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

5 Maths Gems #178

Welcome to my 178^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Inverse Proportion
I really like this tweet from @catrionateaches. When teaching inverse proportion I always talk about constant products but then I head straight into the formula y = k/x. Catriona suggests a subtle change in method. 

2. Graph Transformations

MathsPad has published another brilliant interactive tool for the Higher GCSE topic graph transformations. It shows how points on the original curves map on to those on the transformed curves. There is a separate section for quadratic graphs, which is particularly useful for relating completed square form to graph transformations. 

There is also a section for trigonometric graphs, where transformations of the graphs of y=sin(x) and y=cos(x) can be explored.

It's great to see a new resource published for teaching graph transformations - I always find that this is the GCSE topic for which it's trickiest to find suitable resources, because many tasks still include stretches (these were removed from the syllabus back in 2017 - GCSE now just covers reflections and translations).

Do check out MathsPad's full range of interactive tools - some of them are free to use even if you don't subscribe (you really should subscribe to MathsPad though!).

3. GeoGebra

It's worth following @geogebra to see ideas for interactive GeoGebra maths resources that can be used for demonstrations in lessons or student activities. Here are a few recent examples:

⚖️ GEOGEBRA RESOURCE! 📏

Try this FREE GeoGebra Exploration resource to convert units within a given system of measurement. Check it out! https://t.co/RQuWgxlNTR#mtbos #iteachmath #math #mathematics pic.twitter.com/qbp4U8DIFj

— GeoGebra (@geogebra) February 27, 2024

📦🐭 GEOGEBRA RESOURCE! 🥡🐱

Try this FREE GeoGebra Practice resource to draw box-and-whisker plots from a set of data. Check it out! https://t.co/VsqOGblJ2P#MTBoS #iteachmath #math #statistics pic.twitter.com/GAz9gbyLAR

— GeoGebra (@geogebra) February 27, 2024

🦾 GEOGEBRA RESOURCE! 🎰

Try this NEW & FREE GeoGebra Exploration resource to convert a number from standard form to expanded form one place value at a time. Check it out! https://t.co/vAIXvL5g48#MTBoS #iteachmath #math #mathematics pic.twitter.com/UXSN3RHQ69

— GeoGebra (@geogebra) March 4, 2024

4. Pythagoras
@nathanday314 shared a clever set of questions on Pythagoras' Theorem. There's a lot of challenge here (check out Question 12). Question 3 is deliberately impossible, and note the subtle differences between Questions 3, 4 and 5.

5. Prime Factors

@StudyMaths shared a video showing how to use the interactive Prime Factor Tiles on MathsBot to find a lowest common multiple, and in response @MrCowardMaths shared this really lovely task.

Update
Here are some other things you might have missed:

• The NCETM continue to publish their set of secondary mastery professional development materials. Their first set of Key Stage 4 materials focuses on numerical structure. These materials contain lots of teaching ideas that are well worth exploring. 
• @1stclassmaths has shared GCSE Predicted Paper 1 for both Edexcel and AQA. After Paper 1 takes place in May he will publish Predicted Paper 2s, and after Paper 2 he will publish Predicted Paper 3s. These papers will be very high quality so I recommend following @1stclassmaths for updates.
• @cclay8 has shared some more of her excellent calculator guides for the new Casio model. 
• @MattTheApp continues to share numerous resources for GCSE preparation on Maths White Board including maths formula sheet familiarisation tasks.
• @AMercerMaths shared a fantastic example of a curriculum booklet on diagonals in quadrilaterals. 

My school is still seeking an A level teacher to start in September. I can offer 100% A level teaching, or alternatively I can offer a timetable with Year 11 - 13 (or similar) if that's more desirable. Our students are a delight to teach and my team is awesome. If you live in Surrey or South London, this is an amazing opportunity. Please get in touch (email resourceaholic@gmail.com) if you're interested - I'm very happy to arrange a tour or call.

I'm presenting at two maths conferences in the next four weeks. The first is #mathsconf34 which is near Bristol:

And in the Easter holidays I'm presenting at the Shape Up conference in Stratford-Upon-Avon:

Finally, it's been a while since I've hosted a social event so I'm excited about this... more information coming soon.

5 Maths Gems #173

Welcome to my 173^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Graphics
@boss_maths has started to share a series of editable graphics for use in maths teaching. These lovely visual aids can be adapted and used as you see fit. Here's an example from Sudeep's pressure PowerPoint.

Check out Sudeep's hashtag #WednesdayVisual for more in this series.

2. Maths Advance

I spotted some challenging questions from Maths Advance on TES and this led me to the website mathsadvance.co.uk. This website is packed full of challenge questions for loads of GCSE topics. It's well worth a look. To access the solutions you'll need to subscribe.

