19 April 2019


This week I spent four days at the ATM-MA Conference. It was great! I went to a wide variety of sessions and have come home with a lot to reflect on. In my current role (working mainly to improve Year 11 results) I feel like I've started to lose sight of what mathematics teaching is all about. Next year I'll be teaching only Year 7 and 8 and am looking forward to trying some new approaches. This conference presented the perfect opportunity to gather my thoughts.

A residential conference is a very different experience to the one day events I usually attend. There were numerous opportunities to do lots of maths and meet lots of new people. I enjoyed the social activities and I was impressed by the venue and the way the conference was organised by the ATM.

I'm a trustee of The Mathematical Association and very proud to represent them at events like this. The members of MA Council are lovely and I believe that the work they do is really important to our profession. Not only do they have an incredibly rich history going back to 1871, but they also have exciting times ahead with Ems Lord of Nrich as President and Hannah Fry as President Designate. If you want to join, secondary membership is only £5.20 a month. I'm already looking forward to the two night MA Conference in 2020 which I'm absolutely certain will be awesome. I hope that lots of my readers will join me there.

I've decided to use this blog post to share five ideas and resources I saw at #ATMMA19. Obviously I'm not sharing any of the big ideas and deep thinking in a short blog post - you have to actually go to these conferences for that sort of thing - but there might be a few helpful things here that people haven't seen before. I enjoyed literally every single session I attended at this conference and haven't talked about them all in this post, but do have a listen to me and Craig Barton chatting about the first two days of the conference on Craig's podcast:

Conference Takeaway - #ATMMA19 Day 1

Conference Takeaway - #ATMMA19 Day 2

1. Etudes
Colin Foster did an excellent opening plenary. Here I'm just sharing one activity we had a go at during his talk: 'Percentage Change'. Visit his website mathematicaletudes.com for lots more like this. You really have to have a go at these tasks to get how good they are. The idea is that students develop procedural fluency in rich problem solving contexts.
2. Nrich
Craig and I had a great time at the Nrich workshop run by Alison Kiddle and Charlie Gilderdale. We did three tasks which are all linked from the conference page on the Nrich website.
In Which is Bigger?  students can try out some numbers, do some algebra, draw some graphs... it can go in a number of directions. Consider how sketching the graphs might help you think about the final two pairs of expressions above. The task comes with some great extension activities which I really enjoyed completing.

Polygon rings was a highlight of the conference for me! I love a bit of angle geometry. I particularly liked how fun it was to put together our polygon rings using ATM Mats, knowing with absolute certainty that they would fit together perfectly because we'd worked out the angles.
Steve Lyon and Mike Anderson from STEM Centre ran a session in which we all got to have a go at some tasks from old SMILE resources and then talk about which tasks we enjoyed. There are c2000 SMILE resources which have been scanned in and uploaded to the STEM Centre website. It's an overwhelming number of resources so a good place to start is with the SMILE cards here which are organised by topic. 

There were a number of delegates in this session who had never heard of SMILE. I use SMILE resources occasionally but I know there are hundreds I've never seen. The resources that Steve and Mike had chosen for this session are in booklets here. I didn't try all of them but particularly enjoyed 'Multiplication Review' (SMILE Card 2386) where students are asked to look at five different multiplication methods and try to understand what's going on. Although I'd looked at 'Russian Peasant Multiplication' before I'd never actually taken the time to think about why it works. It was a nice thing to work out.
If you like this then also check out this brilliant pack of SMILE activities 'Multiplication Makes Sense'.

I think that working on a set of SMILE resources like we did in this workshop would make a really good maths department meeting.

4. Standards Unit
Heather Davis led a workshop on 'Reasoning with geometry and fractions in KS3' where we discussed some tasks that I'd not used before. I use the Standards Unit a fair bit but had not seen the 'Dissecting a Square' task.
Students are asked to work out what fraction and percentage of the square each section is. When looking at this task we had some interesting discussions about what prior knowledge is required, what reasoning is involved, and what assumptions must be made to complete it. Following this task students are asked to make up their own dissection on a grid with 100 squares - this becomes a really interesting task for understanding percentages. Some great examples are also provided for class discussion.
Although I was introduced to the Standards Unit on my PGCE it took me a quite a few years to realise that instead of just using the tasks, I should actually read the suggested approaches and discussion prompts that go with each task. The resources and their accompanying notes are absolutely brilliant.

We did a lot more in Heather's session that really got me thinking, but I will just mention one more thing here: Heather gave us a 'what's the same, what's different?' picture to ponder:
I noticed that both shapes had one pair of parallel sides. Heather started the discussion by asking who had spotted the most boring thing that these shapes had in common. I was about to offer my suggestion because I thought it was going to be a pretty common answer, but then others offered answers like 'they're both shapes' and 'they're the same colour'. Then it got a bit competitive, with people trying to come up with something even more boring. And as a result I started noticing more and more things about these shapes. The great thing about this start to a discussion is that it gets even the most reluctant or least confident students contributing, noticing things, and smiling. What a lovely idea.

