5 Maths Gems #116

Welcome to my 116^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. New Resources
I featured TES author cparkinson3 in Gems 110 back in May. He has now joined Twitter (@CP3fxy) and has been busy sharing lots of lovely free resources. For example check out his collection of ten lessons on expanding and factorising and his collection of four lessons on algebraic fractions.

2. Dice
Ed Southall (@solvemymaths) noticed that if you just google 'D6' (or 'D4, 'D20' etc) then this cool interactive dice tool comes up. I love how geeky the internet is.

3. MathsPad
Having taught nothing but A level and GCSE for a few years, it's quite a change for me to be teaching only Year 7 and 8 this year. I'm loving the fact that most of my lessons now feature resources from my favourite website MathsPad.

Here's an extract from one of their latest Stem and Leaf resources.

MathsPad's full October 2019 resource update is here - I love the look of their new real-life graphs resources and look forward to using them one day. Plus there's a load of lovely stuff on metric units which I'll be teaching soon.

4. A Level
A level teachers might be interested in these new resources:

• Jack Nicol (@geomathsblog) shared a website made by one of his Year 13 students. It searches through WJEC exam papers and returns results by keyword for A level subjects Maths, Physics, Chemistry, Biology, Computer Science, Economics, Business and Psychology. This might be helpful to both teachers and students. Try searching for 'parametric' to see how it works.
• Tom Bowler (@Ridermeister) of the Exeter Mathematics School has shared a collection of interview questions to help prepare candidates for the mathematical questions that might be asked in university interviews. 
• CrashMaths (@crashMATHS_CM) updated their resources for the Edexcel Large Data Set.

5. Trigonometry Task
Another one of my favourite resource writers, Dan Walker (@360maths), shared a rich task for consolidating trigonometry with Year 11.

Update
My school workload is insane at the moment, but I'm hopeful (!) that things will calm down a bit after half-term. September is always tough isn't it? I have a new job that's totally different to anything I've done before, plus I'm teaching topics I haven't taught in a decade. I'm very much enjoying my new job - it's so exciting to be in a brand new school. You might have seen on Twitter that I'm excited about my classroom equipment (a fab new visualiser and a lovely Classwiz emulator) and I've been really enjoying teaching proper maths again, free from all the exam pressure. For one of my classes I've been trying Memory King and Five for Five - they seem to be working well, and I will blog about these things soon (if I get time...!).

I recently blogged about my book 'A Compendium of Mathematical Methods' which is available to order now for delivery in December. I sent a draft version to Emma McCrea, Craig Barton and Ben Sparks and was delighted by their feedback.

I need to reclaim some of my weekends to spend more time with my children so I've turned down the opportunity to speak at a number of conferences this year, but I will be at #mathsconf21 in Peterborough next weekend. I'll be sharing some awesome resources in my workshop 'Calculator Crisis'. It's fab that one of my favourite maths authors Alex Bellos will be there too (I suggested he come along so I'm delighted that it's happening!).

I recently presented a couple of workshops at #mathsconf20 in Edinburgh. It was nice to be given the opportunity to say a few words to all delegates about the benefits of joining The Mathematical Association.

You can now join the MA for only £2.50 a month - that's such a small amount of money to be part of the oldest subject association in the world! And it comes with a large discount off our awesome Easter 2020 conference. If you decide to come for the whole conference (2 nights/3 days) then members save £50 on tickets - so it's well worth joining even if just for that.

Speaking of CPD, the 'Marvellous Maths' course I'm running with Craig Barton is fast approaching. It's shaping up to be a really exciting day - there are a few tickets left so book now if you want to come!

Here are a few more bits and pieces that you might have missed:

• I shared an algebraic function machines resource that I made for my Year 7s. It drew out some key misconceptions and generated some useful class discussions. 
• I had a lovely evening at Rob Eastaway's book launch for his brilliant new book 'Maths on the Back of an Envelope'. 
• Did you see that a London school boy came up with a new divisibility test? 'Chika's Test' is such a great story to share with your pupils.

I'll leave you with this fun game from Christian Lawson-Perfect (@christianp) based on @DavidKButlerUoA's 'number dress-up party' puzzle. All the numbers have come to a party in fancy dress. Which numbers can you correctly identify?

Long Live Stem and Leaf

I planned to write a post about teaching stem and leaf diagrams. But then I realised that many maths teachers consider them to be pointless, a waste of teaching time and a welcome removal from the curriculum.

Now let’s think about this for a minute. Admittedly stem and leaf diagrams are rarely used in ‘real life’. In fact the only common examples we can find are timetables, such as the Japanese train timetable shown in the picture below (more examples here). But does this ‘uselessness’ really mean that stem and leaf diagrams shouldn’t be taught? If that’s the case then a number of the topics we teach in maths should be taken off the curriculum. 

