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 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) but it can also be used as a standalone tool.

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!

Gem Awards 2022

Last week it was resourceaholic.com's eighth birthday! It's become a tradition for me to mark the anniversary of my blog by publishing an annual 'Gem Awards' post. Here I look back at all the ideas I've shared in my gems posts over the last year and choose some of my favourites.

1. Mathematics Award
The beautiful website Mathigon won Best Website in my first ever Gems Awards back in in 2015. This time I'm giving it an award in my Mathematics Category, which has previously been won by Nicholas Rougeux for his stunning interactive recreation of Byrne's 1847 edition of Euclid's Elements. 

The website Mathigon has gone from strength to strength. It features an incredible online textbook, a brilliant interactive tool PolyPad, and a collection of lesson plans and activities that are well worth exploring. 

The two features that make it worthy of my Mathematics Award are its Timeline of Mathematics and its Almanac of Interesting Numbers. There's even a timeline scavenger hunt - a really well-designed activity where students can explore the history of maths. This kind of thing is perfect for extra-curricular maths clubs. It's also great for teachers looking to expand their subject knowledge.

Highly commended in this category are:

The History of Mathematics Project from Momath and Wolfram, which is like an online maths museum. I featured this in Gems 151.

And the mathematician profile cards and accompanying activity from Amplify that I featured in Gems 155.

2. Most Useful Resource Award

Never has a resource saved me so much time as @gcse_math's collated GCSE questions. I featured this resource in Gems 155. The key difference between this and similar resources is that it includes questions from three awarding bodies, meaning there's an abundance of exam questions for each topic. They're really well organised, meaning it takes seconds to find what I'm looking for. I'm finding this resource incredibly helpful when planning my GCSE lessons, and when making end of unit tests. I'll also make use of it when planning CPD sessions. Thank you to @gcse_math for taking the time to make this resource and for so generously sharing it. I should also thank the awarding bodies for writing the questions - there are often brilliant questions in GCSE exams!

Highly commended in this category are the NCETM Checkpoints, and the DfE's Key Stage 3 Maths Guidance. Both resources are very high quality, which is not surprising when you look at the team of experts behind them. The Key Stage 3 Guidance provides valuable CPD for Key Stage 3 maths teachers, with plenty of prompts for department discussion. 

Checkpoints are diagnostic activities designed for Year 7 children. Do check them out if you haven't already. 

3. Hidden Gem Award

Richard Tock has shared some fantastic resources this year through his blog and TES account. I love the clutter-free style of his resources and the carefully thought-out examples and tasks. I'm giving him the 'Hidden Gem' award because I think his lovely resources are relatively unknown and more teachers should check them out.

In Estimating the mean from a grouped frequency table, his lesson starts with some work on finding midpoints. 

and leads onto to a well scaffolded task on finding the mean.

Half or two? was designed as a starter task in response to a misconception Richard identified in his class. 

In Venn Diagrams and Simultaneous Equations, Richard shares a nice idea for a task that students might do by trial and error, before learning a method to work out the coordinates.

Have a look through Richard's blog for lots more great ideas for lessons and tasks.

Highly commended in this category is Segar Rogers (@SegarRogers), a maths teacher and talented task designer who shares his tasks on startingpointsmaths.com. Examples of his recent work include this task on the mean which utilises Pointon and Sangwin’s Taxonomy. 

It's also worth checking out his recent work on speed, orders of operations, fractions of fractions, cuboid volumes and vectors.

4. Best Blog Award

This year's Best Blog Award goes to Dan Draper (@MrDraperMaths) for his excellent blog 'Opinions Nobody Asked For'. Dan regularly posts witty and insightful pieces about his experiences in the classroom. He thinks deeply about topics and freely shares the excellent resources he has developed.

Here are a few examples of tasks - first, an exercise from his excellent post about the order of operations:

And from the post x=a, y=b: When?, a task where pupils practise filtering information on a diagram.

And finally, from his post Interleaving Circle Theorems 1, an example of a circle theorems question that brings together loads of previously taught content including trigonometry and area.

Highly commended in this category is Paul Rowlandson's (@Mr_Rowlandson) blog 'Pondering Planning in Mathematics' which won my 'Best New Blog' award in the 2019 Gem Awards. I always enjoy reading Paul's ideas - his blog posts have a lot of influence on what I do in my classroom. His recent post 'Using Numbers to Highlight Connections' got me thinking about connections between topics that I'd not really considered before. 

