16 February 2019

5 Maths Gems #104

Welcome to my 104th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Don Steward
Hurrah for the return of Don Steward!

He has been busy publishing loads of new resources on his website recently, covering topics such as ratio, vectors and linear graphs. I can't keep up with it all.
Extract from GCSE line questions

His new resources include a number of different ratio and proportion tasks including a useful set of ratio with algebra questions. Thank you Don!
Extract from Best Buys
2. Starters
Thanks to Danielle Moosajee (@PixiMaths) for sharing a huge collection of free starter questions. She has created a mixed topic starter for every lesson of the year. They are grouped by target grade, with packs for grades five and nine created so far. This might be a time saver for lots of teachers.
3. Structured Recall
For years I have made good use of Susan Whitehouse's topic summary resources at A level. They work really well as a revision activity - students have to explain a method and complete an example for the various skills within topic.  Here's what it looks like for linear graphs.
I like these so much that a couple of years ago I tried to make a set of them for GCSE in the same format (ie one column for the method in the student's own words, one column for an example question) but I didn't have time to complete them. So I have a folder of unfinished attempts.

I was reminded about these sheets when I saw Miss Walker (@MsWalkerMaths) tweeting about a similar idea that's she has been trying with her students. This is slightly different to the topic summaries though, because the questions are intentionally less specific (including prompts such as 'Tell me about parallel lines').

She also shared some great examples of her students' work.

4. Interhouse Competitions
I have written before about national maths competitions which normally involve taking students out of school. Gemma Elizabeth‏ (@gemma_harney) recently tweeted to ask about ideas for interhouse maths competitions that could be run within a school. Some great ideas were shared so do read the thread.

Coincidentally I was doing my regular batch of TES reviews a couple of weeks later and found a set of resources that could be used for a monthly maths challenge in schools. Thanks to beedup on TES for sharing a nice simple format. The idea is that students who want to take part choose one of two challenges and then have to solve the problem and explain their thinking. The prize goes to the entry with the best explanation. Using Nrich problems or similar it would be pretty quick to create a set of these so the competition could run every month all year round.
5. Hook, Line and Sinker
John Rowe (@MrJohnRowe) has published a really lovely eBook for maths teachers. You can read about it and download the book here.
John says, "I wrote this book to help Maths teachers who simply don’t have time to navigate the thousands of resources available online. This isn’t tailored to a specific country’s standards/ curriculum outcomes, rather a collection of mathematics resources sequenced in a way that I would probably do it as a teacher".

In his book John provides an example sequence of the resources he would use in the teaching of trigonometry and Pythagoras, algebra, indices, quadratics and probability. It's great - do have a read!

I have two big things going on at the moment… My GCSE revision book went on sale and we had loads of bulk orders from schools wanting their students to take these home over Easter. Read about it here. Around the same time, Matt Parker asked me to host his book launch. All 180 tickets sold out in only two days, which was insane. I’m now busy making all the final arrangements for the maths event of the year. If you're coming, check the website for updates.

In other news, I led two large conferences last week, making it my busiest week of all time! The first was a DfE conference in Northampton where I presented on 'Countdown to GCSE'. For those of you who asked for a copy of my presentation, you can download it here. During the TeachMeet I also shared a short presentation about animations - those slides are here.
200 primary and secondary teachers enjoying
Andrew Jeffrey's keynote at #teachmathsnorthants

Two days later was a Harris inset day - I was responsible for organising and hosting the KS3/4 maths strand for about 180 teachers. As part of that I ran two topics in depth sessions. I am so pleased it's half term now because it was an exhausting week! Great fun though.
I recently appeared on the podcast Relatively Prime where I was full of enthusiasm and optimism, but a few days later got really upset by the way a student spoke to me at school, which made me uncharacteristically miserable. The contrast between the highs and lows in this career is astounding at times.

I am looking forward to the flurry of conferences in March. The first is #mathsconf18 which is in Bristol on 9th March. I’m presenting on units and I know everyone will think that doesn’t sound like an appealing session! Trust me, I have some really cool stuff to share.

