5 Maths Gems #202

Welcome to my 202^nd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Visual Maths Builder
@mrallanmaths shared his new website visualmathsbuilder.com which helps teachers create clear, classroom-ready representations. It's free and no login is required - use it to create animated visual models that show how and why methods work.

2. Complex Numbers

Maths teacher Neil Kendall has developed another free resource to add to his incredible collection at korovatron.co.uk which includes Graphiti, Vectorama and Trimension. His new resource Komplexiti is for teaching complex numbers. Essentially it's an interactive Argand diagram designed for A level Further Maths but has graphing calculator features too.

You can enter complex numbers in any form and display them as points or vectors, solve any equation (e.g. roots of unity) and see the roots plotted, and plot loci in the complex plane including loci inequalities. View a gallery of its features here.

If you're teaching complex numbers then also check out Dr Austin's new resources for this topic.

I was recently asked if I could make a resource library for A level Further Maths. I mainly use MadasMaths, ZigZag and Integral in my further maths teaching, but as both Zig Zag and Integral are paid resources it's hard for me to make a comprehensive free resource library for this qualification.

3. Core Maths Compendium

I rarely get the chance to feature Core Maths resources in my Gems so I was delighted to spot new website edgarpoels.github.io/Core-maths-compendium/index.html from @edgarpoels. This free AQA Core Maths resource hub for teachers features slide decks, worksheets, mocks, revision booklets, end-of-topic tests and exam-style papers. This collection of resources is extensive - Core Maths teachers will be very grateful to Mr Pohl for pulling all this together and sharing it for free.

4. Website Summer Updates

I've seen some new websites and some website updates over summer, including:

• The incredibly useful PowerPoints on gcsemathsquestions.co.uk have been updated with November 2024 and June 2025 questions. The best thing about this site is that it features questions from Edexcel, OCR and AQA, which you don't get anywhere else. Because it pulls together three exam boards, there's a huge bank of exam questions for every topic. I use it all the time!
• Maths Rocket's question database has had a major update over the summer. Search a topic, get all the questions that have ever been asked on it, click through to the paper and mark scheme.
• Maths teacher Jon Glover contacted me about his new site mathsvault.uk. The site includes cover lesson packs and lots more. Jon is running a Countdown competition for teachers where you can win departmental access to the website. 
• I also received an email about mathorio.com which features over 300 free step-by-step maths lessons with worked examples, interactive graphs, and quizzes.
• MathsPad has some fantastic new resources for subscribers including Interactive Direct Proportion Bars, Cumulative Review Exercises and new resources for a number of topics including 'two triangle trigonometry'.

5. Mathsaurus Puzzles

My youngest daughter is now starting Year 8 - last year she used an excellent free course on mathsaurus.com to prepare for the UKMT Junior Maths Challenge. Because she's signed up to emails from Mathsaurus, which arrive in my inbox, I spotted that she was recently offered a free puzzles course.

There are 45 puzzles in the course, everything from chessboards and river crossings to missing digits, magic squares and overlapping shapes. Every puzzle is accessible enough for anyone to have a go at. The puzzles come in nine sets of five, with printable worksheets and animated video solutions.

These might be helpful for teachers running puzzle clubs. Alternatively, let parents and students know about the course so they can access it directly.

HoD Space
If you missed my blog post about my new project HoD Space then do check it out. Since I wrote it, HoD Space has really taken off. We already have nearly 300 members, which is amazing given it's been the summer holidays and a lot of people only engage with professional development in term time. I'm expecting a huge influx of new members over the next few weeks! We are still offering a completely free four week trial if you sign up any time in September, so join us now to see what it's all about - there's no obligation to join when your trial ends. I've missed EduTwitter very much since its demise a couple of years ago and I feel like HoD Space has brought that magic back! It's like Twitter but with longer answers... I'm loving it. I get to chat to maths teachers every day, and share ideas and feel inspired. And learn a lot! (the conversations about maths department budgets and about Ofsted are good examples! Join if you want to see them...). We're still waiting for responses to a couple of posts: one about Welsh medium resources and one about the exam structure in schools in Northern Ireland, so if you can help with either of these please join - you don't have to be a Head of Maths.

