5 Maths Gems #180

Welcome to my 180^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Area
I love @catrionateaches's suggestion that students write a 'plan without numbers' when attempting to answer compound area questions. They do the reasoning before they plough into the calculations. See Catriona's tweet for more examples.

I very much enjoyed @MrDraperMaths's recent post 'Area's Just Times' which is well worth a read. It features a number of excellent tasks.

I also like this clever little task from @giftedHKO, from her brilliant set of resources on sector area.

2. Factor Fish

@MrChapmanMaths shared a nice resource which encourages students to think systematically when finding all the factors of a number: Factor Fish. I've added it to my resource library. I've seen variations of this idea elsewhere (bugs, rainbows) but I've not seen fish before!

3. Crossword

Emily at SAMI has shared a brilliant A Level Maths Cryptic Crossword. Maths teachers will enjoy having a go at this!

4. Dr Austin
Dr Austin has been busy producing a constant flow of new resources. I use a lot of her tasks in my lessons so I am very grateful for this website. Recent additions include resources for equation solving, probability, two way tables, sequences and standard form.

5. MathsPad
It was great to see a new MathsPad update in July. They have shared a Thermometers Tool which can be used to introduce and explore negative numbers. They have also completed their collection of Year 10  booklets, and added new GCSE Revision worksheets on Probability and Indices and Surds. We are big fans of MathsPad at my school!

Update
I haven't written a gems post since April! I've never left it this long between posts before. It wasn't intentional... I always have a lot going on in the summer term with a number of family birthdays and social stuff, but on top of that school has been insanely busy lately. 

In June I hosted the launch of Matt Parker's new book Love Triangle. It was a great evening - thank you so much to everyone involved. All the entertainment was excellent and again I thought Foxdog were the funniest thing ever. Matt's book has very quickly become a bestseller. I highly recommend it to maths teachers - it would make an excellent summer read.

Last week I spoke at the London South West Maths Hub Conference about Challenge without Acceleration. I was nervous to present to an audience of predominantly primary teachers - I adjusted my talk to make sure it covered topics that we teach in both Key Stage 2 and 3, and in doing so realised just how many topics we have in common. It was a lovely conference and everyone was very friendly.

I'm looking forward to going to Belfast for the first time in August to present on both challenge and methods. I also look forward to the next Complete Mathematics conference which is on 12th October at Astrea Academy in Sheffield. I was disappointed to miss the June conference (I was at a concert!) so I'll make sure I attend the October one.

The book Teaching A Level Maths from Rob Southern and Susan Whitehouse has recently been published, so if you teach A level then get your order in now. I have very much enjoyed teaching three Year 12 classes this year, and am looking forward to having even more A level on my timetable next year. I will make sure I get a copy!

I have had many teachers contact me to say thanks for the idea I had to stock up on the old Casio calculator model by asking Year 11s to hand them in after their GCSEs. It sounds like it was a huge success in lots of schools! Ironically I had so many plates spinning at the time I didn't end up doing it myself, but I'm very pleased that other schools benefitted.

Chocolate for calculator swap worked a treat. Thanks for the idea @mathsjem 🍫 pic.twitter.com/IiUJDmPWtd

— Drew Sherratt (@DrewSherratt23) June 14, 2024

Thanks to @mathsjem for this great idea! Definitely one we'll use each year! pic.twitter.com/saaN4AXyf7

— Wyedean Maths 🎲📐📊 (@WyedeanMaths) June 19, 2024

On Friday night I went to a fantastic end of year Maths Department celebration at Flight Club. The members of my team are all legends and I'm looking forward to working with them again next year. One week to go until the summer holidays!

I will leave you with these lovely questions from @1stclassmaths. Check out his sets of questions by topic for more like this. 

AI Maths Resources

I've been sceptical about the potential of AI to produce high quality resources. I'd much rather have a set of carefully crafted tasks created a skilled maths teacher than a worksheet of random repetitive questions churned out by artificial intelligence.

However, a new collection of resources has come to my attention that may start to change my mind.

Maths teacher Duncan Grantham contacted me to explain how he's been using Chat GPT to write LaTeX code to generate maths resources. The underlying ideas behind these resources are atomisation and depth. Duncan's goal is to make resources that are hugely detailed that anyone could pick up and use with very limited editing. There are examples for teachers to work through, questions and worksheets, answers and so on.

The first resource Duncan sent me is about prime factor decomposition. It starts with a whole series of non examples and examples just getting students to think about what product of primes actually means:

Then a series of questions around getting students to just read off the prime factorisation:

Then a bit of working backwards:

Before actually just doing it for real:

The second resource is about about solving linear equations.