Later in the month, at #educatingnorthants, I’m presenting on methods (my absolute favourite thing to talk about). I recently saw a good blog post from Nick Corley (@MrCorleyMath) on alternative methods for expanding double brackets which is worth a read.

If you're not a member of a subject association then do consider joining the oldest subject association in the world. The lovely people at The Mathematical Association are now offering membership by monthly direct debit.
It's only £5.20 a month for secondary membership, and even cheaper for trainees, NQTs and primary teachers. Join here.

I’m off on a family holiday to Scotland on Monday - it will be the first time my daughters go on a plane, which is very exciting. If you’re on half term next week too, enjoy!

I'll leave you with this fun angles problem shared by a colleague of Tom Bennison and prettified by Ed Southall. Given it's a square, find the marked angle. In theory, a Year 7 should be able to do this one.

8 February 2019


On Saturday 2nd March I will be hosting the launch party for Matt Parker's new book Humble Pi. It's going to be the biggest maths event of the year! Thanks to unbelievably generous sponsorship from the wonderful people at Jane Street, I've booked one of the coolest venues in London and we have an evening of amazing entertainment lined up.

For only £Pi2 a ticket you'll get a copy of Humble Pi, a champagne reception, maths speakers, activities, canapes, drinks and loads more.

Wait until you see what the Foxdog guys do! It will be so much fun.

We have 160 tickets available but I sold half of them in less than 24 hours so book now! Everyone is welcome. Hope to see you there!

1 February 2019

Memorising Facts

I took over a couple of Year 11 groups in December and was really surprised by how few GCSE facts and formulae they knew. When we reviewed their mock exam I noticed that they'd all got a question wrong where they were asked to find the perimeter of a semi-circle. It turned out that none of them could recall the formula for circumference, so were unable to even score the first mark on this three mark question.

In class we do loads of work on problem solving, reasoning, exam technique and everything else, but I realised that if they don't know the basics then it's really hard to move forward. Of course knowing things in isolation isn't helpful at all. Once they've memorised their facts then they need to know what to do with them. The application is the hard part. But if we can get the facts and formulae sorted, this gives us an opportunity to focus on the real challenges at hand.

Gaps in fundamental factual knowledge are pretty common at maths GCSE. Examiner feedback for Edexcel shows, for example, that students struggle to recall the number of grams in a kilogram. It's such a shame for them to lose marks on things like this. We do so much work with them over the years on developing their conceptual understanding and reasoning skills, but one of the few things we really need them to do on their own in the run up to their GCSE exams is commit facts to memory. That's just how GCSEs work - there is an element of memorisation in every subject. In maths that includes unit conversions, area formulae, trigonometric ratios, polygon properties, angle facts, circle theorems and more.

In an attempt to fix this I started giving my students knowledge quizzes in class. Each lesson I gave them one quiz they'd done in a previous lesson and one quiz they'd not seen before. At first they knew barely any answers. But after trying the same quiz three or four times, they started to remember things. And they loved that. Suddenly they were able to access a lot more problems in lessons. Success is motivating, and it really has started to have a big impact on their confidence at this vital time.


In an ideal world our Year 11 students would go home for the Easter holidays and revise all their subjects, committing facts to memory and practising exam papers. What often happens is that they look at a revision guide or a set of revision cards or an app, and hope everything will just stick in their heads. When I was at university I made myself sets of questions and photocopied them, completing my quizzes again and again until I got full marks every time. Ideally our students would do something similar at GCSE and A level. But although we can advise them to do so, they often don't do it. So this is where I'm going to try to help...

I have put all my quizzes into books which now form part of the new 'Knowledge Quiz' series. They have just gone to print so will be on sale from 1st March. The books contain multiple copies of the same quiz so students can tear out a quiz, have a go, check the answers, and then try again in a few days. After completing the same quiz a few times and memorising the facts, and they can come back and try again a month later.

The books will be £8 to buy from Amazon, but they will be discounted to £5 if schools bulk buy directly from John Catt. I envisage that some schools will buy copies for their students to take home over Easter, and some schools might buy copies for each student to use in class (saving the teacher a lot of time and photocopying budget!).

Either way, I'm hopeful that this will close the huge gap in factual knowledge and allow us to focus on the important stuff.