Update

The end of the summer holidays is fast approaching for me. I have mixed feelings about the year ahead: I'm very excited to be teaching Year 10 for the first time in ages - I get to teach surds, my favourite topic! - but I'm a bit nervous about next summer's early exam dates (two GCSE papers and one A level paper before May half term!) and the squeeze on teaching time. We don't start lessons until 8th September which is very late. I'm also worried about our Year 12 class sizes - we currently have 30 signed up for our A level Further Maths class which is a bit bigger than I'd like. 

This summer my department smashed our A level and GCSE results (we're a totally non-selective state school and we achieved 21% Grade 9 in GCSE and, coincidentally, 21% A* in A level!) which was wonderful. August was a great month! I got to celebrate the wedding of Sarah, a wonderful maths teacher who I've worked with for the last seven years, who married science teacher Sam in a beautiful wedding in Kent. 

And Jamie of drfrost.org married Esther in Taiwan, and a group of us enjoyed a lovely afternoon celebrating with them in Jamie's garden a few weeks later.

I love getting back in the classroom in September, but am always sad to say goodbye to the summer holidays. 

I'm looking forward to seeing lots of you at BCME in October half term. 

I'll leave you with cute Chrome Dinosaur Game shared with me by Alex Oliinyk. This is a free, ad-free, no-login version of the Chrome dinosaur game (the one everyone plays when the internet dies). Pupils play a 30-second round and instantly have real data to work with: site-wide, the median score is about 175 while the mean is nearly 590, so comparing class data against the real player distribution opens up skew, outliers, and why the mean can mislead. There's a printable lesson plan and pupil worksheet mapped to the National Curriculum. Enjoy!

Game by chromedino.com

HoD Space

When you get promoted to a new role in a school, whether it's as Key Stage Coordinator, Head of Department, Head of Year, or a Senior Leader, you probably don't get any training on how to do that role. If you're lucky the previous job holder is around to show you the ropes, but sometimes you just have to wing it, all by yourself. 

For the last couple of years I've been increasingly keen to offer training courses for newly appointed Heads of Maths. But in order to start a training business I'd have to stop being a Head of Maths, and that's not going to happen (I love my job!). I do already support Heads of Maths from across the country all the time - through my blog but also through email - over the last two months I must have received over fifty emails asking about my scheme of work. But it's very labour intensive for me keep sending advice and resources to individual Heads of Maths. So I was in need of a big idea to solve my problem - how to better upskill and support Heads of Maths - and along came Craig Barton, who always has good ideas. What if I delivered my Head of Maths training online, and provided resources to download directly, and we created a community where Heads of Maths could connect and help each other? Like Twitter used to be, with the constant sharing of advice and ideas and resources, but better - without the adverts and the politics and the hate. Craig introduced me to the Circle app, which is exactly what we need. We genuinely believe this is going to be a game changer, so we've invested in it and we're now ready launch our exciting new project: HoD Space. 

I've only been using the app for a week myself, and we only have a few members at the moment, but already I'm absolutely loving it! You can join too - the more members we have, the better it gets - and it will cost your school less than the cost of a training course. But it's so much better than a training course. You get my training, my resources, a weekly podcast where Craig and I will discuss the big topics that are coming up in the forums, and you get an entire year of expert support instantly available. Imagine being at work and knowing you have access to expert mentoring in your pocket. People who you can ask for help with difficult decisions, difficult conversations, or even the routine stuff - how do I decide on GCSE tiers, how do I set up my department tracker, how do I go about recruiting a new member of my team?  The impact is going to be huge.

Let's have a quick tour... I'll show you some screenshots from the app.

It's ridiculously easy to navigate. When you first join, read the welcome section then add a post in the introductions section and either me or Craig will say hello. Also complete your profile so we have information about your role and your school (this will come in handy later, when the community is large and you want to connect with people who, say, offer the same qualifications as you). 

There are various spaces where you can post questions. Sometimes there will be a quick answer, sometimes a lengthy discussion. If something causes a lot of debate, Craig and I will pick it up in our weekly podcast (we've just posted our first podcast episode). The space running the department is for the practical side of the job. Examples of questions might include:

• Where do you put your non-specialist teachers, and what support do they get?
• How do you structure TLRs in your department?
• How do you handle movement between sets during the year? 
• What's the best thing you spent money on this year?
• What do you do for Year 11 intervention?
• How do you handle a teacher whose behaviour management isn't working?

If there's something you'd rather ask without your name on it, you can send it through an anonymous question form, and we'll post it on your behalf.

