4 January 2015

5 Maths Gems #21

Happy New Year and welcome to my 21st gems post - this is where I share five teaching ideas that I've seen on Twitter in the past week. Now I'm back at work from maternity leave, I expect these posts will become fortnightly rather than weekly. Sadly, marking and lesson planning will mean I have less time to gather ideas from Twitter.

My aim for 2015 is to continue to work towards a post for every topic, so that when you're planning lessons you can refer to these posts and there's everything you need - concepts, ideas, resources, enrichment and links. I really hope these posts reduce the amount of time you have to spend searching the internet. My latest post was on Teaching Indices, and you can see the full range here.

1. Brilliant
I've been enjoying the questions from brilliant.org this week. It has a big range of mathematical problems that you could use in lessons (algebra, geometry, calculus, mechanics etc). Plenty of the problems are available for free - full solutions, extra problems and a bunch of other stuff is available for a small subscription.

Here's a couple of examples of problems for your students:
Some topics also have explanations and interesting worked examples - check out the chapter on the volume of a pyramid. The associated quiz has questions like the one shown below.
So if you're looking for interesting questions to use when teaching a specific topic then you might find Brilliant helpful.

Also, if you're looking for some challenging problems to have a go at yourself, I recommend you like Brilliant.org on Facebook - you'll get a nice flow of problems in your newsfeed. Here's what Facebook presented me with this morning - this is a level 2 question (levels go from 1 to 5, with 5 being the most difficult).
2. FOIL
Whether or not you teach 'FOIL' as a method for expanding brackets, watch the video below.

By the way, I don't think there's necessarily anything terribly wrong with teaching 'FOIL' as long as students know that the order doesn't matter. When I was at school I was just told to 'multiply everything in the first bracket by everything in the second bracket' and as a result I use a range of FOIL, FIOL, FOLI and FILO on the board... sometimes my students who've been taught FOIL think I'm doing it wrong. It's really important that we emphasise that there is no set order. I suppose FOIL just helps students keep track of their workings.

3. BODMAS
Sticking with the excellent videos from @minutephysics, if you haven't seen this one about PEDMAS (that's BODMAS in the UK), it's well worth a watch (thanks to @JustinAion for sharing). The order of operations turns humans into robots!

4. Furbles
I may be the last maths teacher to hear about Furbles, but in case anyone else hasn't heard of them, they deserve a mention here. Thanks to Hannah (@missradders) for bringing this cute statistics teaching tool to my attention.

Furbles can be used to teach statistical graphs and probability - if you've not seen them before then have a play around - there's two web-based versions on the website, plus a downloadable version here. Examples of Furbles-related questions are shown below, and there's a more comprehensive list here (thanks to @clwatson999 for sharing this link).
• Which is the best graph to show you which is the most and the least?
• What would the key for this pie chart look like?
• What is the probability the next starred Furble will be … a purple triangle with 4 eyes?
You can also ask students to make a set of Furbles to give particular chart properties or a specified probability distribution.

5. Euclid the Game
A few people have recommended Euclid the Game to me and I finally got round to having a good look at it. I see what all the fuss is about now. I'm teaching loci and constructions soon so I think I'll book an IT room to let my students have a go at this game. After a short tutorial in which they learn how to use the basics of GeoGebra, students are asked to do a series of constructions.
What I like about it is that students who normally just learn a procedure for these constructions have to think about how the constructions actually work (ie they're not just drawing arcs). It's a great game so if you've not seen it before, do have a look.

Well that's it from me today. Hope you all have a good first week back at school!