These books cover the majority of facts and formulae required at GCSE. I am not suggesting that maths is a subject that just comes down to facts and formulae (of course not!) and neither am I suggesting that this is the only exam preparation a student needs to do (of course not!) - this is just a simple resource to help students memorise things.


There's more exciting news! These books are part of a series. I asked some of my favourite science teachers to create similar books for Chemistry, Biology and Physics. So thanks to Adam Boxer, Gemma Singleton and Ruth Ashbee, we have a whole series of Knowledge Quiz books coming out soon. It turns out there are a huge number of facts to learn for science (around nine times more facts than maths!). There are so many things to memorise for science, I have a feeling that these books are going to be hugely beneficial to students preparing for their GCSEs this year.

If this series is well received then we will extend it to other subjects and key stages next year. This is exciting!
"The Knowledge Quiz series is a deviously simple and effective way for students to revise for GCSE subjects".

I'll make sure I bring copies to the events I'm attending in March so that teachers can have a look. I can't wait to show people!

27 January 2019

5 Maths Gems #103

Welcome to my 103rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Surds
I love teaching surds! Here's a nice surds task from Peter Drysdale‏ (@pwdrysdale). It's a multiplication table with lots of blanks to fill in.
2. Puzzles
If you're a fan of geometry puzzles, check out Ed Southall's Instagram page where he has collated all his puzzles in one place, and continues to share new puzzles on a regular basis.
And while you're on Instagram looking at his puzzles, don't forget to follow my Instagram account too!

3. Boss Maths Non-Examples
I first blogged about Boss Maths (@boss_maths) back in Gems 89. When using their site recently I noticed some features in their lessons that I'd not seen before. The examples and non-examples are really useful for clarifying definitions and concepts.

Here's an extract from their Circumference of a Circle lesson:
And another extract from their Recognising and using Fibonacci type sequences lesson:
4. Hooks
Julia Smith (@tessmaths) has been collecting mathematical hooks for lessons. You can find them in this padlet. Hooks are items of interest which might spark discussion or could be used to introduce a topic in the maths classroom. Some of them might work well for form time discussion too.
5. February Half Term Maths Challenges
Thanks to Lisa Baggaley (@charowen13) for sharing a link to the 2019 Mathematical Education on Merseyside Challenges (MEM). I first blogged about this competition back in Gems 37.

MEM has been running take-home competitions in February half term since the late 1970s. Together, these competitions attract about 2,000 entries annually, with Challenge aimed at Years 7 and 8, and Senior Challenge aimed at Years 9 and 10. A third competition, Open Challenge for students aged 18 and under, is organised by Liverpool Mathematical Society.

If you want your students to enter, you can find the questions and instructions here.
On Wednesday 13th February there is a free DfE-funded maths conference in Northampton for 200 primary and secondary teachers. There will be a keynote from Andrew Jeffrey, and then secondary teachers will attend three workshops and a TeachMeet. The workshops are: Chris Reilly on Challenging Topics at GCSE, Peter Mattock on Mathematical Thinking and me on preparing Year 11s for GCSE exams. There are still a few secondary spaces available so book now if you want to come.

Finally, do check out the awesome maths videos and animations on the website www.etudes.ru. There's loads of cool stuff on this website. I particularly like the video on Reuleaux Traingles. Thanks to WTungsteno (@74WTungsteno) for sharing. Here's an extract from a video on Pi which would work well in a first lesson on circumference:

21 January 2019

5 Maths Gems #102

Welcome to my 102nd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Grade Boundaries and Exam Dates
You might have already seen Jonathan Hall's (@StudyMaths) GCSE grade boundaries page. I find this page surprisingly useful! He has now updated it with the November 2018 grade boundaries.
Also, don't forget about the Exam Countdown page which is really useful for quickly checking exam dates.

2. Algebra Resources
Thanks to Sarah Carter (@mathequalslove) for sharing a set of free algebra resources from Region 18 ESC (@Region18ESC). Examples include:
3. Core Maths Links
Catherine van Saarloos (@CoreMathsCat) has created a regularly updated list of links for Core Maths teachers. I know that many Core Maths teachers struggle with the lack of teaching resources and the time it takes to prepare lessons, so hopefully this will be helpful.