5. Don Steward
It was wonderful to see Don Steward again. I first met him when he presented at my school back in March 2016. His workshop was on probability - he spoke about its place in the curriculum, showed us some wonderful tasks for teaching it, and shared some fascinating historical context.  He has shared his presentation in three blog posts:

Obviously there's loads of great stuff here so you should download the presentations. In this post I'm just sharing a few extracts.

This question is lovely: 
Students can of course try some numbers, though I expect that most teachers would go straight for algebra.

Don's set of 'probability and words' tasks are great fun. I have used these before. 
Don's ideas on teaching systematic listing are fantastic. For example, here is one way of thinking about the ordering of A, B and C.
A nice idea when teaching students systematic listing is to present them with lists with bits missing:
And check out how beautifully animated this is:
There is so much more to talk about from this presentation but I can't share the whole lot here! So do check out all of Don's slides on his blog.

My Presentations
I presented twice on Wednesday. First I did a five minute slot during David Acheson's talk 'Proof by Chocolate etc'. I spoke about amusing contexts from old maths textbooks. Later I did my own 1.5 hour presentation on the evolution of vocabulary in maths teaching. I might present some of that at La Salle's next conference in Sheffield so I'm not sharing the slides on here. If you were at the presentation feel free to email me for a copy.

I take every opportunity to present at conferences for two reasons - first because I'm always so excited to share all the fascinating stuff I've found, and second because I think it's really important that both women and classroom teachers put themselves forward to speak at education events. We can't complain about being underrepresented if we don't volunteer to speak. At this conference, where anyone was welcome to submit a workshop proposal, I worked out that about 43% of the speakers were female. That's not bad, but given that our profession is dominated by women, we could do better. I really really encourage all teachers, particularly females, to consider submitting a presentation for next year's conferences when the time comes. If you have a particular area of expertise, or do something interesting in your classroom, or if you've done some research, or you want to share some great tasks and activities, then please do get involved.

Finally, listeners of the podcast will know that Craig and I were rather hopeful that we might win the quiz again after last year's surprise victory. We pulled together a great team (me, Craig, Andrew Taylor, David McEwan and David Bedford), and here we are all looking rather optimistic at the start of the night:
We definitely chose the wrong round to play our joker, but we still ended up coming third which made me very happy because we won Easter eggs! Well done to the teams that came first and second (including our quiz nemesis, the lovely Alison Kiddle) - very well played.

I also want to say thank you to Jen Shackley, Andy Sharpe, Ben Sparks and David Bedford for keeping me company at and after the slightly bonkers (but delightful) open mic event on the last night of the conference. What fabulous people.

See you all again next time!

15 April 2019

Foundation Tier Revision Resources

I've been teaching a fair amount of Foundation tier GCSE this year. It feels like there are fewer revision resources available for Foundation tier compared to Higher tier, so I've collected some together in this post for ease of access. There's nothing new here - it's all in my epic GCSE revision resources collection - but hopefully this post will remind teachers of some of the things that are available to use in the classroom in the last few weeks before exams start.

Ruler booklets
These booklets from tannermaths.co.uk were designed for the old GCSE but are still very useful. They contain loads of wordy questions, including a fair few on ratio and proportion. They are well presented and come with answers.
Revision mats
Everyone loves a resource printed on A3! There are a number of Foundation revision mats available from sources such as Access Maths, PixiMaths and Miss B's Resources. I recently used these from TES for key Foundation skills. I like it that they are editable - as I went through and worked out the answers I tweaked a few questions and changed the order a bit. I'm a big fan of editable resources!
Confidence boosters
The maths team from Edexcel (@EmporiumMaths) have recently shared sets of 'Practice Tests: Aiming for 4'. These six papers comprise Grade 1- 3 questions from Foundation past papers in order of difficulty as found by students (ie they start with the questions that most students got right). These are intended as a confidence booster for students aiming for a Grade 4.

On Access Maths you can also find a set of 'Start with Confidence' resources which contain 'opening page' questions.

TES user scottyknowles18 shared a set of key skills booklets for Foundation pupils. At work this year I was asked to make a PowerPoint to accompany his algebra booklet. I designed the PowerPoint to be used in form time interventions but it can be used in lessons too. Each section includes key points, a couple of examples for the teacher to go through, a diagnostic question and answers.
The maths team from Delta Trust have also shared Foundation 'Securing a Grade' Revision Booklets on TES.