It starts by getting students familiar with the definitions e.g. 'what is an equation?':

Some nice tasks about the properties of equations:

Thinking about what solving actually means:

Then learning about manipulating equations:

Thinking about inverse operations:

And then getting students to solve equations where they have to show working out:

Before ultimately something a bit more standard:

ChatGPT made these resources so there may be mistakes or things that don't make sense. 

But isn't it interesting what AI can do?

I think there are loads of good ideas here.

Duncan has shared these two resources:

• Prime Factorisation
• Solving Linear Equation with an Unknown on One Side

If teachers find these helpful, he will continue to produce them and will share a large collection on his own website.

GCSE Paper 2 Resources

We are very fortunate in maths education to have so many hard working teachers and tutors preparing materials we can use between GCSE Papers 1 and 2, and later between Papers 2 and 3. 

My final timetabled lesson with my Year 11 class is a double on Friday 24th May, in which I plan to use the 1st Class Maths Practice Paper 2. 

We also have a 1.5 hour session over half term (optional for students, but I expect high turnout) in which I might use the Preparation Papers from Corbett Maths (before anyone asks - it's totally optional for my team to come in for this, and yes - we do get paid for it!).

I could write a blog post where I list all the various predicted topic lists and papers for all exam boards, but why replicate what's already done so well elsewhere? I highly recommend Colleen Young's post GCSE Maths Revision – Paper 2 and Adam Creen's Best Guess GCSE Dropbox. Colleen and Adam are very good at keeping track of everything that's published. Thank you both!

Assessing Year 10

We disagree about a lot of things in maths education but I think there’s one thing that makes total sense to everyone: we should never assess students on content they haven’t yet been taught. Doing so has absolutely no benefit to their learning.

Picture the scene:

A Year 10 student works hard and wants to do well. They enjoy maths and they always get good marks in end of topic tests. In the summer term they have been taught some challenging topics: probability, surface area and inequalities. They have a strong understanding of these topics.

As their end of year assessments approach, they put a lot of effort into their revision in all of their subjects. They diligently practise all the topics they’ve been taught in maths throughout Year 10, working particularly hard on surds and quadratics which they learnt back in September but feel a bit rusty on.

This student has been taught well and they have worked hard, so they feel confident and motivated. They look forward showing off what they've learnt in their end of year assessments. They want to make their parents and teachers proud.

The day of their end of year maths assessment arrives. They sit at their desk in the exam hall. Their stomach flips and their mind races as they look through the questions. It is a full GCSE paper. They haven’t been taught half of the content yet.

They leave the assessment with tears in their eyes. Not a single question came up on surface area and inequalities. All that work in the summer term and all that revision… and not a single question. And worse – there were big questions on vectors, iteration, circle theorems and functions. Five markers. But they’ve never been taught these topics so how could they possibly know how to do them?

This student is really upset. They worked so hard and they were not given the opportunity to show what they knew. What was the point in the questions on topics they'd not been taught? They don't understand. They ask their teacher who mumbles something about data. It makes no sense.

The child feels let down. They lose their confidence and their motivation.

***

To those schools who still do this, I would love to know what your rationale is. In the past I have heard teachers try to justify it but none of their reasons make any sense to me.

We wouldn't dream of giving A level students a full A level paper halfway through the course, so why on earth would we do it at GCSE? An English teacher wouldn't dream of giving an assessment on a book they hadn't yet taught.

It is not difficult to make a more suitable Year 10 assessment. The easiest approach is to take a past GCSE paper (choose one that specifically includes questions on topics you've recently taught) and remove the question on topics they haven't studied yet. Replace them with equivalent difficulty questions on topics that they have studied. Simple. It doesn't take long. If you're struggling to do this, feel free to email me for support and advice.

Love Triangle Book Launch

Tickets are now on sale for the book launch of Love Triangle by Matt Parker.

If you fancy coming you'll need to move fast as these tickets will sell quickly!

Information here: lovetrianglelaunch.weebly.com.

A lot of my readers attended the launch of Matt Parker's book Humble Pi back in 2019 and had a fantastic time. They will be pleased to hear that Fox Dog Studios are making another appearance! 

Here are two videos filmed at Matt's last book launch. The first one was during Fox Dog's performance - it shows how much fun the audience was having! The second one is about superpermutations.

Who knows what will happen at this one.

I hope to see you there on 15th June. Book now!

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.