4. Joint Maths/Science CPD
For years I have been meaning to create a CPD session relating to the crossover topics in maths and science. Thankfully Teresa Robinson (@teresaarob1) - Lead Mathematics Adviser for the Russell Education Trust - has shared an awesome CPD session that is designed to be run with both maths and science teachers. Thank you to Teresa for her generosity in sharing this fantastic piece of work, and to Mel (@Just_Maths) for blogging about it. Mel's post explains how to run this CPD.
5. Times Tables Booklet
I am very fortunate to be part of a Maths Hub that is currently hosting a visit from Shanghai exchange teachers - it's a great CPD opportunity for me. Last week I met Eva who is a primary teacher from Shanghai. She ran a great session for my team on how she teaches division. I asked her about teaching times tables and she said that in Shanghai children tend to memorise their times tables at home before she teaches them. This means that her job is just to teach them to understand what times tables mean. In this country we have to help with the memorisation too, so our primary teachers have far a bigger job to do.

Eva shared an adorable little times tables booklet that is designed to help with understanding. I took it home and gave it to my Year 2 daughter who absolutely loved it. I don't think it will help her memorise her four times tables but it did help her make sense of the ideas of grouping and repeated addition. You can see instructions for something really similar here - thanks to @WycombeBus for finding this link.

In case you missed it, I recently blogged about 'Five for Five', a teaching idea that works really well with students who lack confidence in maths. I was also interviewed for the Cambridge Maths blog: Seven Questions with Jo Morgan.

I added a new page to my blog: 'Online Historical Maths Textbooks' which lists links to free online maths textbooks from the 16th century to the 20th century. It might be helpful for researchers, or for people like me who just have an interest in the history of maths education. In addition, I added a number of new events to my conferences page where you can see upcoming maths education events in the UK. Both pages can be accessed at any time from the 'Extras' menu on the right hand side of my blog (if you're viewing on a mobile, you have to scroll down and select 'View web version' to see this menu).

Did you hear the calculator news? The Casio fx-83GT and fx-85GT (currently used by the vast majority of secondary maths pupils) have been discontinued. They'll only be in shops while stocks last. So if one of your current Year 11s loses their calculator before this year's GCSE exams you can't guarantee they'll get an identical replacement. The calculators you'll probably be telling all your incoming Year 7s to buy in September are the Casio fx-83GTX and fx-85GTX, which look like the A level Classwiz but have less functionality. These aren't yet available on the high street but will be soon. As always, Adam Creen's blog is the place to go for calculator availability and pricing.

Last week  I did a couple of Twitter polls on hours of maths lesson. In case you were wondering how your school compares to others, here are the results:

I am delighted to share the news that from July 2019 I will be Assistant Principal at Harris Academy Sutton. I am so excited about working at such an incredible school. This science specialist school is part of the London Cancer Hub (sharing a site with the Institute of Cancer Research and the Royal Marsden Hospital) and is moving to an amazing new building in September. The school will only have Year 7 and 8 next year, which presents a wonderful opportunity for a teacher looking to develop their pedagogy without all the exam pressure that comes with Year 11. We will do proper maths teaching, in depth, and our small team will be totally teaching and learning focused. I can't wait. We are currently recruiting for both maths teachers and a Director of Maths. Please come and join my team! Email me (resourceaholic@gmail.com) or DM me on Twitter to discuss.

I did three presentations last week - I spoke to Harris NQTs about methods, I presented on Large Data Set at the London A level Pedagogy Maths Hub work group, and I did my Indices in Depth session at the London MA/ATM Branch alongside my Twitter buddy Ed Southall. I'll be presenting at a number of conferences over the next few months - if you're at one, please do come and say hello.
Have you booked your ticket to #mathsconf18 yet? It's in Bristol on 9th March and it's guaranteed to be a great day. I'm presenting on unit conversions, which sounds really dull but I promise it will be worth coming along. Trust me!

I'll leave you with this great tweet from @kyledevans. Have a lovely week!