3. Dr Austin
@draustinmaths has continued to produce new resources over the holidays, including tasks for negative numbers, decimals and factors and multiples. Thanks Amanda! I'll add these to my resource libraries. 

4. MathsPad

MathsPad have continued to publish more of their high quality curriculum booklets, the most recent additions being Year 10 Higher Chapters on Primes, Bounds & Calculator Methods and Formulae, Simultaneous Equations & Sequences, and a Year 10 Foundation Chapter on Indices and Standard Form. These are all available to subscribers - this is the subscription I recommend the most to maths teachers! I use MathsPad resources literally every day... Below you can see some examples of tasks from the new booklets.

5. Escape Room

@emmaemma53 made a Team Challenge for her Trust-wide maths enrichment competition, which had an “Escape Room” theme. You can find the resources she used here. Thanks for sharing Emma! 

Marvellous Maths 3

The biggest event for maths teachers this year is of course Marvellous Maths 3 - a full day of top quality maths CPD, presented by Craig Barton and myself. We now have three confirmed venues. The first course is on 18th October and it takes place at my lovely school in Sutton, South London (those of you who attended Marvellous Maths 1 in 2019 will remember the excellent lunch!). Then on 19th October we'll be at the very fancy Worcester Racecourse which is brilliantly located right in the middle of Worcester - it's near the station plus there's plenty of parking. On 20th October we'll be in Craig's hometown of Bolton at the Science and Technology Centre. 

For information and booking see mathscpd.weebly.com. We're excited to welcome our fabulous sponsors on board - AQA and OUP. It's shaping up to be a really exciting event, not to be missed. We've already sold lots of tickets but don't worry - we do have space on all three courses (we know most people will be putting in CPD requests at school in September). I recommend getting the ball rolling as soon as possible though - when we ran Marvellous Maths 1 in 2019 it did sell out quickly. For our Early Bird ticket, with 20% discount, you'll need to book by 8th September. Why not bring the whole department along? 

Resource Libraries
If you're new to teaching then you might not know about my resource libraries which contain listings of resources for Key Stages 3 to 5, organised by topic. I use these libraries every day when planning lessons as they provide a quick way to browse quality free resources. The easiest way to access my resource libraries when you're planning lessons is using the menu across the top of my blog.

I try to keep my Key Stage 3 and 4 libraries updated on an ongoing basis, and this year (now I'm teaching A level again, after a five year break), I will start to sort out the broken links in my Key Stage 5 libraries. I'll also add any great new resources that I discover. 

Update

I know lots of you will have been having a break from thinking about teaching over summer. Here are some things you may have missed, for when you're ready to get back into school mode:

• Ofsted published Coordinating mathematical success: the mathematics subject report in July. If you're teaching maths in England then you really should read this. If you find the format annoying, @mrshawthorne7 shared a helpful PDF version. And @mrmarchayes produced an excellent written and visual summary at marcrhayes.com.-of-ofsted-s-maths-subject-report-coordinating-mathematical-success
• MEI announced the return of their annual competition Ritangle which starts on 2nd October. This is aimed at A level mathematicians. 
• A level maths legend @TLMaths has been busy extending his video collection to cover lessons on GCSE topics.  
• I blogged about Year 7 Assessments and I shared a Twitter thread on Sixth Form Taster Day Activities.
• In preparation for the possible demise of Twitter, which was once the very best place for sharing teaching ideas, a lot of teachers have set up accounts on Threads. You can find me there as @mathsjem, but I'll still mainly be posting on Twitter until it totally implodes.

If you want to start preparing for September, you might find these resources helpful:

• My Year 7 Maths Activities post which features ideas for first lessons with Year 7
• My Displays page which contains loads of fantastic maths displays for corridors and classrooms

Over the last few days I've been planning my first department meeting of the year, and my first A level lessons. I've also started to prepare some CPD for my team on the new model of Casio. For this I'll be using @cclay8's cards. 

Apart from that, I've been having a lovely relaxing summer so far. I enjoyed drinks with my wonderful maths department on the last day of term...

I met up with Paul, Megan and David to say goodbye to the absolute legend Paul Rodrigo - he's off to teach maths in Sweden.

And I even managed to brush up on my history of maths whilst lounging by the pool in Gran Canaria! Fermat's Last Theorem by Simon Singh is absolutely brilliant - I can't recommend it enough.

Good luck to to everyone with A level and GCSE Results Days coming up. Enjoy the rest of the summer holidays!

5 Maths Gems #171

Welcome to my 171^st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. GCSE Revision Update

There's no shortage of GCSE revision resources but I made another revision mat anyway, because I needed one for a revision session the day before Paper 2.

There are separate versions for Foundation and Higher and they can both be downloaded from TES.