Japanese train timetable. Source: Wikipedia

Much of the maths we teach at Key Stage 3 helps pupils access more advanced topics (all roads lead to calculus?!). Maths begets maths. So do stem and leaf diagrams lead us anywhere? Do they help pupils develop any useful skills and understanding?

I'm going to say (in a sheepish whisper) that they do. Stem and leaf diagrams are one of a set of tools that could be used to develop understanding of the concepts of median, mode, quartiles, spread, skew and outliers. I think they are accessible to low ability pupils. I think that pupils enjoy creating them. I think they lead to interesting discussions when comparing two sets of data. I certainly don't think they should be a compulsory topic at any age, but I see no harm in teachers using them if they like. Isn't it nice to have that freedom?

John Tukey, the inventor of stem and leaf diagrams, wrote "If we are going to make a mark, it may as well be a meaningful one. The simplest - and most useful - meaningful mark is a digit" (source). Excellent point Mr Tukey. Did you know he also invented the box and whisker plot?

John Tukey is also quoted as saying "There is no data that can be displayed in a pie chart, that cannot be displayed better in some other type of chart". I agree. In the same way many of you don't like stem and leaf diagrams, I don't like pie charts (this excellent blog post about the misuse of pie charts is worth a read).

Right, now I've attempted to justify this blog post, here's my lesson ideas:

Starting Point
You could start by presenting your class with a large set of data (like the one below) and asking them what the mode is. It's hard to spot. Ask your pupils for ideas on how could we organise this data so we can easily see the mode.

12, 54, 21, 56, 32, 14, 42, 23, 20, 48, 21, 34, 12, 15, 16, 42, 47, 46, 32, 21, 45, 43, 21, 34, 26, 32, 17, 18, 45, 21, 44, 32, 12, 23, 45, 24, 35, 38, 28, 18, 29, 20, 10, 36, 12, 42, 47, 32, 47, 37, 12, 54, 23, 17, 29, 38, 32, 12, 17, 13, 21, 34, 12, 15, 16, 42, 47, 46, 12, 16, 43, 23, 16, 46, 52

I find stem and leaf plots rather pleasing to the eye. Much nicer to look at than a boring list of unordered data.

An alternative starting point is a 'beat the teacher' game, which I've adapted from an idea by the NCETM. In this activity, pupils think of a number between 10 and 40. Each number is called out in turn, while pupils make a list in their books. Meanwhile the teacher also makes their own list, but organises it as a stem and leaf diagram. Once all the numbers are listed, the teacher asks the class to work out median, mode and range. The teacher will do it much quicker from their stem and leaf diagram, hence he/she wins the race.

Physical Activities
This blog post is about introducing stem and leaf diagrams using post-it notes. It's a lovely idea for an engaging and accessible lesson. Mr Collins shared a similar idea in this blog post, but he uses students and desks instead of post-its. If you like the idea of human stem and leaf diagrams then you might also like these breath-holding activities - one from Don Steward and a similar one from the NCETM.

Data Types
Encourage pupils to think about different types of data - what is suitable for a stem and leaf diagram and what isn't? For example, could the total number of goals scored per game in a season of football matches be displayed in a stem and leaf diagram? Probably not, because the data would mostly be single digit numbers. Try my worksheet for more on this.

Mini Projects
Don Steward has some nice activities involving stem and leaf diagrams, such as this this Presidents Longevity Project. I also like Tim Jefferson's mini-project about bus timetables. Taking this timetable project further, you could ask pupils to think of other ways to present timetables - this post 'Visualizing a train timetable using a stem-and-leaf plot' suggests a nice alternative.

Extensions
There's opportunities to extend this topic by looking at variations in the way data is presented (for example using 'split stems') and interesting features of the data (eg outliers, bimodal data, skewness).

Back-to-back stem and leaf diagrams are useful for comparing data. Writing comparisons between data sets - whether represented by stem and leaf diagrams or box and whisker plots - is something that pupils (especially EAL pupils) often find difficult.

There's lots of S1 (A level) stem and leaf questions - like the one below - that could be explored at Key Stage 3 (which begs the question, why were they considered suitably challenging for A level?).

Edexcel S1 November 2004, Question 1

I rarely disagree with people or play devil's advocate so this post is a bit risky for me! Be nice. If you do teach stem and leaf diagrams then I hope you find these ideas helpful. Thanks to those on twitter who shared their views and ideas (especially @srcav - who is not a fan of stem and leaf diagrams!).