5 Maths Gems #179

Welcome to my 179^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Maths Advance

I blogged about Maths Advance in Gems 173 - it's a website full of excellent challenge questions, perfect for high attaining classes. I've now had the pleasure of meeting the author of the website, George Bowman, at two recent conferences. Here are a couple of examples of his problems:

The problems are available for free, but subscribing to the website gives access to answers plus full video solutions.

2. A Level Topic Frequency and Advice

Thank you to @the_chalkface for sharing his analysis of topics appearing in Edexcel's A Level Maths and Further Maths exams. 

And thanks to @JohnRubinstein1 for sharing his 'advice for A level maths'.

3. GCSE Revision 

@draustinmaths has added to her excellent collection of revision grids. New additions include More Quadratic Equations and Inequalities, Circle Theorems, and Sine and Cosine Rules.

@MrMorleyMaths has added a number of new resources to his website mrmorleymaths.co.uk including Suggested Revision Booklets for Higher and Foundation Edexcel Paper 1, plus around 70 new How To Sheets with worked examples and exam questions.

Ken Stafford's website mathslinks.co.uk has been updated with worksheets containing Edexcel Past Paper questions for every topic, with handwritten worked solutions.

Also, check out these lovely hand-drawn posters of the GCSE syllabus from @mindmapmaths. These were shared four years ago but somehow I missed them at the time!

For more revision resources check out my GCSE 9 - 1 Revision Resources page. Or if you're looking for some handpicked recommendations and guidance on how to structure your revision lessons, see my recent blog post about GCSE revision.

4. Algebraic Fractions

@andrewmaths1 sent me some great questions from his travels in Canada. Here's one of my favourites:

I also like this one, for reasoning about graphs:

5. 1st Class Maths

I'm a big fan of the high quality resources produced by @1stclassmaths. They come in the style of both AQA and Edexcel. Recent additions include kinematic graphs, capture recapture, enlargements, algebraic proof, equation of a circle, tangent to a circle, circle theorem proofs and vectors. These are linked through my resource libraries. 

Update
Here are some things you might have missed:

• LUMEN launched their Key Stage 3 curriculum: learn about it here. 
  
• Your students might be interested in this Polypad competition. The deadline for entries is 17th May. 
• Designing your own maths resources? This geoboard from @StudyMaths makes very neat diagrams.

I've been busy since my last gems post. I had a great day at #mathsconf34:

And I enjoyed my visit to Stratford-Upon-Avon for #jointconf24, where I attended an excellent session on A Level by Rob Southern and Susan Whitehouse. Their book Teaching A Level Maths is out soon.

I recorded a podcast with Craig Barton which has had some lovely feedback.

🚨New episode🚨@mathsjem discusses 10 strategies that led to her and her team's incredible GCSE Maths results. Jo talks a lot of sense - apart from when it comes to mini-whiteboards. Enjoy!https://t.co/HJAFMHRFoo pic.twitter.com/14eQWhkovn

— Craig Barton (@mrbartonmaths) April 3, 2024

I also recorded a video explaining the Factor Method for finding a HCF and LCM (this has also had some surprisingly nice feedback, but I don't think I see a career as a YouTuber in my future...).

And I enjoyed a great night out at Puttshack (highly recommended for a work social) with my fantastic team.

I have a vacancy to join my team - it closes on 15th April. If you're looking for a change, and you want to work somewhere where it's a pleasure to teach maths to students with excellent attitudes, apply now. I can offer majority A level teaching, or a range of classes from Years 7 - 13, or just Years 7 - 11 if preferred.

This month marks the tenth anniversary of resourceaholic.com. I've written 478 blog posts in the last decade! Check out the archive here.

I'll leave you with an idea to get some spare Casio 83GTXs for classroom and exam lending. Since Casio discontinued this model but we still have three year groups using it, it would be helpful to ask departing Year 11 students to donate their calculator after their last GCSE exam (provided they won't need it next year). As an incentive, we might stand outside the physics exam as students come out and offer a swap - chocolate for calculator!

The Factor Method for HCF and LCM

I've blogged and presented about methods for finding a Highest Common Factor and Lowest Common Multiple numerous times, but I still think that The Factor Method* deserves a bit more love. 

[*also known as The Ladder Method, and various other names]

When I trained to be a teacher I was told that the Venn Method was THE way to find HCFs and LCMs. A few years later a colleague showed me a very different method that she'd learnt from a student, and this is what started my fascination with methods. I went on to write the book A Compendium of Mathematical Methods. 