There's a similar space for curriculum and teaching, where questions might be about schemes of work, feedback, marking, qualification delivery models, enrichment, and so on. With upcoming curriculum tweaks, and perhaps even more significant shifts in curriculum on the horizon as proposed by the new prime minister, there will be a lot to discuss here over the coming years.

There's also a space for recommendations and things to celebrate (I love this - a space where you can share things that have gone well at work - something most of us never do in public on social media).

There's also a surveys section where I will regularly gather information that we are all dying to know about each other's schools! Like the old Twitter polls that we all loved. I've started with two surveys on curriculum time (Year 7 and 11). Now I just need everyone to sign up to the free trial and complete my surveys!

In my video library I'll share two CPD videos each month, each one around 10 to 20 minutes long. I've already posted videos on planning September Inset meetings, setting Year 7, what to do on Results Day, and communicating with your team. I've also recorded videos on communicating with parents, setting up department trackers, scheme of work design, recruitment, and seating plans - these will all be published on the app soon. I have loads more videos in the pipeline, including assessment design, Year 11 intervention, running UKMT competitions and so on. 

Anyone can post in the resources to magpie section. I've already put some stuff here, and there's more to come from me in September. Soon I hope it's full of content shared by hundreds of Heads of Maths.

The members section is where networking happens - find HoDs in local schools, find HoDs who offer the same qualifications as you or have the same challenges, connect with them directly, maybe even visit them. There are literally thousands of Heads of Maths in the UK - imagine what we could do if we all joined forces. This is networking at its smartest. 

And what might come next for HoD Space? I can imagine in-person events (HoD Space conferences?), HoD Space for English and Science... So many ideas! So much potential.

I want join! What should I do?
Join today on a totally free trial. If you join now, you'll get full access for four weeks at no cost (free trials are normally only two weeks, but we're offering four weeks this summer only). We won't even ask for your card details up front. Then when you go back to school in September, ask your school to pay for your membership from the school's CPD budget. Given the impact it will have on the maths department, it will be very easy to justify. And if they won't pay, don't worry - you can take your career development into your own hands - we offer a cheaper membership if you're paying with a personal card. 

This isn't just for Heads of Maths - perhaps you're a 2ic, a TLR holder, or an aspiring Head of Maths. This is for everyone who wants to learn how to run a maths department, wants support for the department they already run, or just has an interest in what we're doing - join us on a trial to see if it's right for you.

Sign up today at hodspace.com. If loads of you sign up to the free trial and start posting questions or joining the discussions, it will start working really well. I need lots members so everyone can see how good it's going to be! Make sure you download the Circle app to access it - the app is brilliant. 

I'm really looking forward to chatting to you and sharing ideas on HoD Space. See you there!

 

5 Maths Gems #201

Welcome to my 201^st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Volumes of Revolution

My excellent A level student Samarth made a website volumesofrevolution.co.uk. He has very kindly shared it so that A level Further Maths teachers can use it in lessons when teaching volumes of revolution.

The website is very easy to use. You can create piecewise functions to make some interesting solids, and there's transparency settings to allow two different functions to be seen one inside the other. You can play and pause an animation of the rotation being performed, and sign in with Google to save projects. 

To minimise Samarth's costs (he's heading off to university this September!), the website will only run on weekdays. He's also included a buymeacoffee link to help keep the website  running. I'm very proud of Samarth and hugely impressed by his level of skill and attention to detail in creating this website. 

2. Clumeral

Emma Lark showed me the lovely puzzle site clumeral.com made by David Lark and Jamie Evawin. You work out the three digit numbers using clues and a process of elimination. Once you do today's puzzle you get access to the archive. I think both maths teachers and students will really enjoy these puzzles!

3. A Level Resources

Because most of the maths teachers frequently posting on Bluesky are A level teachers, I always have loads of lovely A level resources to share in my gems posts these days! Here are some I've spotted recently:

• @mrlevmaths.bsky.social shared some ideas for introducing students to double angle formulae.

He also shared a resource for reciprocal trig functions. 

• @andrewmaths1.bsky.social found a great website with TMUA practice papers: jzmaths.com/papers. There's also a very cool Easter Egg hunt that students (or teachers!) might enjoy completing this summer. 
• @sxpmaths.bsky.social has shared a blog post about all the changes he's been making to the sequence in which he teaches A Level Maths. This post includes a link to one of Stuart's booklets - Unit 1 : Points and Lines.
• @markywillis63 on Twitter shared a new series of Year 1 A-level questions by topic with both answers and worked solutions. 