5. Teacher Website Award
The award for Best Teacher Website goes to Amanda Austin (@draustinmaths) for her brilliant website draustinmaths.com. When Amanda makes a resource for her own students, she publishes it on her website so we can all benefit from it for free. This is a really kind thing to do, and is much appreciated by teachers like me who make a lot of use of her resources. I particularly like all her 'Fill in the blanks activities' which feature both scaffolding and challenge.

A number of other websites deserve a special mention in this category, including:

• mathswhiteboard.com from @PiXLMattTheApp. This rapidly developing website features loads of useful functions like worksheet generators and QLA tools.
• @nathanday314 has two excellent websites: mrdaymaths.com which features tasks and teaching resources, plus the recently launched website interwovenmaths.com.

Running (and regularly adding to) a high-quality website whilst teaching full time is no mean feat.

6. Best Game Award

I absolutely love Nerdle. This quick daily maths puzzle has become part of my morning routine. The format isn't really new (I used to play the mastermind board game in the 80s which based on a similar logic) but the online games of this ilk that sprung up at the start of 2022 have become hugely popular and there are now loads to choose from: Wordle, Nerdle, Heardle, Movidle etc. 

This award goes to Numble, an app made by Olivia Gibson and shared by her teacher @mathsDJ. This game is impressive for a number of reasons, including:

• it's easy to play
• it helps students learn divisibility rules
• it's fun
• it was created by a sixth form student.

Highly commended in this category is MathsPad for their Times Table Sequences Game which is a really fun way to practise both times tables and sequences, and is great for both primary and secondary children. I enjoy playing this with my Year 5 daughter.

Also Highly Commended in this category is the excellent No More Primes from Nathan Day. 

7. Best CPD Award
The Best CPD Award goes to the book If I Could Tell You One Thing which was published by The MA and edited by Ed Southall. What I love about this book is that is features a wide range of advice from experienced maths teachers and experts on lots of different topics. There's something for everyone here, and because it's a collection of short chapters, it's easy for a busy maths teacher to dip into it.

Highly Commended in this category is the new podcast from Craig Barton 'Tips for Teachers'. This fantastic new initiative brings us snippets of sensible advice from expert teachers, available in either podcast or video format. 

Can I give myself a special mention for a gem award? Maybe that's not cool, but I was really pleased with how many teachers made use of my CPD video "Key Stage 2 Maths Curriculum Summary for Secondary Teachers". 

I should also say that all the CPD providers I mentioned in last year's Gem Awards are still awesome.

8. Best Resources Award
James and Nicola from MathsPad are the winners of the Best Resources Award this year for their fantastic collection of resources, particularly their new range of curriculum booklets. Their booklets are available for Year 7, 8 and 9 (so far) and are packed full of brilliant tasks for each topic, featuring lots of depth and challenge. Here are some examples of their activities:

What a fantastic collection of resources.

*****

Well done to all the winners of the Gem Awards 2022! And thank you to all the maths teachers who share their ideas and resources. There are many people who I've not mentioned here who have helped to fill my gems posts over the last year. We are lucky to have such a strong and supportive community.

If you're new to my blog and you enjoyed this post then visit my Gems Archive you'll find an index of 157 gems posts - they are all full of great ideas and resources. For the 'best of the gems', you might also want to check out the Gem Awards 2021, Gem Awards 2019, Gem Awards 2018, Gem Awards 2017, Gem Awards 2016 and Gem Awards 2015 to see who has won awards previously. 

Happy 8th birthday resourceaholic.com. Thank you to my readers for all your support!

5 Maths Gems #131

Welcome to my 131^st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Self Marking Sheets
Phil Rhodes (@Philmaths314) has shared a free set of Self Marking Google Sheets. As the name suggests, these are sheets that mark themselves. ⁦‪You can assign your class these Self Marking Google Sheets in Google Classroom. The site is very easy to use: choose a sheet, create your own copy and then assign to your pupils. When they input answers, they get an instant score.

2. A Level Knowledge Organisers
I am quite often asked about A level knowledge organisers, so it's great that there are now some available for teachers who wish to use these. 

Thank you to @Lucyjc1612 for sharing knowledge organisers for mechanics and statistics.

And thanks to @misschakera for sharing knowledge organisers for pure topics. 

I have now added these to my A level resource libraries and my Knowledge Organisers page.

Thank you also to Jake Goodman and Rachel Mahoney who emailed me some Key Stage 3 and 4 knowledge organisers for inclusion on the Knowledge Organisers page. 

3. Pedagogical Prompts

@DanielPearcy has published a new website danpearcy.com containing collections of tasks, prompts and resources.

