17 March 2019

5 Maths Gems #106

Welcome to my 106th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Maths4Everyone
I have written about David Morse's (@Maths4Everyone) resources a number of times before. I use them a lot in lessons, particularly his packs of GCSE questions by topic. Up until now I have always accessed them through TES, but now David has updated his website so his free primary and secondary resources are easily accessible without a login.

One clever feature of the website is the 'click-to-zoom' functionality where you can zoom in on a particular question or solution when you go through answers with the class.
I also like the way his new codebreakers give an anagram - this stops pupils from giving up on the maths as soon as they've worked out the sentence which is a common problem in codebreakers!

2. Facts and Basics
Thanks to Adam Smith (@Adam_SmithMaths) who has shared 'Facts and Basics' resources for A level and GCSE. These quizzes include facts, formulae and short procedural questions to help pupils practise the basics.
3. Notation and Symbols
Thanks to Karen Campe (@KarenCampe) for sharing a link to the article "Learning Mathematical Symbolism: Challenges and Instructional Strategies" by Rheta N. Rubenstein and Denisse R. Thompson. There's lots to think about here.

In the table below, the last example is particularly worth discussing. At Amy How's Rekenrek workshop at #mathsconf18 she mentioned that she would never say 'zero point six' - she'd always say sixth tenths instead. I've heard other people say this too, and I wonder why I still continue to say decimals in such an unhelpful way. When I say 0.42 out loud to pupils, perhaps I should consistently say '42 hundredths' instead of 'zero point four two'. I have a feeling we (ie many teachers in this country - I know I'm generalising) might be a bit behind other countries with this.
The article includes teaching strategies:
"Students may also be instructed to record symbols in their own personal symbol table or card file, in which they write the symbol, record in English how to say it, and give examples of its use". 
Other ideas include asking pupils to invent 'graffiti' for mathematical symbols (examples below - these are similar to the calligrams I have featured in previous gems posts) and asking pupils to make their own examples and non-examples.

4. Mathigon
I first blogged about the amazing website Mathigon in 2014, and it was a winner in the 2015 Gem Awards. The content goes from strength to strength. The writer Philipp Legner has recently published a brand new free course 'Circles and Pi' that contains countless interactive explanations on circles, spheres, and conic sections. It is such a cool website - have a play with the animations and you'll see what I mean. Here's a trailer for the new content:

5. AQA Additional Maths Pilot Questions
A few years ago I wrote about using old Linked Pair Pilot questions with GCSE classes and shared some examples of good questions. I can also recommend old AQA Additional Maths Pilot papers too. To explain why I've been using these: twice a week I run morning intervention with a Year 11 top set at a school in Croydon. It's taken a while for the pupils to warm up to me, but we're getting there now. We spend an hour doing challenging GCSE-level questions together. It works well when I sit and work out the solutions alongside them. The problem is, because I'm not their teacher I have to be careful not to give them questions that their teacher might have already used. So I search for suitable questions elsewhere. Here two questions we enjoyed last week:

If you're preparing students for their GCSE exams then don't forget I have a large collection of revision resources here.

I've been super busy this year with various projects, hence the lack of blog posts. I do update things behind the scenes all the time though, even when I seem quiet! This week, thanks to lovely contributors, I added some new primary topics in depth packs and some new Pret homeworks.
My books, and the science books in the same series, have been selling well to schools. I'm now starting to look for authors for other subjects and key stages to further extend the series. I really hope they help Year 11s to do some revision over Easter. Just to clarify a few key points: 1) They are for students, not teachers. There's really no point in a teacher having a single copy, unless they tutor. 2) They are specifically aimed at the students who need support to get started with independent study. 3) They are literally just for memorising facts and formulae, nothing else. I explained the idea in this post last month.

Last week I went to a great event at Amazon with loads of cool maths people like Alex Bellos, Conrad Wolfram and Colin Hegarty. The Head of Amazon UK is a mathematician and he wants to support maths education. No doubt I will update my readers on this initiative over the coming months.

If you were at my Humble Pi book launch then do check out the superpermuatations video that was filmed at the event.

