## 17 November 2014

### 5 Maths Gems #14

Welcome to my 14th weekly gems post - this is where I feature five of the best teaching ideas I've seen on Twitter each week.

You may or may not know that I've been writing these posts while I've been at home on maternity leave. My baby keeps me busy during the day, but my evenings are blissfully free from marking and lesson planning so I have a rare opportunity to reflect on my teaching and gather new ideas. It's a shame that all teachers can't take a mini-sabbatical every five years to do the same. When I go back to work in January I'll have 100 maths teaching gems in my toolkit - it will be hard to know where to start!

1. Two Truths and a Lie
Two Truths and a Lie is traditionally an icebreaker game - someone tells you three facts about themselves and you guess which one is the lie. For example my brother might tell you that he was once bitten by a donkey, he was once bitten by a snake and he was once bitten by a monkey. Bizarrely, only one of those statements is a lie. So let's take this game and turn it into an activity that prompts mathematical discussion.

This idea came from a tweet by @TCM_at_NCTM:

 Polygons (source: mathsisfun.com)
This tweet made me realise that I'm guilty of lazily telling my students that polygon is 'just another word for shape' when in fact I should be more specific - a polygon is a 2D figure with at least three straight sides and angles (the word derives from the Greek 'many-angled'), so a circle is not a polygon.

The two truths about quadrilaterals ('a square is a rectangle' and 'a rectangle is a parallelogram') will also prompt interesting discussions about definitions. The quadrilateral family tree might help clarify things. The Euler diagram below is also helpful.
Here's a couple more examples of mathematical 'Two Truths and a Lie' activities:
A related idea, Maths Lies (where the teacher tells one deliberate lie per lesson - see my first gems post) is still one of my favourite teaching ideas ever.
 xkcd.com
2. Wikipedia and visualisation
This week I discovered Wikipedia for Schools in @claganach's post 'Wikipedia in the classroom – do you know all it can do?'. Wikipedia for Schools is a version of Wikipedia in which specific articles have been selected based on their relevance and suitability for school children. The selected articles have been checked and tidied up (but thankfully have not been 'dumbed down'). There is a mathematics section which would be a good place to start if your students are doing any research in maths. I had a quick look at the polygon page and I've already learnt lots of new things - for example that a megagon is a million-sided polygon. This can be used as an illustration of a well-defined concept that cannot be visualised. Go on, try to picture a million-sided polygon... Impossible? Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.

Speaking of things that can't be visualised, I absolutely loved this post 'From 1 to 1,000,000' from @waitbutwhy (shared by @mathtans). The writer takes us through a series of visualisations from the number one up to one million (the post ends with a million dots!). I've talked before about ways to develop students' number sense (see Gems 7 about Estimation 180). Show your students the dotty pictures so they get a good sense of the magnitude of numbers.
The image above reminds me of the 'If the World Were a Village of 100 People' visuals I talked about in Gems 1 - this is a nice way of conceptualising data that might help students understand percentages.

3. Creative Mathematicians
Thanks to @gareth_metcalfe for sharing this brilliant video 'What is a mathematical proof?'. The video explains why mathematicians spend most of their time trying things that don't work. Students are often reluctant to try a different approach if their first attempt at answering a question is a dead end. Show this video at school to encourage your students to be creative in their mathematical thinking.

4. Communicating Reasoning
Continuing the theme of encouraging students to try various approaches to solving problems, brilliant NQT blogger @MrDraperMaths gives us the post 'Maths You Can Redraft'. His idea - which I'm definitely going to try with my Year 12s - is to give students one challenging problem for homework and make them focus on the written communication of their thought process. It's all about constructing reasoned arguments, a skill that A level students often lack. Mr Draper has created an excellent homework sheet for this purpose - see his post for full details. Ed Southall (@solvemymaths) provides a whole set of puzzles that you could use to build students' mathematical thinking and communication skills - the example below is one that I particularly enjoyed tackling - see solvemymaths.com for the full range.
 Source: solvemymaths.com
5. Five Expectations
Prize-winning mathematical cake-baking duo @danicquinn  and @MsBWellbrook set out their 'five expectations for a beautiful maths book' using the graphic below. This is a really clear and effective way of communicating expectations (the Why? bit is particularly important). Thanks to @MrReddyMaths for sharing this idea. I've made my own version - click here - which you're very welcome to borrow and adapt.

What I've been up to
Last week's gems post (unlucky 13) was my most popular post ever, with almost 2,000 views in a week. I also wrote a post on circle theorems last week that I was particularly proud of. I love my gems posts and my resources library, but it's my topic specials that I think people will find the most helpful. I like to think that new or recently qualified teachers will really benefit from these posts when planning to teach a topic for the first time.

If you like my blog then please vote for it in the UK Blog Awards (click here to vote). There are over 50 blogs in the freelance education category and only ten will go through to the next stage. My blog is tiny compared to the super-successful, well-established blogs I'm up against. I've only been writing it since April but I've done a lot in that time - I put my heart and soul into it, so if you find it useful then your vote would be very much appreciated.

Finally, do you receive Chris Smith's (@aap03102)  weekly newsletter?  If you don't already subscribe then email him now to get on the mailing list. This week he featured Pret homeworks which you should take a look at if you haven't seen them before. Chris also featured the excellent puzzle below, which I'm looking forward to giving my students when I return to work in January.