There have been a number of predicted papers and topic checklists made following GCSE Paper 1. For Edexcel, Adam Creen has collated them all here.

My school does AQA and we'll be making use of the predicted papers from Maths Planner and 1st Class Maths in the between-exam period.

On the morning of Paper 2 and Paper 3 we'll use my breakfast revision resources. We did the same for Paper 1 - we had two hundred students warming up in the hall. There was a great buzz and the resources worked really well.

2. Probability
I'm teaching probability to Year 7 after half term. I'll be making use of @TickTockMaths' new resource.

I always like the style of Richard's PowerPoints - you can find the whole collection on ticktockmaths.co.uk.

@taylorda01 also shared a probability trees resource, part of his Backward Faded Maths collection. I find that this is a topic where some students need a lot of scaffolding.

3. Certificate in Further Maths
@draustinmaths has reorganised her website and added a new section for AQA's Level 2 Further Maths. Resources include a Stationery Points Fill in the Blanks and an Exact Trig Values Match Up.

This page is linked through my Further Maths page. 

4. Tasks

Thanks to @MiddletonMaths for sharing some resources on their Twitter feed. Two examples include a worksheet on finding the area of trapezia and one one prime factorisation, both created using the Pointon and Sangwin taxonomy.

5. Roots and Primes

I enjoyed this thread from @MathsImpact with ideas for tasks relating to roots and prime factorisation. Here are a couple of examples - read the thread for more.

Update

I look forward to chatting to lots of maths teachers at two upcoming events:

• #mathsconf32 in Derby on 24th June where I'm presenting 'Challenge without Acceleration'
• The MEI Conference in Keele on 29th June where I'm presenting 'Good Task, Bad Task'.

I'll leave you with this new set of free resources from GeoGebra. This includes the addictive game 'What's Your Angle?', plus 'Find the Treasure' which might be nice when teaching coordinates at primary school, and 'Picking a Marble out a Jar' which might be useful when introducing probability.

5 Maths Gems #163

Welcome to my 163^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. The new school year has brought a flurry of activity on Twitter, with tonnes of great resources being shared over the last few weeks.

1. Zeroes and Ones

@TickTockMaths shared a couple of nice tasks to prompt discussion about writing superfluous digits. 

The first task is Do we need that 0?:

And the second task is Do we need that 1?:

2. Frequency Trees

Thank you to @blatherwick_sam for sharing this lovely frequency trees and ratios task. 

3. Graph Axes

Thanks to @mrshawthorne7 for sharing a great task for finding the equations of linear graphs where there's variation in the scaling of the axes. Charlotte says there’s some nice discussion to be had around Questions 1 and 4 (they're the same equation but ‘look’ different) and Question 5 and 6 (they ‘look’ the same but are different equations). The full resource features a mix of positive, negative and fractional gradients and some questions where given the equation the students need to label the axes. It can be downloaded from sketchcpd.com. 

4. Nets
Thank you to @joann_sandford for sharing a feature of @MathigonOrg's Polypad that I didn't know about. You can use it to create and test nets of 3D objects. Check out the gifs below where I had a little go myself. In the second gif you can see what happens if you make an incomplete net. It's very easy and it's fun! 

5. Tasks

There have been loads of fantastic tasks shared on Twitter recently, including a number by @ChrisMcGrane84 which you can find on his website startingpointsmaths.com. Examples include this task on working backwards from volume:

And this one on substituting negative numbers:

I've also seen some excellent tasks on standard form from both @MrE_Maths and @nathanday314.

@MrE_Maths shared a thread with lots of tasks featuring both scaffolding and challenge.

And @nathanday314 shared a thread and resource showing his approach to teaching standard form, including his narrative on the history and usage of standard form.

 

Conferences

Somehow I ended up presenting at three conferences in four days, which was stressful and a lot of hard work, but brilliant. I do love a maths conference.

On Wednesday I was at the Pixl Conference at The Oval in London. I'm not a Pixl member so it was fascinating for me to get an insight into how Pixl supports maths teachers through high-quality CPD, apps, resources and assessment (for example they provide mock exams - the kind that students won't be able to find online! - and grade boundaries). It's a really good model. The conference itself was a bit different to usual - it was a series of very short sessions, which meant it was buzzy and high-energy with lots of quick ideas. I did a ten minute keynote on challenge. It was a fun day, and the lunch was absolutely delicious!

On Friday I was at the Harris Federation conference. I work for a Harris school - every year all Harris staff have an Inset in October at the Excel Centre, with well over 4000 people attending. In the middle part of the day everyone goes to a role-specific session. I was asked by the maths consultant team to run the Key Stage 3 maths room which had around 130 delegates in it for a 2.5 hour session. This is a long time to run a room by myself, so in the middle part of the session I had everyone spend time trying out some challenging Key Stage 3 tasks from mathsvenns.com, Don Steward, MathsPad and mathshko. Everyone got really stuck into these tasks which was great. It was ironic that I shared excellent Don Steward tasks when Harris Federation has blocked access to Don Steward's website in all Harris schools, and despite my requests they will not unblock it. Incredibly frustrating. Anyway, if you attended this session then thank you for your excellent engagement - if you work for Harris and you want the slides, the maths consultant team will share them after half-term.

