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.

5 Math Gems #199

Welcome to my 199^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Trimension

Following on from the release of Vectorama (Gems 197) and Graphiti (Gems 196), Neil Kendall has completed a third project 'Trimension'. This tool allows the construction of 3D models to help illustrate 3D Pythagoras and trigonometry problems. The key feature is the ability to extract internal triangles into a flat diagram. Neil has included four pre-built examples from past GCSE papers to illustrate what it can do (just go to add > examples).

This is a fantastic tool for teaching 3D Pythagoras and trignonomety - thank you Neil!

2. Interwoven Maths

Nathan Day (‪@nathanday) has made some updates to his excellent website interwovenmaths.com, including a new page of small tasks and a contents page showing all the resources and ideas now available on the site.

There's loads to explore on Interwoven Maths including this Quadratics Always Sometimes Never.

Nathan also shared Class Duels - a maths game featuring over fifty topics from across Key Stage 3 to 5. It can be played in two-player mode (split screen, which can be done on an interactive whiteboard) and single-player mode. 

3. Exam Countdown

Nathan Day also shared a newly updated Edexcel Exam Countdown page which includes both GCSE and A level (including Further Maths) and shows dates for 2027. Interestingly, there are two GCSE papers before half term next year, and A level Paper 1 is before half term too.

4. A level

@andrewmaths1 posted a link to a website that I've not seen before. mathstutorneri.com is great for students aiming for an A*. There's a booklet of challenge problems and a set of exam papers.

It's nice to have another website we can use for high challenge. We've always directed our A* students to MadasMaths which I first blogged about in 2016. This week's Edexcel A Level Paper 1 had two questions that were very similar to MadasMaths questions, so clearly it's a good idea to use this website! If you're not familiar with MadasMaths, there's IYGB practice papers for maths and further maths (don't ask what IYGB stands for...!) and there are also booklets by topic. I often use questions from these booklets in my maths and further maths lessons (tip for new users: zoom in on the PDFs to see full worked solutions hiding in the booklets). 

5. Tasks 
There's been a number of new tasks and resources shared on Bluesky and Twitter in the last few weeks.

Here's a nice task from ‪@4301maths on equations of parallel lines. 

@dalechapman shared a couple of tasks: one on simultaneous equations and one on constructions.

@canning_mrmaths shared a Quadratic Graphs Venn task designed for learners to think deeply about different features of quadratic functions. The task has four variations levelling up in difficulty.

@giftedHKO shared some distance time graph questions.

And @draustinmaths.com shared some new resources for simultaneous equations.

Thank you to everyone who shares resources!

Update

We're halfway through external exam season (for my department, eight exams down and eight more to go!). This is what we've had at my school so far:

• AQA GCSE: Paper 1 was nice! I thought Paper 2 was difficult on both Foundation and Higher Tier. On Higher there was a question where students had to draw a two way table and some of them said they didn't know what that was!  Eek, there goes four marks. Yet if they'd been given a two way table to interpret or fill in the gaps they would have had no problem. So we must get them drawing more two way tables in lessons! There were two questions on Foundation requiring equating coefficients - we need to change our Foundation scheme of work to ensure this is explicitly taught in future. One paper to go!
• Edexcel A Level: Paper 1 was difficult. There were some tough questions, fiddly answers and a few questions where students would be unable to do part b without managing part a which is frustrating. Some of our students have lost a bit of confidence but hopefully Paper 2 will give all students the chance to show what they know. The Further Maths (Core Pure) papers were both ok and I'm looking forward to Further Statistics 1 this Friday (my favourite module!).
• AQA GCSE Statistics: We switched to AQA this year and our students were pleased with Paper 1. We entered Year 10 for the first time (see my post about our Option Block Experiment) - they were terrified going into the exam, but all smiles coming out! 

For 'best guess' papers please continue to check Adam Creen's dropbox which includes GCSE (maths and statistics) and A level.