Useful websites
CorbettMaths has 5-a-day activities (numeracy, foundation and foundation plus) plus practice questions and practice papers. Maths Genie has questions by topic too. MathsBot has GCSE revision tools where you can adapt resources so the questions are suitable for your students. MathsBox has loads of helpful resources for Foundation tier, including a couple of freebies: there's a Big Mistake activity and a Foundation relay.
Breakfast revision
Last year I made three sets of breakfast revision resources for Foundation tier students:

They are not designed for a specific board or exam series so can be used every year. They are intended to be printed on A3 and used as a warm up on the morning of the exam. I included editable versions (so you can remove the word 'breakfast' if you want to use them in class) and answers.
Topic tests and exam questions
Also have a look at what your exam board provides. For example a number of AQA exam questions over the last two years have been similar to questions seen in their collection of topic tests. So using questions from the topic tests in revision might be a good idea! And for Edexcel, the Emporium has a number of useful resources. Look in the GCSE folder marked 'Practice Papers & Questions' and you will find resources such as collections of crossover questions, one mark questions from Foundation papers and themed papers.

Self quizzing
If your pupils don't know their facts and formulae then they might find my Foundation Knowledge Quiz book useful. Schools can buy in bulk for £5 per book. These books are particularly helpful for pupils who would otherwise do nothing at home - it gives them a very easy-to-use resource for independent study.

Between exams
Given that this year we have a relatively short time back at school after Easter before exams start, I will probably go straight into mixed topic revision lessons (as opposed to the topic focused lessons I have been doing until now). I will particularly focus on non-calculator topics in the last week of normal lessons before their GCSEs start.  Between exams, when we will occasionally see pupils on the days they don't have exams, I will be using the resources that are published every year (by very helpful people) to revise the topics that haven't yet come up (I'm sure Adam Creen will keep track of these on his blog).

See my revision resources posts for more resources - plus there are loads more on TES. Good luck for the final few weeks with Year 11!

4 April 2019

5 Maths Gems #108

Welcome to my 108th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. SMP
Christian Bokhove (@cbokhove) and his team have been working on this project for a while so it's exciting to see the launch of smp2.co.uk. They have created PDFs of dozens of old SMP maths textbooks and booklets. Read about the aims of the project here.

Click ‘Access to SMP’ to register and download the materials. It's free and there's absolutely loads of material to look through. It's hard to know where to start! I'm very grateful to those involved for all their hard work on this.

Here's a randomly picked example of a task on calculator use. It's from Book G1.
And here's part of a task from a Level 3 booklet 'Coordinates 2 - Extension'.
2. Storyboarding
Thank you to Dale Chapman (@MrChapmanMaths) for sharing his storyboarding idea. This is where students create a simple set of instructions with pictures to explain a procedure. I blogged about a really similar idea for teaching constructions in Gems 30 back in 2015, but subsequently forgot all about it so this is a great reminder! Plus it's good to see it in use for bearings, and I wonder what other topics would lend themselves well to storyboarding.

3. GCSE Revision
As always at this time of year there's been a flurry of new revision resources.
  • Simply Effective Education sells Key Cards, which is (in my opinion) the best GCSE revision app available for maths and science. They have also shared some free revision races on TES
  • I was asked to make a PowerPoint to accompany Mr Knowles' (@SK18Maths) Foundation algebra revision booklet . It was designed to be used in short daily form time interventions but can be used in longer revision lessons too.

4. Fill in the Gaps
At Educating Northants last week Craig Barton (@mrbartonmaths) shared a new type of resource: Fill in the Gaps. We had a go at it during the workshop and it was brilliant. Try it and you'll see what I mean.
Go to variationtheory.com to download this ratio task, plus one for percentages and one for quadratics.

5. A Level Resources
Tom Bennison (@DrBennison) shared a 'Question a Day' revision resource for Year 13. 

@MrsGRVHS shared a padlet for A level maths with links to resources and useful websites.

@naikermaths added another AS Pure Practice Paper to the collection. These papers contain old specification exam questions but they are organised for the new specification so they are helpful for revision. The mark schemes for these AS Practice Papers can now be accessed without a password to help students in their revision for their A level exams.

Finally, while looking at MEI A level things on OCR's website, I discovered this command words summary. I have added this to my displays page.

I've been to three lovely conferences in the last two weeks - Habs Girls, Educating Northants and the London Thames Hub Primary Maths Conference.
At Educating Northants I recorded a Conference Takeaways podcast with Craig Barton that you can listen to here.
I also went out with my friends Gill Leahy and Dil Dias from the London Thames Maths Hub to see Hannah Fry do a talk about her book Hello World. It was brilliant.
During Educating Northants I went to a workshop on primary mastery by Nicky Moksa and she shared this grid of number facts. You can read more about it on the NCETM website here and here.

I have made quite a few updates to my conferences page lately - there's always a lot going on in the summer term. I'm looking forward to speaking at the Kent and Medway Secondary Maths Conference on Monday 8th July.