On Saturday I was in Manchester for #mathsconf30. This was brilliant. With Rob Smith running a full tuck shop, it felt like a real return to the full pre-covid experience. I attended some excellent sessions and really enjoyed chatting to lots of teachers, many of who were at their first in-person conference. I presented on Area in Depth which seemed to go well, despite some weird projector problems! If you attended my workshop - thanks very much for coming - you can access my slides on my Topics in Depth page. After the conference, Craig Barton and I recorded a podcast at Piccadilly Station where we shared our top tips from the conference. It's a super-short podcast (under half an hour!) so do have a listen.

If you attended any of the three workshops I delivered this week and you want to say thank you, you can buy me a drink here or support me by paying £4 a month on Patreon. Many other maths websites have adverts that provide an income stream but I don't have any adverts to help cover the cost of hosting my website. So any donations are gratefully received. Thank you!

Update

At all three conferences people asked me how my new role is going. I'm really enjoying being Head of Maths. It's nice to do a role I feel so confident in. I'm lucky I get to work with such a great team. I might blog about some Head of Maths stuff over half-term. 

My brilliant colleague Morgan made an amazing door display with her tutor group for Black History Month. It's fabulous. She got the graphics from Twinkl. Nira Chamberlain, who is featured on the display, tweeted about it:

Dear @mathsjem . Can you personally thank your students and colleagues from me for including myself on such a wonderful #BlackHistoryMonth design maths poster door. I am touched and humbled. @Mathematical_A @ICMS_Edinburgh @aimafidon pic.twitter.com/Y24ak2qUfk

— Professor Nira Chamberlain OBE PhD HonDSc 🇯🇲 (@ch_nira) October 14, 2022

Over the last few weeks I've been attending Open Days at my local schools. We're choosing a school for my eldest daughter Maddie who is in Year 6. My nearest secondary school is a Catholic school which she won't get into. We live in a grammar school borough but we decided not to enter her for the selection tests, so that left us with four comprehensive schools to look at, including my own. All the schools we looked at had brilliant maths departments - it was so interesting to get the chance to look around! 

My school's Open Day tour ran as a self-guided route around the school. The maths department was set up in the canteen. This gave us tonnes of space so we put maths puzzles out on three big canteen tables, and I was delighted that all three tables were quickly full of Year 6 children and their parents doing maths together, assisted by our brilliant student helpers. The engagement in these puzzles was incredible.

Open Day today. Massive amount of engagement in the puzzles we put out. Loads of parents sat down and had a go with their children which was fantastic to see. Loved having a room full of adults and children doing maths together. ❤️ Source: https://t.co/9Cz0dvjL0o pic.twitter.com/TQVlXltnXB

— Jo Morgan (@mathsjem) October 1, 2022

My school is a fairly new building and we have tried to keep things uncluttered, so the maths corridor has plain walls and - until recently - nothing mathematical about it. One of the first things I did when I became Head of Maths was to add a bit of personality - we now have a lovely wall sticker. Sticking this up during a lunch break was very intense! 

Here are some blog posts and resources you might have missed:

• My favourite maths blogger @Mr_Rowlandson blogged about Pythagoras following his #mathsconf30 talk. I was gutted I couldn't attend this talk - it was on at the same time as mine. 
• @my_mathsticks blogged about how he uses etymology in his teaching. He has a book coming out next month called Mathematical Etymologia. This is exciting - I love this kind of thing and talk about it a lot in my lessons.
• @TickTockMaths published some new lessons including adding and subtracting decimals, solving linear equations with fractions, rounding and order of operations.
• @draustinmaths published more new resources including some for GCSE Further Maths and some for circle theorems.
• The Mathematical Association announced the dates of its next annual conference. It will take place at the University of Warwick on 3rd and 4th April. It's a joint conference with all the maths subject associations. Save the date - this will be great!
• With the return of the dubiously worded GCSE formula sheet, it's worth reminding ourselves of resources which might help students practise using it: Dave Taylor shared this resource in April and Mel at JustMaths shared this blog post.

I'll leave you with three nice problems for you or your students.

First, @mcnally_gerry shared a simple but lovely surds task that I really like:

Next, @mathsimpact shared a problem from an old Key Stage 3 SATs paper. These papers are always packed full of lovely questions.

Finally, here's a great puzzle from @aap03102's brilliant maths newsletter.