Never trust anyone who says that a particular method is the best way of doing something because there is absolutely no research to back up their claim (it's a great shame that no one in maths education academia does large scale studies comparing methods - it seems like a big gap in our profession's pedagogical subject knowledge). However, I think it's reasonable to describe something as a favourite method. The Factor Method is definitely my favourite.

I've a made a 28 minute video explaining in detail how to find HCFs and LCMs using the Factor Method. This is a video for teachers, not for students. In it I model a number of examples, including those that might spark discussion. I also talk about how we can use this method to find an HCF and LCM of three numbers, and how we can easily use the Factor Method to work backwards.

I'm not a YouTuber so please forgive the ropey handwriting...

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 #177

Welcome to my 177^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. MathsLinks

I discovered the website MathsLinks through TES. It's run by maths teacher Kenneth Stafford. He has collated lots of resources in one place. For example, on his GCSE Questions by Topics page he has included links to websites such as Corbett Maths and Maths Genie for every topic.

He has produced numerous other resources including Grade 1 GCSE Maths Questions where he has combined the first two pages of Foundation GCSE maths papers, and a set of questions on Reverse Mean. 

Check out Kenneth's TES page and website for more.

2. Oak National Academy
It's good to see the collection of maths resources at Oak National Academy has grown since I last blogged about them in Gems 175. Here are a few extracts.

From Problem solving with factors, multiples, squares and cubes

From Angles on parallel lines traversed by a straight line

From Problem solving with polygons

3. OAT Maths

Thanks to @jemmaths for sharing some new algebra units published by OAT Maths: The Cartesian Grid, Introduction to Sequences and Linear Inequalities. Check out the carefully sequenced slides and booklets.

4. Etymology Update

One of my favourite resources of all time is @boss_maths' amazing vocabulary resource. It aims to relate mathematical terms to key words from other subjects that share the same etymology. It has recently had an update.

5. Tasks

Here are a few nice resources I've spotted on Twitter recently.

A prime puzzle from Sarah Farrell, suitable for Key Stage 2 or 3:

A task on solving quadratics by factorisation from @DrStoneMaths:

An area task from @brynspiration in which students have to find the area of the polygons, where no perpendicular lengths have been given:

@ChrisMcGrane84 shared a really nice logs task:

Update

I've not posted much on my blog recently but I've very been busy in the background. Thanks to maths teacher Alastair Mundy, who kindly offered to help out and has been an absolute legend, I've finally got my Key Stage 3/4 resource libraries in order. I've fixed broken links and added some new resources - everything is now in much better shape. I still have work to do: my next step is to fix my A level pages.

I also published a post on GCSE revision resources and one on A level resources. 

The start of 2024 saw a very well-deserved MBE for my brilliant friend Chris Smith (congratulations Chris!).

I'm looking forward to conference season. I will be at #mathsconf34 in Yate (near Bristol) on 16th March presenting on 'Ten Strategies for Good GCSE Results'.

Over the Easter holidays I'll be at the Joint Conference of the Mathematics Subject Associations in Stratford-Upon-Avon. I'm running a nice long session in Pythagoras so we'll have time to get stuck into some fun maths.

I have a couple of vacancies on my team, so if you're looking for a change of school in September then do come and join us. We're based in South London. Here's my fabulous team at the Christmas party:

One of our two vacancies is for a mechanics teacher. We currently have a thriving Year 12 cohort (we are by far the most popular subject in the school, with three A Level Maths classes and one A Level Further Maths class). Most of the A level teaching is done by me (statistics specialist) and my colleague (mechanics specialist). Sadly my colleague is relocating in September so I need to replace her, preferably with an experienced A level teacher. For the right candidate we'll be able offer a timetable where the vast majority of classes are A level (Year 12 and 13 Maths and Further Maths). The Year 13 Further Maths module they'll be teaching is Further Pure 1. I think this is a really appealing job - my school is lovely, and teaching A level is a delight. If you have any questions about the role, or you want to visit prior to interview, feel free to contact me (resourceaholic@gmail.com). The closing date for applications is 26th February 2024.

I'll leave you with these lovely magic squares from Chris Smith. Did you know that Don Steward had an entire blog of magic square activities? Check it out at medianmagicsquares.blogspot.com.