4. Riddle of the Day

Gabriel Sobrino emailed me about the website riddleoftheday.org. Riddle of the Day is an independent bilingual site publishing one logic or mathematical puzzle each day, with progressive hints and fully explained solutions. I thought this might be helpful for maths clubs and competitions in schools.

Riddles are classified by difficulty level. For example here's one of the easier ones:

5. Constructions
@giftedhko.bsky.social has started writing a monthly newsletter for her department. Her July 2026 issue focused on construction:

Helen has some fantastic construction resources on mathshko.com.

 

I also spotted some constructions tasks on Transum when reading their latest newsletter. Their updated constructions activities give students the chance to practise compass skills, with each task leading to a measurable result: students complete the construction on paper, measure a length or angle, and enter their answer online for immediate marking. 

Whilst on Transum I spotted this cheating poster, updated to mention AI - I think it's worth talking to students about this in September (particularly A level students).

Update
On the last two days of the summer term I had the privilege of attending an event hosted by XTX Markets and Purposeful Ventures. You may already be aware of XTX's generous charitable donations in the sector, supporting organisations such as UKMT, Axiom Maths, Maths Horizons and Dr Frost (if you're interested in finding out more, read mathsexcellencefund.org, and XTX's philanthropy page). Over the course of the residential event, which was held at the very quirky but beautiful Brockett Hall in Hertfordshire, we discussed how to build more future mathematicians. 

For me it was incredibly worthwhile to consider the whole 'talent pipeline' from primary school through to PhD. For example on Thursday we broke into small groups and I ended up spending most of the day in a pair with Tom Crawford (his YouTube channel is popular with my students!) discussing in great depth how we can get more A level students to choose maths degrees. I loved how intellectually challenging this event was for me - I had the opportunity to do a lot of deep thinking and generate solutions to big problems. I really enjoy this kind of thing. I also loved catching up with a number of people who I haven't seen in years, and meeting lots of new people with fascinating jobs. There were plenty of attendees who work closely with schools, including people who do some teaching in schools as part of their jobs, but I was the only classroom teacher at the event - I hope I did a good job of representing my profession. I'm very grateful to XTX for the invitation.

Exciting New Project

It was good to see Craig Barton at this event - we always have lots of ideas for how we can support secondary maths teachers, and this time we've come up with something which we think is going to be brilliant. I don't want to give any spoilers here, but watch this space because we'll be launching it really soon. It's aimed at Heads of Maths and aspiring Heads of Maths. I genuinely think it's going to be a game changer.

Future Events

La Salle's maths conference dates for 2026/27 are:

• 5th September 2026 - Maghull High School, Liverpool (tickets now on sale)
• 14th November 2026 - Trinity Academy, Barnsley
• 20th March 2027 - Penrice Academy, St. Austell
• 5th June 2027 - The Duston School, Northampton

I can't make the first one unfortunately but I hope to be at others!

I will definitely be at BCME, which falls in October half term for me. I hope to see lots of you there. Make sure you apply for a bursary!

As the weather has been so relentlessly hot this year, I will leave you with a great example of a misleading graph to share with students.

Whatever Happened to Vulgar Fractions?

 Back in 2018 I was asked to write a couple of guest blog posts for La Salle. I wrote this post about vulgar fractions and another post about factorising non-monics. These posts no longer appear on La Salle's website so I'm re-posting them here. 

*********************

My Longman maths textbook from the 1960s tells me about the ‘Fraction family tree’. Its members are the brothers Vulgar Fraction, Decimal Fraction and Percentage, plus of course the illegitimate son Ratio who we don’t like to talk about.

Vulgar fractions are simply two integers (the numerator and denominator) placed above and below a fraction bar. They are also referred to as ‘common fractions’. I know the terms vulgar fraction and common fraction from my childhood but I never say them in my own classroom.

A Bostock and Chandler textbook from the 1980s tells us that “Usually we refer to common fractions simply as fractions and to decimal fractions simply as decimals”.

This alludes to the fact that during the latter part of the 20th Century the terms ‘vulgar fraction’ and ‘decimal fraction’ fell out of common usage in schools, leaving us with ‘fraction’ and ‘decimal’. With this change in vocabulary I don’t think we have lost any precision – the terms fraction and decimal are fit for purpose. So, although some lost mathematical vocabulary fills me with sadness, I don’t mourn the loss of the word vulgar.