12 January 2019

Five for Five

My friend Ceri recently told me about something she does in her maths lessons. It works really well for pupils who lack confidence in maths. I asked her permission to share it here. It's simple but effective. She calls it 'Five for Five'. I'm sure there are teachers all over the world doing something similar. Here's Ceri's version:

Start by producing a set of five mixed topic questions for the week. It's important that these are tailor-made for your class. You could download something generic, but it doesn't take much longer to write the questions yourself once a week. The advantage of writing the questions yourself is that you can choose five topics that are relevant to your class, for example something they struggled with on a recent assessment, or something they learnt for the first time a few weeks ago. Writing the questions yourself also means you can can get the difficulty level right.

Here's an example of a typical set of questions:

Ceri follows the schedule described below (of course this can be adapted if you don't see the class five times a week).

Ceri gives her class the five questions at the start of the lesson. They have a go on their own, but Ceri knows (because she wrote the questions) that they will struggle. Ceri then spends a good amount of time - half the lesson if necessary - going through the questions. Her pupils annotate their questions with detailed notes.

Ceri gives her class the same five questions with different numbers. Pupils complete the questions on their own but are allowed to look at their work from previous day. Ceri spends a shorter amount of time going through the questions afterwards.

Ceri gives her class the same five questions but again with different numbers. Again, they can refer to their notes and answers from the previous lesson. This is now a fairly quick starter activity. Often they can do it in five minutes ('five for five in five') but there is no time limit. There's something else for pupils to get on with until everyone is ready.

Same again. By now they should be getting them all right.

Same five questions, different numbers, but this time they start the lesson by completing the questions on their own in test conditions without looking at their notes. Even without their notes, it's very likely they will now get them all right. 

Success is very motivating for pupils who struggle in maths. Going from zero marks on Monday to full marks on Friday is very powerful for transforming a pupil's attitude and confidence.

Let me know if you try it.

Thanks to Ceri for letting me share this!

1 January 2019

5 Maths Gems #101

Happy New Year! Welcome to my 101st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Euclid's Elements 
Nicholas Rougeux (@rougeux) has made something incredible. He has recreated Byrne's 1847 edition of Euclid's Elements including interactive diagrams, cross references, and a new poster of all the original illustrations.
You can read an in-depth blog post on how it was made here. It's absolutely wonderful.
2. Retrieval Facts
Jonathan Hall (@StudyMaths) added a retrieval facts section to mathsbot.com. It's primarily designed for printing but can be projected onto the board too. I can see this being a helpful revision tool for Year 11.
If you think that regular quizzing is a good way for students to learn facts and formulae, then look out for an exciting new book which will be available for students to buy in 2019. Listen to the end of my recent podcast with Craig Barton if you want to know more about this.

3. Surds Bricks
Thanks to @pwdrysdale for sharing this surds activity. Each brick is the sum of the two beneath it.
4. A Level
Whilst preparing some CPD on Large Data Set for A level I discovered this cute video explaining how oktas work. If you teach Edexcel A level then you might find this helpful. The Examiner Report suggests that most students taking their A level exam in June 2018 were clueless on oktas.

While we're on the subject of A level, do check out this letter from a cat food company. @mathematicsprof wrote to them about how they could minimise material if each can’s height equals its diameter. They wrote back to explain that it's way more complicated than maths problems suggest. Next time I teach optimisation I will be showing my students this letter!
A level teachers might also like this Integration a Day Advent Calendar. Designed by Tom Bennison (@DrBennison) for Christmas, this would work well at any time of year - an integration question every lesson is a very good idea!
5 . Puzzling App
Henk Reuling (@HenkReuling) has created a free puzzle app which involves adding and multiplying integers. It's great fun for teachers, and it might be useful for students learning to work with negatives too.
It's really fun so do have a go.

In case you missed them, I wrote two posts over the Christmas holidays:

Check out @literallyjustq's latest thread about calculator functions which includes a calculator 'cheat' for finding the nth term of a quadratic sequence. 

Thank you to Jamie Frost (@DrFrostMaths) for hosting drinks for maths teachers at his house again last week - I had a great evening.

I'll leave you with @Blogdemaths' lovely 'How to Draw a Regular Pentagon, IKEA Version' (inspired by the work of @ideainstruction).

All the best for 2019.