Dan introduced his Pedagogy Prompts at the Seneca conference yesterday. These are designed to prompt discussion amongst maths teachers, to help develop teachers' pedagogical content knowledge. Dan suggests that discussion of these prompts might form the first ten minutes of a maths department meeting.

For the above prompt, Dan suggests the following questions:
1. Which formula do you use for the cosine rule? A formula that isn’t listed above?
2. Why might you stress the importance of number 2?
3. Is there a context in which you would consider teaching number 3? Is it a problem that this doesn’t appear in textbooks or formula books?

I found this really interesting. When I teach the cosine rule I always verbalise it only using the third formula, but have never seen it written down like this.

4. Planning Tool

Thank you to @timdolan who has created a planning tool to help maths teachers think through a topic or series of lessons before they plan in more detail. 

5. New Resources

Here are some new resources and activities that have recently been shared on Twitter:

• The classic Standards Unit resources have always been awesome. It's great that Ben Sparks (@sparksmaths) has started to turn some of these brilliant lessons into Desmos Classroom Activities. 
• @DJUdall shared this resource for exact trig values.
• @steelemaths uploaded a new resource to TES on Fibonacci-like sequences involving a little bit of algebra. 
• I used to work with colleagues who went crazy for the Pirate Game at the end of the summer term. Fans of this game may be pleased to hear that @AdamWteach has created a Google Classroom version!

Blog Posts to Read

• My favourite maths blogger @Mr_Rowlandson has shared a brilliant new blog post about posing questions in different directions.
• Check out @jnovakowski38's blog post summarising the best places to go for different sets of virtual manipulatives, along with presentations and articles to support the use of them. I have featured most of these websites in my gems posts over the years but it's great to have them all in one place. The only thing I'd add to this list is the wonderful MathsBot.com. 


• @InteractMaths shared a post with a range of carefully thought out median and range tasks.

CPD

Complete Mathematics Conference

Thank you to La Salle for sharing all the recordings from #mathsconf23 on their website. If you want to keep track of what you've watched, this session tracker shared by @MrWilliamsMaths is very helpful.

ATM CPD

The ATM has been publishing short CPD videos on its website. One example is The Words We Use with Jenni Ingram which is a seven minute exploration of the use of language in mathematics and how small changes can alter meaning. 

Senenca Conference

I really enjoyed the three hour Seneca conference on Saturday morning. It was a great length and format. The short talks were a fantastic way to showcase new speakers and - in a very rare thing for a maths conference - there was a good balance of men and women speaking. I spoke about Lowest Common Multiple - this was a mini-topics in depth presentation. You can watch it here, along with the other excellent presentations. 

Do check out the Padlet shared by Emma Bell (@El_Timbre) during this conference.  This will be of particular interest to teachers who teach GCSE re-sit. Emma shared her incredible work on 'The Focused 15' - fifteen interconnected topics to focus on with re-sit students.

Also check out the If The World Were 100 People video that Emma showed during her presentation. I have blogged about a few '100 people' resources in the past but this one was new to me.

My CPD Videos

The Order of Operations Topic in Depth presentation I recorded with Craig Barton back in February has now been published by TES. You can find it on my CPD Playlist, alongside all my other CPD videos.

Update

Two weeks left! I can't wait for the summer holidays. It has been a challenging term all round. 

My school is running our annual personal development week next week - this means I haven't had to set any maths work, but there's lots of other stuff going on including a virtual Sports Day and a Discovery Day, where I get to run a live lesson teaching students a load of fascinating stuff about banknotes (my chosen topic, which I know a lot about from my previous career). In the last week of term the maths lessons are back on but we also have our students coming in for end of term tutor group assemblies, which is really exciting. We're also doing end of year reports (consisting mainly of form tutor comments) which I have whole school responsibility for, so that will keep me busy. 

My own children have a lot going on too. Neither of my daughters (Year 1 and Year 3) have been back at school (the little one goes to an infants' school which couldn't accommodate Year 1), but their schools have planned some lovely end of term stuff, so they're happy. In terms of their maths, my Year 1 daughter is still doing the daily White Rose lessons, as well as using a few apps like Hit the Button and DragonBox. My Year 3 daughter does the White Rose lessons too, as well as Times Tables Rockstars. I recently realised that the Bronze 5-a-Day sheets from Corbettmaths Primary are perfect for her too (I don't know why I didn't think of that earlier!) so that's a late addition to our daily routine.

I will leave you with this fantastic video 'The Story of the Vinculum' from @jamestanton. It's brilliant.