The term vulgar fraction had been in use for centuries before it died out – it can be found in mathematics texts from all the way back in the 1500s. Here we can see it appear in a snappily titled textbook from 1741:

Textbooks from the 1700s and 1800s not only show that the term vulgar fraction was in common usage, but also provide some interesting definitions and explanations.

For example, in “A Treatise on Arithmetic, theoretical and practical” (Loomis E, 1856), we have this explanation:

It’s the last part that I particularly like: “This mode of expressing decimal fractions is used to avoid the inconvenience of writing the denominators’. I never thought of it like that. Just like the percentage sign is used as a shortcut to avoid writing a denominator of 100, decimal notation is just a shortcut.

All this talk of vulgar fractions made me wonder about the word vulgar. It’s a rather odd word to use in mathematics. A dictionary gives us the following definitions:

1. lacking sophistication or good taste.
2. making explicit and offensive reference to sex or bodily functions; coarse and rude.
3. [DATED] characteristic of or belonging to ordinary people.

Now I’m pretty sure that fractions don’t go round making offensive reference to sex and bodily functions. Certainly not in my classroom. Clearly the third definition is the relevant one here – the idea of being ordinary or common.

It turns out that the word vulgar comes from the Latin word vulgus meaning ‘the common people’, and it was first used in English in the fourteenth century. It then referred to something that was in common or general use or something customary or done as a matter of everyday practice.

The meaning of the word vulgar changed over time. It started as “relating to the ordinary people” but came to mean “commonplace”, and by the seventeenth century it had become “lacking sophistication or good taste”. One of the only places that the word continued to mean ‘ordinary’ was in mathematics. I think it’s a bit sad that a word meaning “of the common people” came to be associated with crude, uncouth and obnoxious. But I’m not sad that I don’t have to say the word ‘vulgar’ to a room full of teenagers anymore! That was asking for trouble.

In other news, did you know that it’s uncool to call a fraction improper these days? Apparently it’s a bit of an insult to fractions greater than one to suggest they’re not proper… Who knew.

A History of the Grouping Method

Back in 2018 I was asked to write a couple of guest blog posts for La Salle. I wrote this post about factorising non-monics and another post about vulgar fractions. These posts no longer appear on La Salle's website so I'm re-posting them here. 

*************

Factorising a quadratic when the coefficient of x² doesn't equal one (a 'non-monic') is apparently one of the more challenging skills that our pupils learn at GCSE. I've seen many pupils struggle with it, even those who achieve a grade 8 or 9 at GCSE and go onto take maths at A level. Interestingly, it doesn't seem like it should be challenging at all. I think it's way more straightforward than some of the harder reasoning questions that come up at GCSE - so why do pupils struggle with it so much?

When I first became a teacher, I taught my pupils to factorise harder quadratics in the way I've always done it: by inspection. Simply write out two empty pairs of brackets and try some numbers - thinking logically about what those numbers could be - until your terms expand correctly. It's very quick once you get the hang of it. In my NQT year this method was met with frustration by my Year 11s. They wanted a more defined procedure. I looked online to see if I was missing something and discovered 'the grouping method' which I then showed them as an alternative. I felt that it was an unnecessarily convoluted method but they clearly preferred having a set of rules to follow rather than having to reason for themselves. It made me a bit sad.

The grouping method, explained in a GCSE maths textbook published by OUP in 2016

This grouping method, particularly the last step where terms are gathered together, is a bit of a leap of faith for pupils who have never seen this kind of factorisation before. It kind of seems like magic.

Ten years on, I still prefer inspection (the 'guess and check' method) but I teach my pupils the grouping method as an alternative. I know they'll see it elsewhere even if I don't teach it to them - in textbooks, revision guides and online videos. I find that only the strongest pupils favour inspection - most pupils choose to use the grouping method but very often forget it. Days before the GCSE exam I hear cries of 'what's that thing you do to factorise hard quadratics? Something to do with the middle term...?'. The steps in the grouping method are not intuitive, and as a result it's difficult to remember.  

Given I had never heard of the grouping method before I started teaching, I was surprised to learn that it's actually an incredibly popular method. In fact, it appears to be the method that most maths teachers now use to teach non-monic factorisation.

How did I miss this method during my time at school? I did my maths GCSE in 90s. I have a couple of Bostock and Chandler textbooks from the 1990 - both only feature inspection, with no mention of grouping.