My recent post aimed at Heads of Maths Tasks for the Summer Term went down well - I've had lots of emails asking for advice and resources. I'm always happy to help but bear with me at this time of year when there's so much going on at school - I will always reply within a week!

I'm looking forward to the MEI Conference next month - always one of the highlights of the year! I hope to see lots of you there. I will leave you with this fantastic present gifted to Emily Rae by a student - I love this!

5 Maths Gems #198

Welcome to my 198^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. GCSE Question Distribution

Thanks to Jamie Frost for producing a detailed breakdown of skills that have appeared on past GCSE papers. Other websites have analyses by topic, but Jamie has such an extensive database of past exam questions that he has been able to produce a much more granular analysis, for all exam boards and including IGCSE. 

I teach AQA at GCSE and when I teach circle theorems I always say 'alternate segment theorem seems to come up a lot in exams' - this was just a hunch, but now I know for sure - it does indeed come up a lot! Of course just because something has appeared in exams a lot in the past, it doesn't mean it will continue to do so (in fact, the opposite could be true - perhaps this year's GCSE exams will contain a lot of topics that haven't been tested in a while) so this data can't be used to make predictions. It's still interesting though. Thank you to Jamie for sharing it. 

Each skill includes a link to a randomly generated example question. Schools subscribed to Dr Frost can generate worksheets from these which can be printed or set as online tasks.

2. E2E Revision Sheets

@ThtPedagogyGeek has created a nice set of resources called E2E (Example to Exam) Revision Sheets. The idea is that you model the worked example - students copy it down and take notes, then complete the three questions. These are designed for GCSE revision.

3. Diagram Creator 

There are numerous online tools to create diagrams but I often find them unintuitive or overly complex, or they require a login. Thank you to @TickTockMaths for sharing a Geometry Tool designed for creating simple diagrams quickly. He made it so he could insert diagrams into lessons created with his Slide Creator (see Gems 197).

4. Corbett Maths Key Stage 1
Key Stage 1 teachers will be pleased to see that John Corbett has extended his popular 5-a-day range to Key Stage 1. He has made the first level (Ruby) with Emerald and Diamond to follow. 

I know that secondary teachers sometimes find these primary resources helpful too (I'm thinking of our Entry Level classes). 

5. A Level Resources

We had a difficult logs and integration question in our Year 13 mock this year that even our strongest mathematicians struggled with, so I'm pleased to see this lovely little task from ‪@mrlevmaths.bsky.social‬ for practising this specific skill.

Also thanks to ‪@karenshancock.bsky.social‬ for a resource on 'Power Equations' which is useful for Year 12 and also Year 11 L2 Further Maths students. 

Other resources on Karen's website that might be helpful for both Year 12 and L2 Certificate in Further Maths include Factorising with Surds and Graphical Solutions. Thank you Karen!

Also thanks to ‪@adamsfax.bsky.social‬ for his 'Edexcel formula sheet in a page'. We'll print these in September for all A level students to keep in the front of their book.

Big Mathematical Ideas

Colin Foster (one of the wisest men in maths education) has launched a new website: bigmathematicalideas.org. He has written a chapter on each of the five big mathematical ideas.

 

I believe this should be compulsory reading for every trainee teacher. No matter how good you are at maths when you train to be a teacher, the thing that everyone needs to develop is their pedagogical subject knowledge (not just how to do the maths, but how to explain the maths). But it's not just for trainees. I've been teaching for a long time now and I think my subject knowledge is pretty strong, but within a few minutes of reading this website I was thinking deeply about things that I haven't thought deeply about before (the big multipliers table in Section 1.5.2 had me wondering why I'd never shared this with students).

Reading this website will probably be my summer holiday project, or perhaps something I do in my gained time this term. I will use it to write next year's professional development sessions for my department.