GCSE Revision

I've blogged about GCSE revision resources numerous times before, but with many schools running mock exams in February I thought it might be a good time to revisit some of the highlights. For advice on how to structure and deliver GCSE revision, see my CPD video Exam Countdown.

There are two main types of revision activity: topic focused and mixed topic. In the summer term I might spend the first few weeks doing topic-focused revision (i.e. I select topics where there are gaps and do a mini re-teach of those specific topics) and in the final couple of weeks before exams start I switch to mixed-topic revision and exam technique. Similarly, in the week before mock exams I might do two topic-specific lessons and two mixed-topic revision lessons.

There are a vast number of revision resources in both categories. Here I have picked out my top five from each. For a more comprehensive list of GCSE revision resources, see my GCSE Revision page.

Topic Focused Revision

1. 1st Class Maths
The resources from 1st Class Maths are consistently very high quality, so it's wonderful to see the development of an extensive GCSE revision collection this year. 

These fantastic resources contain totally original questions which are perfect for revision - they're not just collections of past exam questions that you might have already used in your teaching. 

The questions are very well written and are styled in the format of both AQA and Edexcel.

There's also a brilliant 'Ultimate Revision Booklet' which contains one question from each topic. We might print this off for our students to take home over Easter this year.

2. Maths4Everyone

Maths4Everyone is another great source of good quality resources by topic. There are topic grids like the Pythagoras one shown below, as well as sets of practice exam questions.

3. AQA Topic Tests

My exam board at GCSE is AQA, and I love their Topic Tests from allaboutmaths.aqa.org.uk. The other awarding bodies have similar resources available. 

4. Dr Austin

Last year Dr Austin added a collection of revision resources to her excellent website. There are themed revision grids (for example, six algebra revision grids of increasing difficulty level) as well as topic-specific grids.

5. GCSEMathsQuestions

GCSEMathsQuestions.co.uk contains PowerPoints in which GCSE questions from OCR, Edexcel and AQA have been collated by topic in one place. I find these resources incredibly helpful - it's great to be able to draw on a wide range of exam questions on each topic. I'm happy to use questions and resources from any awarding body in my teaching.

Mixed Topic Revision

1. Exam Papers

It goes without saying that students benefit from completing a large number of exam papers in the run up to their final exams. There are plenty of past papers available - both for the current GCSE specification but also for previous specifications (I still use questions from Linked Pair!). Awarding bodies also provide numerous practice papers, and there are papers available to purchase (for example Churchill and Zig Zag). When parents or students say they want extra practice papers to do at home, I normally suggest the CGP papers - these are handy for students as they arrive printed, and the mark schemes are student friendly. 

At this time of year (September to February) we encourage all students to independently complete and mark a minimum of one GCSE paper each week. We support this by running Papers Society after school every Tuesday (attendance is currently around 130 students, which is over half of Year 11). 

2. MathsGenie

There are loads of resources on Maths Genie and it's very user friendly for students. Last year I made good use of their excellent Mini Target Tests for both homework and revision.

3. Corbett Maths 

Corbett Maths is awesome for topic-specific practice (and here's a tip if you're teaching a top set Year 11 - check out the Further Maths section for some great extra questions on topics like surds, functions, circle theorems and algebraic fractions).

It's also excellent for mixed topic practice in the form of both practice papers and 5-a-days. Throughout Year 11 I use Corbett Maths 5-a-days for daily retrieval practice. They come in five different levels - I currently use the 'Foundation Plus' level with my Higher Year 11 class as they're working at Grades 4 to 6. The 5-a-day resources can also be used for mixed-topic revision in the run up to exams.

4. MathsBox

Subscribers to MathsBox have access to a large collection of revision resources including Skills Checks, Focus Tasks and 9 - 1 Assessments. There's lots to explore here!

5. Revision Mats 

Revision mats are available from various sources, for example Third Space Learning. I have made some myself, which are available on TES:

Non-calculator revision mats

Calculator revision mats Set 1
Calculator revision mats Set 2
Calculator revision mats Set 3
Calculator revision mats Set 4 

These don't have to be printed on A3, but students like it if you do!

I will be using these mats with my students, but will probably save them for the final weeks of revision before the GCSE exams this summer. I also have a set of popular breakfast revision mats that I always use on the day of their exams.

I hope this post of my top ten recommendations has been helpful. Don't forget to check out my GCSE Revision page for more excellent revision resources for maths GCSE.