely quite similar it. Being a mathematician, my favourite business office is when Elsa sings almost 'frozen fractals' inward the vocal Let it Go. I had no persuasion what the give-and-take fractal meant until a few years agone thus it seems strange to listen it inward a children's film. It got me thinking - is at that spot whatever value inward teaching our students almost fractals at secondary school? I remember at that spot is. 

What are Fractals as well as why should I care? by George Dallas. This is an incredibly clear as well as accessible article. The best agency to sympathize fractals is to push clit i - the article describes how to push clit a Von Koch curve.

Give your students roughly dotted or triangle graph newspaper as well as they could follow the instructions inward this worksheet to push clit a 'Koch snowflake'. While they're creating their fractals, exhibit them this lovely microscopic timelapse video of existent snowflakes (thanks to @misseyfs for sharing this).

Because I'm writing this post on 1st Dec I'm thinking of Christmassy snowflakes, merely nosotros tin expect at other fractals too. The Sierpinski Triangle is also a dainty introduction to agreement fractals. The awesome website fractalfoundation.org has an fantabulous worksheet (a 'fractivity') in which each of your students brand their ain Sierpinski Triangle - they as well as thus stick them together to brand a 'class fractal'. Show the video on the page Fractal Trianglethon to wow your students alongside giant Sierpinski Triangles!

Alternatively your students could create Fractal Cutouts like the i pictured below.

And this Mathematical Christmas Tree is every bit fractally every bit they come.

If you lot desire to farther explore fractals, your students mightiness survive interested inward this Numberphile video 'Measuring Coastline'.

Whether you lot brand snowflakes, triangles or cutouts, the betoken is that students come upwardly away from the lesson agreement what a fractal is. It may non survive on the syllabus merely it's interesting mathematics nonetheless. And your students volition survive able to say their friends that they sympathize the mathematical reference inward Frozen.

2. Angles
I dearest this angles interrogation from @j_lanier. I'd travel it inward a GCSE revision lesson. Students receive got to apply a number of rules to honor all 4 angles - it's a expert chance for them to practise articulating their reasoning.

3. Pythagorean Triples
I was looking at recent posts on my favourite blog, the ever-brilliant Median past times Don Steward, when I noticed a link to a weblog I'd non seen earlier - Pythagorean Triple Tasks past times Hannah Jones. There's roughly lovely activities here.

By the way, speaking of Don Steward, did you lot know he also has a blog for do resources? These are every bit good designed every bit his rich tasks. There's loads of expert questions for GCSE revision, which you lot mightiness honor useful this calendar week if your Year 11s receive got mocks coming up. I especially similar these grids of 'practice makes perfect' questions. Also, I spotted this fantastic work inward his A & A* questions - a lovely starter for my Year 12s:

4. Semi-circle

Did you lot run across Ed Southall's awesome semi-circle problem? I'd travel this every bit an extension action inward a Pythagoras lesson, merely there's loads of methods for solving it - others receive got used similar triangles, trigonometry as well as coordinate grids. It's both accessible as well as challenging for students from Key Stage 3 upwardly to H5N1 level.

5. Christmassy Maths
I started to write a seasonal maths resources page merely lots of other lovely bloggers receive got done something similar. So rather than reinvent the wheel, I'll betoken you lot inward the direction of:

• @missradder's post Christmaths
• @Ms_Kmp's post ChrisMaths Cheer
• @solvemymaths' post 2014 Christmas Maths Lessons

There are hundreds of fantabulous Christmas-themed maths resources. I'd similar to recommend a few inward add-on to those inward the posts above. There are 2 from Teachit Maths that I especially similar - the 12 days of Christmas budget activity which involves work solving using percentages, as well as Mistletoe as well as Lines which is expert do of at nowadays business graphs. I also similar these resources from Oxford University Press. Most Christmas resources are aimed at Key Stage 3 students, merely your Year 11s mightiness similar this Christmas Shading Graphical Inequalities by frickard on TES. And how almost this lovely Christmas tree logic problem?

Logic work from ageofpuzzles.com

That's it for this week. Please don't forget to conk on tweeting or emailing me photos of misconceptions or mutual mistakes inward your students' work. Thanks!