 

Update

The first half of the summer term is very intense if you teach a lot of exam classes! I know that in some schools Year 11s have already started study leave, but I still have three weeks of lessons left with Year 11. I'm still doing topic-based revision (for example, next week we're revising surds and indices) and mixed revision (often using my revision mats). I always find that my students make masses of progress in our summer term revision lessons so I'm glad my time with them isn't cut short. If you're looking for good revision resources for Year 11, remember my GCSE Revision page has loads of hand-picked recommendations, and Adam Creen's annual 'Best Guess GCSE Dropbox' has been updated with the latest practice papers.  

I had a fantastic to response my last blog post (#mathsconf40) and to my recent conference presentation about Key Stage 3. I received dozens of emails from teachers asking for support on curriculum and assessments, including lots who said they find my gems posts helpful. Since most social media posts are now met with tumbleweed (a few likes and shares, but rarely a response), I often wonder if there's any point blogging for maths teachers these days - it's hard to tell whether anyone is listening. But after the flurry of lovely emails my enthusiasm for writing has returned, so thank you to everyone who got in touch. 💗

No doubt you saw that new research on setting in maths was published by the EEF. There are Year 7s in my school who struggle to add single digit numbers, or to multiply integers by ten, and others who find it easy to solve complex algebraic and geometric problems. Teaching these children in the same class doesn't make any sense to me, and I feel it would particularly let down the students who struggle the most and would benefit from being in a smaller group. Maths teachers are sometimes made to feel like they're evil or lazy for teaching in sets when they are actually trying to do the right thing for the students who need the most support. The narrative that schools often assign their 'worst' teachers to teach the lowest attainers is insulting nonsense. Most Heads of Maths prioritise the students who find maths difficult, and assign absolute superstars to teach them.

Here's a round up of some recent developments, in case you missed anything:

• Jonny Griffiths has updated his website carom-maths.co.uk which houses a collection of forty activities bridging from A Level Mathematics to University Mathematics. This is a great set of resources for a Sixth Form maths club. 
• Maths Genie has had a big update! Set up a free account to access useful resources, like the GCSE mini tests. 
• A few teachers have been in touch to ask about the RULER resources from Ben Tanner. These popular resources used to be available on Ben's website but it no longer exists. Helpfully, Tim Stirrup shared an archived version of the website, where you can still download the booklets.
• The QAMA is back - but this time, as an online version instead of a physical calculator. QAMA requires an estimation before it will work out an answer. It's great for developing number sense. If students don't have access to devices to use the online calculator in lessons, it could instead be used by the teacher in modelling. 
• Recently I've received a fair few emails from teachers who have either used AI to create tools for teachers or have created a platform where students can use AI to support their learning. For example, on gcsemathsai.co.uk students type in any topic or question and get instant step-by-step worked explanations. It covers the full GCSE syllabus and is free, with no account needed. One thing that stood out for me on this website is the misconceptions for each topic (e.g. look at 'common mistakes' for inequalities and arc length and sector area) which might be helpful for teachers planning lessons.
• Hannah Fry is going to be on the next Celebrity Traitors (our favourite family viewing - my daughter is obsessed with it)! Cue me telling everyone who will listen about the time Hannah bought me a drink and we hung out at BCME...

I'll leave you with these new 'squareas' puzzles from Transum. These are fun and come in multiple levels of difficulty. 

Thanks for reading!

5 Maths Gems #197

Welcome to my 197^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Dr Austin A Level Revision
It's always great to see new Dr Austin resources. Latest additions include a Harder Reflections Practice Grid and a Negative Enlargements Practice Grid, plus some new A level resources on Logs, Hyperbolics and Polar Coordinates. An A Level Revision section has also been added, featuring revision grids for Year 12 and Year 13.

2. New Online Tools
I've seen a number of excellent new online tools recently:

• Vectorama - I featured Neil Kendall's free resource Graphiti in Gems 196, and now he has published Vectorama which is designed to help teach vectors, matrices and transformations in 2D and 3D. It is helpful for everything from introducing the basics of matrix transformations to teaching eigenvectors in Year 13 Further Maths. Worksheets have also been provided so students can investigate the concepts themselves. This is a fantastic tool - thank you Neil!