Grouping to factorise quadratics in the 1950s

This probably explains why I'd not seen it before. It wasn't in fashion when I was at school.

Looking further back I was surprised to see that older textbooks do feature the grouping method. Here, in New Algebra for Schools (Durell, 1953), we see an example of the grouping method. Durell recommends this method for both monic and non-monic quadratics.

The inspection method in use in the 1990s

Note though that this follows on from extensive use of grouping elsewhere. By this point in the textbook pupils have had considerable experience of factorising expressions like p(a + b) + q(a + b) and ax - ay + bx - by. This is absolutely key. There is a clear progression here that I feel is often missing from modern teaching of factorisation. I'm not sure it make much sense for pupils to only use the grouping method for non-monic quadratics, having never done any kind of factorising by grouping before.

 An exercise in factorising by grouping, to be completed prior to learning how to factorise quadratics by grouping

Later, this chapter tells us that simple quadratic functions can often be factorised at sight without using the grouping method. It says "use the grouping method whenever you are not able to obtain the factors by inspection, quickly".

Another textbook from eight years later (The Essentials of School Algebra, Mayne, 1961) also features both the grouping and inspection methods. Again, earlier in the chapter there is a considerable amount of work on the skills and understanding required for the grouping method. Of inspection it says,

"After a little practice, the pupil will be able to reject mentally the impossible pairs of factors... With simple numbers it is slightly quicker than the method of grouping terms, but the grouping method is the method to rely on. It should always be used whenever the pupil is not able to obtain the factors quickly be inspection."

So it seems that the grouping method may have been popular in the mid-20th Century.

Looking even further back, in Elementary Algebra for Schools (Hall & Knight, 1885) we are told that we should factorise non-monics by inspection:

"The beginner will frequently find that is it not easy to select the proper factors at the first trial. Practice alone will enable him to detect at a glance whether any pair he has chosen will combine so as to give the correct coefficients of the expression to be resolved".

There's no mention of any alternative methods here.

I haven't yet read enough old textbooks to track the full history of the grouping method, but from what I've seen it has come and gone over the years, and sadly seems to have become detached from prerequisite skills along the way.

If teachers are teaching the grouping method to factorise non-monics and have not already taught pupils how to factorise expressions like p(a + b) + q(a + b) and ax - ay + bx - by  then I think they may be trying to teach too many new skills in one go. It's something to think about.

********

There are, of course, dozens of methods for factorising non-monic quadratics, some more 'tricksy' than others. Read my book A Compendium of Mathematical Methods for more on this.

5 Maths Gems #200

Welcome to my 200^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. MathsPad
MathsPad's May and July updates includes lots of fantastic new resources.

Their Topic Key Facts Sheets are designed in a two-column question and answer format, so that pupils can self-test by covering up the second column. Very helpful for revision at Key Stage 3 and 4, they can be found at the top right of their curriculum pages.

MathsPad has also shared two packs of 'Grade 9 Club' Question Packs: Pack A and Pack B. These include worked solutions for each question. 

They have also published a series of Foundation One Markers containing non-calculator one mark questions for GCSE Foundation on a mixture of topics. The skills recur from one sheet to the next, so pupils get repeated practice of each skill.

There's other new resources too, including more in the Building Blocks range (aimed at secondary school students who need support with the basics), more Higher GCSE revision packs, and an inverse functions matching activity. We love MathsPad at my school - it's well worth the subscription.

2. X Why
Andy of m4th5.co.uk has shared a graphing tool for classroom use: X Why. It can be used to see graph transformations happen, draw instant inverses, put your own labels on curves and points, see integrals and areas under curves, draw tangents and normals and much more. Graphs can be exported to worksheets and presentations, and axes are auto-scaled for degrees and radians.

3. NCETM Professional Development Materials

The final set of the NCETM's Key Stage 4 Professional Development Materials is now available, completing the full suite of Secondary Mastery Professional Development Materials for both KS3 and KS4. This set covers Key Stage 4 Geometry including transformations, circle theorems, trigonometry and 3D shapes. As with the other sets, these materials contain lots of fantastic ideas for getting your students thinking. For example, there's a task where students are asked to identify which of the diagrams correctly show the alternate segment theorem.

I also like what they've done here with bearings diagrams in non-standard orientations...

... and I like relating vectors to throwing a ball.