Nikki Martin (@nikki_nzmartin) completed her work on the Primary Topics in Depth project. This series of packs feature maths misconceptions, approaches and resources for Years 1 - 6.

My daughters discovered Sumaze Primary last week which was awesome - my 7 year old was totally in love with it and really happy when she completed every level. It's an amazing maths app for young children.

I look forward to seeing lots of you at the ATM/MA conference which is coming up soon. Before then, I'm very much looking forward to some time with my family to recover from the hectic month of March.

Finally, I'll leave you with the exciting news that Desmos now does box plots! If you haven't seen this before then do have a play.

25 March 2019

5 Maths Gems #107

Welcome to my 107th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Foundation GCSE Revision
Thank you to Edexcel for providing a helpful compendium of one-mark questions from Foundation tier papers from the last four exam series. These can be downloaded from the Emporium.
Foundation GCSE teachers might also be interested in the revision clips from a new series called 'The Maths Show'. This series is produced by BBC Teach and features Matt Parker (@standupmaths).
If you're preparing students for their GCSE exams then don't forget I have a large collection of revision resources here.

2. Year 6 Maths Resources
Thanks to Mr Morgs (@_mrmorgs) for sharing a list of free maths resources to help prepare children for their SATs. No doubt this will be really helpful to Year 6 teachers.

Other helpful Year 6 maths resources include all the past SATs mark schemes condensed into one page each from Sophie Bee (@_MissieBee) and a PowerPoint of SATs questions linked to the contents domain from Thomas Timson (@filtered_k).

3. A Level Resources
I'm delighted to share some resources for A level teachers.

Susan Whitehouse (@Whitehughes)‬⁩, who has been one of my favourite A level authors for many years, has put all of her resources on a new website. You can now download the whole collection in one go.

CrashMaths (@crashMATHS_CM) have started adding more A Level Practice Papers to their website. You can download AS Maths Paper 1, Gold A here.

Mo Ladak (@MathedUp) has shared an updated version of a really helpful resource for A level students: "A level Maths Takeaway". This includes videos and practice questions by topic.

Finally, in a recent twilight session of the London A level pedagogy workgroup run by Carlos Karingal (@CarlosaurusK) I suggested making more use of goal-free problems at A level. Here are some examples:

4. Protractors
Whilst researching for an upcoming presentation on angles I read about a University of Exeter study from 2002 which suggested that there might be benefit in using protractors without numbers. Using a blank protractor removes the common difficulties we see with students using dual-scale protractors. Without numbers, pupils simply count off the scale in order to measure angles.
This idea seems obvious now, and indeed many tweeters have told me that they already do this. It's easy to print blank protractors on acetate. In response to my tweet about this the following tools and article were shared:

MathsPad (@MathsPadJames) updated their free constructions tool so you can remove the numbers from the protractor and zoom in.
BossMaths (@boss_maths) shared a great blog post about teaching measuring angles, and a Geogebra applet with an unnumbered protractor.
Tom Francome‏ (@TFrancome) shared the article 'Empty Protractor' from the ATM journal Mathematics Teaching.

5. Maths in Science
Thank you to Dr Sue Thaw‏ (@aegilopoides) for creating a PowerPoint containing Foundation exam questions from science GCSE papers that involve maths (percentages, probability, graphs, using data and equations). It's so helpful for maths teachers to see the maths that comes up in science.
If you're a maths teacher working together with your science department then do check out the joint maths/science CPD I featured in Gems 102.

I'm looking forward to speaking at two conferences this week: Primary Maths London on Friday where I'm speaking about angles, and Educating Northants on Saturday where I'm speaking about methods. Look out for a Conference Takeaways podcast with Craig Barton on Saturday.

Last weekend I spent the day with Megan Guinan at the Habs Girls conference where I particularly enjoyed the keynotes from Lucy Crehan and Vic Goodard.

If you're looking to attend a conference in the summer term then there are lots to choose from - check out my events page for listings. I'm speaking at researchED Rugby which has a great maths strand and at the MEI Conference which has three days of brilliant workshops for teachers of Key Stage 3, 4 and 5.

If you're a primary teacher then you might be interested in the launch of the 'First Mathematics Challenge' - a national maths competition aimed at children in Years 3 and 4.

I shared the news on Twitter that a calculator is now available that allows students to secretly access the internet and send messages during an exam. It may be a hoax, but if it's real then we need to keep an eye out for these. The top sticker can be peeled off so it looks like a Casio. It's quite expensive, plus a huge risk for students, so let's hope that stops this from becoming a problem!
Have you seen this website all about the history of Smile Maths resources? It's full of interesting stuff.

I'll leave you with this visual prompt from @MathIsVisual which is designed to get pupils thinking about the area of a triangle.