• Reflections - Callum Adamson created a tool for modelling reflections in Gemini (download the file and it will run in your browser). You can use the shapes in the drop down menu or upload pdf versions of slides or worksheets and use an interactive mirror on top. In the picture below you can see I've uploaded a page from an AQA topic test and it looks very cool.

• Slide Creator - @TickTockMaths made a Slide Creator which is designed to create maths lessons quickly. Lessons can easily feature example problem pairs, interactivity, fill in the blanks and so on, all using pre-built templates. Check out some examples of lessons: area of a circle, assigning probabilities and factorising quadratics (open these on desktop, not a mobile).

3. A Level Resources
Recently I've seen some new A level resources that are worth sharing.

@andrewmaths1 has been tweeting a series of A level questions on X (thread here).

I like this scaffolded logs resource from @mrlevmaths.bsky.social.

And this great parametrics resource from ‪@karenshancock.bsky.social‬.

Finally, this isn't new but I hadn't seen it before so thought it might be useful to share. Whilst looking for an A level resource online I found the website mathematicswales.com. It features A level questions by topic - always helpful!

4. Mr Barton Maths
In Gems 195 I wrote about some of the fantastic new features on mrbartonmaths.com. Since then even more features have been added so do spend some time exploring it. For example, there's a problem solving section with loads of fantastic lesson ideas.

You can choose a topic and see suggestions for rich tasks and questions that get students thinking.

5. GCSE Revision

We always see a flurry of new Paper 1s being shared at this time of year - it's really helpful to have access to new GCSE resources that our students haven't seen before. It's important to be clear with students that it's not possible to guess what will appear on GCSE Paper 1 this summer so while these papers are great for practice, they can not be considered 'predictions' (though after Paper 1 there is an opportunity to narrow down the topics and attempt to guess what might come up in Papers 2 and 3). Here are the new (free) Paper 1s I've seen:

• 1st Class Maths (Edexcel Paper 1 H and F are already published and AQA is coming soon).
• Hannah Kettle
• Bennett Maths
• New website luckymaths.co.uk has Foundation practice papers 

If you're looking for good quality GCSE revision resources there are loads of them on my GCSE Revision Page - I've added a link to this page at the top right of my blog so you can access it quickly at this time of year. It includes some resources I've made myself including revision mats, the original breakfast warm ups, and the revision quiz I made last year which I'm looking forward to using again (see this post). 

Update

March was a busy time at school, the highlight being our annual Maths Week. This involves a treasure hunt, a daily puzzle, a Sparx contest and an assembly about a mathematician (this year I did it on Turing). 

We are always delighted when we see students attempting to solve the daily puzzle as soon as they arrive at school, and students crowded around the maths office at break eagerly discussing their ideas. We find it difficult to find suitable puzzles for all year groups - this year we took some of them from this helpful resource. 

Delivering assemblies is nerve-racking enough, but to add extra pressure I had a researcher from the Department for Education observing me this year. My school was selected as one of sixteen schools nationally recognised for high engagement, attainment and attendance, so we are part of their research on 'how schools foster belonging'. It was convenient that they happened to conduct this research during Maths Week, which is one of the best house events in my school's calendar.

Did you see the latest comment on my Words to Avoid post? It made me laugh.

I'm very much looking forward to the MEI Conference in July. Bookings are now open. I highly recommend this conference - it's always brilliant.

I'm also looking forward to #mathsconf40. I'm concerned it's going to be a particularly exhausting way to start the busiest half term of the year (I have a Parents Evening on the Thursday and a trip to Derby for mathsconf on the Friday night, both at the end of six period days!) but at least there's a Bank Holiday a couple of weeks later to aid recovery. It's always good to see everyone at mathsconfs, and it looks like there's an interesting range of talks on offer. I've written a new workshop on 'Challenging and Engaging Key Stage 3 Mathematicians' which I'm looking forward to sharing. I hope to see you there!