4. A level 
In my last lesson with Year 12 this Friday I will be teaching Year 2 Binomial Expansion with Partial Fractions - I never understand how anyone manages to fit the entire A level curriculum into such limited time! I'm perpetually running behind with my A level classes. But if you have a spare lesson with Year 12 at the end of term, they might enjoy this murder mystery revision task from Danielle @PixiMaths. You can download it here.

Another A Level resource that caught my eye recently was a set of statistics tasks posted by MrLevMaths. Read his blog post for more.

5. Esheets and Whiteboard Workouts
I discovered two websites that aren't new, but I've not seen them before. 

esheets.io from Richard Linnington features self marking worksheets, maths puzzles and games (including end of term maths activities) and teacher visualisation tools. I particularly like the sheep tethered to a building and sheep with a sliding ring.

Whiteboard Workouts from southportmaths.co.uk are PowerPoints that are designed for mini whiteboard questioning.

A Milestone
I started this blog whilst on maternity leave in April 2014. My first post was about a method for matrix multiplication. A lot of my earlier posts were about methods. Later I started writing more about resources. I wrote my first gems post in August 2014, when I realised that there were loads of great ideas and resources being shared on Twitter that needed to be shared more widely, so that all the maths teachers in the country (and beyond) could see them, not just the teachers using social media. Over the years I've been contacted by many teachers who tell me that they find these posts helpful, so I continue to write them. There are a number of authors and websites that have 'found fame' after they featured in my posts! 

Today I've published my 518th blog post, which is the 200th post in the Maths Gems series. I used to post gems posts every week, but it was impossible to continue posting so frequently as my daughters grew older, and my school workload increased. Now I try to write one gems post a month, but it can be difficult to find enough material since the mass exodus of maths teachers from Twitter. Back when the new GCSE was introduced in 2017, social media was packed full of teachers sharing resources and helping each other out - with another curriculum change on the horizon, maybe we will regain some of that magic once day. In the meantime, I will endeavour to continue posting once a month. If you're new to my blog then I recommend having a look at my back catalogue of gems posts. There's a lot of great stuff in them. 

Events
I had a fantastic time at the MEI Conference as always. I attended on Thursday evening for the dinner and drinks (free bar courtesy of Casio!) and all day on the Friday. I presented on methods to a lovely audience, and enjoyed trying some incredibly difficult geometry problems with Bernard Murphy. Sue Black's keynote was excellent. Shout out to Marc the tutor who sat with me and Megan Guinan after my session and showed us a fun method for factorising non-monic quadratics.

Looking ahead at events that are coming up...

• On the last two days of the summer term my headteacher has kindly given me permission to attend the Future of Maths Education event which is being held by XTX Markets. This is an invite-only event and I'm delighted to be on the guest list. I believe I'm the only teacher attending - in fact I have to go there directly after running a Year 7 trip so I'm expecting to be thoroughly exhausted... but I am really looking forward to it. 
• Mathsconf41 has been announced - it's taking place in Liverpool on 5th September. A conference at the very start of the academic year is a fantastic idea - the perfect timing to inspire and motivate. I'm not sure yet whether I'll attend - as both a mum of teenagers and Head of Department I have a feeling I'll have a million things to do that weekend. But I hate to miss a mathsconf so I will have to have a think about this one!
• BCME 10 is a big deal in the world of maths education, and it takes place in Nottingham on October 23rd and 24th. I loved the last BCME in 2018. To cut the cost for teachers, bursaries and early bird rates are available but you have to act now to take advantage of these opportunities (the deadline for bursaries is this week! And the early bird rate is valid until the end of July). Information about bursaries is here. I would apply for one myself but my school isn't in an area of high deprivation so I don't qualify. I really encourage teachers who meet the criteria to apply for a bursary to help cover the cost - it's so important that teachers attend this conference.

Update

What an insanely busy time at school! Our classrooms were sweltering when it was 37 degrees and we had a few early closures in response to parent concerns about students travelling home in the extreme weather. We also had new staff induction and Sports Day last week (Sports Day picture of my maths team below - minus four members who were busy elsewhere!). Plus I've been hosting lots of visitors in my department who come to see my curriculum in action and find out how we do things. This week is Open Evening and Year 10 are on work experience, and then the following week there are a whole load of trips to run. As I said in my post Tasks for the Summer Term, this time of year is always surprisingly busy! And the delay of SATs results will have me working in the summer holidays (even more so than usual) because I use them for Year 7 groupings.

Have a great week! Thanks for reading.