5 Maths Gems #16

It's December! Time for students as well as teachers to kickoff getting overly excited nearly the upcoming Christmas holidays. There's yet iii to a greater extent than weeks of teaching to learn through though, as well as most schools do mock GCSEs inward Dec or January, thence things are equally busy equally ever. Let's expect at or thence of the ideas that receive got been shared on Twitter this week. I've got lots of overnice geometry for y'all today.

1. Frozen Fractals

I'm non a fan of Disney princess films, only I receive got daughters at nowadays thence I've been forced to picket Frozen many many times. I truly quite similar it. Being a mathematician, my favourite business office is when Elsa sings nearly 'frozen fractals' inward the vocal Let it Go. I had no stance what the give-and-take fractal meant until a few years agone thence it seems strange to remove heed it inward a children's film. It got me thinking - is in that place whatever value inward teaching our students nearly fractals at secondary school? I squall upwards in that place 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 means to empathise fractals is to clitoris 1 - the article describes how to clitoris a Von Koch curve.

Give your students or thence dotted or triangle graph newspaper as well as they could follow the instructions inward this worksheet to clitoris 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, only nosotros tin flame expect at other fractals too. The Sierpinski Triangle is also a overnice 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 then 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 1 pictured below.

And this Mathematical Christmas Tree is equally fractally equally they come.

If y'all desire to farther explore fractals, your students mightiness hold out interested inward this Numberphile video 'Measuring Coastline'.

Whether y'all brand snowflakes, triangles or cutouts, the signal is that students come upwards away from the lesson agreement what a fractal is. It may non hold out on the syllabus only it's interesting mathematics nonetheless. And your students volition hold out able to country their friends that they empathise the mathematical reference inward Frozen.

2. Angles
I honey this angles interrogation from @j_lanier. I'd role it inward a GCSE revision lesson. Students receive got to apply a number of rules to uncovering all 4 angles - it's a proficient 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 yesteryear Don Steward, when I noticed a link to a weblog I'd non seen earlier - Pythagorean Triple Tasks yesteryear Hannah Jones. There's or thence lovely activities here.

By the way, speaking of Don Steward, did y'all know he also has a blog for exercise resources? These are equally good designed equally his rich tasks. There's loads of proficient questions for GCSE revision, which y'all mightiness uncovering 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 y'all run across Ed Southall's awesome semi-circle problem? I'd role this equally an extension activeness inward a Pythagoras lesson, only 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 upwards to Influenza A virus subtype H5N1 level.

5. Christmassy Maths
I started to write a seasonal maths resources page only lots of other lovely bloggers receive got done something similar. So rather than reinvent the wheel, I'll signal y'all inward the administration 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 proficient exercise of forthwith business graphs. I also similar these resources from Oxford University Press. Most Christmas resources are aimed at Key Stage 3 students, only your Year 11s mightiness similar this Christmas Shading Graphical Inequalities by frickard on TES. And how nearly this lovely Christmas tree logic problem?

Logic work from ageofpuzzles.com

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

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