Humble Pi is currently the UK's number one bestselling book which is really exciting.

Last weekend was #mathsconf18 in Birmingham. As usual I had a lovely time, met lots of awesome teachers and attended great workshops. Thank you to David Faram for helping me run the MA bookstand and Rob Smith for driving the MA bookstand all the way from Leicester.

I presented on Unit Conversions - my slides can be downloaded from my Topics in Depth page.

Next weekend I'm speaking at the Habs Girls conference and the following weekend I'm speaking at Educating Northants which is going to be absolutely huge - check out the programme! Look out for a Conference Takeaways podcast from me and Craig Barton afterwards.

Next month it will be the fifth anniversary of resourceaholic.com (so time for my fifth annual Gem Awards!) and coincidentally in the same month I expect to pass 5,000,000 views.

I'll leave you with a problem from Daniel Griller (@puzzlecritic) that he shared in his workshop at #mathsconf18. Enjoy!

The numbers 1, 2 and x are written on the board. Their mean is equal to the product of their median and range. Find all possible values of x.

5 March 2019

5 Maths Gems #105

Welcome to my 105th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. MathsPad
As usual James and Nicola from MathsPad have shared lots of excellent resources with subscribers in their monthly update. Their pie chart tool is great!
This month they also shared a free set of fun cross-sequences puzzles that you can access even if you don't subscribe. I've added this to my algebra resource library.

2. Similar Triangles Problem
Thanks to John Rowe (@MrJohnRowe) for sharing this problem. Similar triangles spiral to form a regular decagon. The task is to find the length marked with a question mark.

3. Missing Steps
TickTockMaths (@TickTockMaths) shared an activity where students complete the missing steps.

You can download his algebraic fractions PowerPoint here. Check out all of Richard's free resources on his blog or on TES.

4. Maths Frame
Ted Burch (@Mathsframe) has converted all his free maths ITPs from Flash to HTML5 so they will work on any modern browser. These interactive tools are useful for for both primary secondary teachers. They are very easy to use. There's loads to explore so do check out the website.

5. Posters
This lovely set of STEM role model posters will brighten up school corridors and provide good talking points.
There's also a nice set of downloadable 'Forces of Nature' posters from Perimeter Institute which includes one of my favourite mathematicians, Ada Lovelace.
It's all been a bit crazy lately. On Saturday night I hosted Matt Parker's book launch in London. Thanks to all the wonderful people who helped out on the night and all the wonderful guests, it ended up being an utterly brilliant night. I had such a good time and loved every minute. After excellent and thoroughly entertaining talks in the amphitheatre from Matt Parker, Jen Rogers, Rob Eastaway, Tim Harford and Dan Schreiber, we ended the night with a show from FoxDog Studios which was the funniest thing I have ever seen! There was loads going on in the reception room too, including James Grime with an Enigma machine, Ben Sparks with 3D Geogebra, Andy Sharpe with Nrich maths games, and Chalkdust with their awesome magazine. Plus of course there was a self-playing piano performing a previously unannounced superpermuation. And the best goody bags ever.
Here's a video of my 180 guests (mostly maths teachers) thoroughly enjoying the interactive show from FoxDog Studios.

Thank you so much to everyone who came, and to our friends at Jane Street for the ridiculously generous support. I think it's time for me to retire from my event management hobby because there's no way I can ever top this one!

In other news, my books have now been printed. These books are for students (not teachers!) - they are designed to help them learn all their facts and formulae for GCSE maths and science. Please either bulk order for your students or point them in the direction of Amazon using these leaflets. I have explained how the books work in this short home video.
I'm ridiculously tired from the book launch (turns out that planning big events at short notice is a bit exhausting!), but still very much looking forward to #mathsconf18 in Bristol this weekend. I do love a mathsconf. I will have some samples of my books if you want to have a look. I will also be doing a talk about unit conversions (a technical glitch meant that people were unable to sign up to it for a while, but there is still space so please come along!), and I'll be helping to run the MA bookstand along with David Faram. Do come and say hello at some point if you're at the conference.

I'll leave you with this calculus comic from XKCD.

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: