#5 Maths Gems 182

Welcome to my 182^nd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1.Bad Graphs

It's fun (and important) to share examples of misleading graphs with students. @ticktockmaths has shared a gallery of bad graphs which will be very helpful. I love the example below: at first glance it seems very clear and the scale seems fine, but when you think about what it's trying to show you realise how misleading it is.

Do check out the rest of ticktockmaths.co.uk - the lessons on there are really nice. Recent additions include one on Mixed Numbers and Improper Fractions and one on Writing Expressions. 

2. Algebraic Fractions

@japleen_kaur1 shared these lovely algebraic fractions questions made by her colleague.

Answers are here. Thank you for sharing these Japleen! I love the creativity. 

3. Fractions Vocabulary

@Scott_Math83 shared three simple questions which highlight the challenges students face when working with fractions and percentages. A subtle change in wording totally changes each question. 

4. Multiples

I love tasks which encourage deeper thinking about factors, multiples and primes. Thank you to @studymaths for sharing this:

Check out @studymaths' feed for lots more excellent tasks.

5. Dr Austin

@draustinmaths continues to share great new A level resources for both pure maths and mechanics. Recent examples include a task on set notation and one on graphical inequalities and regions. Thanks Amanda!

Update
On Friday I was at the Harris October Conference with my lovely colleagues. 

If you want to join my brilliant team, we have a vacancy for a January start. Contact me if you want to chat about the role - but note that the closing date for applications is Monday 14th October so you will have to act quickly!

After a quick stop at post-conference drinks in London, I got the train up to Sheffield for pre-#mathsconf36 drinks. Two sets of drinks on the same day in two different cities was a bit much for me - I'm too old for this and I was beyond exhausted!

 

On Saturday I attended #mathsconf36 which was excellent. It was the best conference I have been to in a long time, and it has rekindled my love for mathsconfs! I went to fantastic workshops led by Rob Eastaway, Sam Blatherwick and Craig Latimir. I really enjoyed these workshops. I ran a session myself called 'Every Mark Matters' where I shared examples of where students lose marks at GCSE. The idea is that we show these examples to our students to help them better understand what's expected. If you attended the conference, my slides will be emailed out next week by the team at Complete Mathematics.

If you've not been to a mathsconf in a while, or you've never been before, then I strongly encourage you to attend the next one. It will be in March - date and venue tbc.

Finally, this week I did the classic paper folding integration activity with my Year 13 class. The idea came from @sxpmaths many years ago and it's always my favourite A level lesson of the year!

#5 Maths Gems 181

Welcome to my 181^st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. A level
I've seen a number of fantastic new A level resources recently:

• From @the_chalkface, exam questions arranged by topic for Edexcel A level Maths and Further Maths. Although similar collections already exist, this may become my go-to: it's well organised, easy to access and high quality.
• From @m4thsdotcom, 160 worksheets for the pure course, targeted by grade.
• A new page for A level resources on one of my favourite websites: 1stclassmaths.com.
• A growing collection of A level resources from @draustinmaths at draustinmaths.com/a-level.
• Year 12 revision sheets with solutions from @mrsouthernmaths.

Thank you to everyone for their generous sharing!

2. Standard Form
@giftedHKO has been tweeting about some of the lovely tasks on her website mathshko.com including this one for standard form:

Check out her website for more like this.

3. Memory Maths
@studymaths has updated the classic 'Memory Maths' game. You can now generate your own. We used to use this at my last school on Open Evening -  parents, children and teachers would be given a mini whiteboard and told to draw a grid. Then they would gather round to write answers on their whiteboards as the questions flashed up. It was always lots of fun - everyone was always excited to see who would be the first to complete their grid.

There's a wide range of games and starters to check out on mathsbot.com.

4. Quadrilaterals

Over summer @EmathsUK shared a really nice quadrilaterals task that I've not seen before. Students are asked to come up with suitable questions to populate the flow chat accurately and then name the quadrilaterals. The task can be downloaded from emaths.co.uk.

5. Circles
@AMercerMaths made a lovely "Sometimes, Always, Never" on parts of a circle which provides lots of opportunities for reasoning.

Update

I haven't written a gems post since July so here's a quick update on what I got up to over summer.

In July @MeganGuinan1 went to drinks to celebrate Matt Parker's book Love Triangle becoming a bestseller. We met the most fascinating people at these drinks, from zoologists to linguists.

In August I met up with fellow South London maths teachers @MeganGuinan1, @LeightonM4ths and @nkl_17. 

And I ended the summer with a trip to Belfast where I had a fantastic experience presenting to a wonderful group of maths teachers from the West Belfast Area Learning Community.

I wrote three blog posts during August that you might have missed:

• Latest Resources and Trends
• Digitising Old Textbook Exercises
• Challenges for a Head of Maths

The start of term has hit like a sledgehammer, like it does every year, and I already feel like I'm at peak exhaustion. I have 33 students in my Year 12 A level maths class, but only enough desks for 32. Year 12 have neither textbooks nor devices because we don't have the budget to buy either. I also have 27 students in my Year 12 Further Maths class which is a shock to the system after having only six last year! It will take a bit of adjusting but we'll make it work. Apart from all that, we seem to be settling into our new school year - in my last blog post 'September Routines' I shared some of the things we have put in place in the first few weeks of term. We were very happy that over 100 students turned up to our first Papers Society - this bodes well. I'm also very much enjoying teaching our new option block class in Year 11 - teaching Level 2 Further Maths in timetabled lessons for the first time is a delight.

I hope to see lots of you attend #mathsconf36 in Sheffield next month. I will be sharing some insights on things students need to look out for at GCSE.

Have a great week!

September Routines

No matter how much preparation work I do over the summer holidays, the first two weeks of September always feel insanely busy and stressful. But I do love the excitement of a new school year, and the opportunity to relaunch and reset everything. Fresh starts all round.

In this post I thought it might be useful to share some of the start-of-year routines and initiatives that we have in place in my department - feel free to borrow anything that you find useful.

1. Classroom Routines
It's important to set behaviour expectations at the start of the year with every class, not just with new Year 7s. Everyone in my team goes through their own classroom routines and rules in their first lessons. Sometimes routines might take a bit of practice - for example, to ensure books are always handed in and out with maximum efficiency. 

Starting this year, the slide below is displayed in every classroom while students pack up. This will be done all year round, so it becomes a standard part of every maths lesson. I spotted a similar slide in my daughter's RS lessons (thank you @MrC_Educate!) and adapted it for maths. After a while the words can be removed, and eventually everything will be so embedded that students won't even have to look at the slide, they will just know the expectations. For now, I'm finding it really helpful - it reminds me to check their uniform before they leave my room. I'm also getting more thank yous than I used to!

2. Corridor Etiquette
The layout of our maths department (a relatively narrow corridor with classrooms on both sides) means that we have to keep on top of things in the corridor to ensure it flows well in lesson changeovers. This year I have introduced the poster below. I decided to wait a couple of weeks to launch this because students already experience information overload at the start of the year. Next week we will talk through it in our maths lessons, and following that we will put these posters up in the corridor and by our classroom doors. Obviously the posters alone won't make a difference - staff will need to work together to help ensure that students do the right thing - but I think written reminders of what we want to achieve is helpful for everyone.

3. Launching Homework Platforms
This seems like an obvious thing to say, but I know that many schools don't do it: I think it's vital to relaunch your homework platform every year. We use Sparx, but the same goes for all online platforms, in all subjects: it's not going to be used well if you don't tell students how to use it.

For Year 7 we do a full lesson launching Sparx. We enthusiastically talk them through how it works and why it matters, we show them videos, and we do a live demo (because the whole department launches Sparx with all classes on the same day, it's not possible for us to take them to computer rooms). For Year 8 - 11, we remind them of how to log in, remind them how to get the best out of the platform, and tell them what has changed from last year. Sparx has made some excellent updates over summer which we were excited to share with students last week, plus we have switched on parent emails for the first time.

4. Student Support
I've blogged before about the student support we offer so I won't go into detail here, but I will describe how we launch our offer. Everything starts next week - we are hopeful for a similar turnout to last year, when we regularly had over one hundred Year 11s at Papers Society.

• Posters are put up in the maths corridor and classrooms
• Maths teachers are given slides to show in lessons in the week leading up to the launch
• The same slides are put into tutor time notices, and shown on the display screens around school
• Parents are informed in a letter home (see below)
• I tell Year 11 parents in person during my presentation at Raising Achievement Evening
• Throughout the year, teachers routinely remind students of what's on offer and encourage attendance 

5. Communication
Last week I wrote to all parents in Key Stage 3 and 4 (I do this every year), and for the first time I also wrote to Year 12 parents. Admittedly these letters are rather long so I know that some parents won't read them, but I do always get some parents thanking me for providing the information upfront so I think they are worth sending. The letters cover all the frequently asked questions - e.g. on UKMT challenges, setting, equipment, homework and so on, which will (hopefully) reduce workload for my team throughout the year because teachers won't get individual emails from parents asking about these things.

Everything mentioned in this blog post can be downloaded here - feel free to borrow and adapt! Hope this helps.

Latest Resources and Trends

In this post I've summarised some of the big maths resource updates from the last twelve months. This is aimed at new maths teachers just starting their career (welcome!), experienced teachers who have just discovered my blog, and existing readers who've not had the chance to keep on top of the latest developments. I hope it's helpful!

GCSE Exam Style Questions by Topic

There are a lot of websites providing packs of GCSE questions by topic. Teachers get a lot of use out of these resources. Often the questions are collated from Exam Wizard or ExamPro, so students might see the exact same questions in past papers and assessments which isn't ideal. But there are also sets of original questions that are written in the style of GCSE questions but not taken from actual exam papers. A good example of these are AQA's topic tests on All About Maths, and the excellent sets of practice questions on Corbett Maths.

 

Over the last year First Class Maths has become another top quality source of exam style questions by topic. I love these resources! They are so well written - packed full of clever questions. Two different versions are provided depending on your preferred format - choose from Edexcel or AQA. Loads of new topics have been added over summer so do check out these resources if you haven't seen them before. 

Booklets

Curriculum booklets are all the rage at the moment. I don't teach using a 'booklet approach' myself, but I often make use of MathsPad's brilliant curriculum booklets, either when setting cover or when looking for good quality tasks to use in my teaching. MathsPad are well ahead of the game, having already published booklets for the entire Year 7 - 10 curriculum, with just Year 11 still to come. Each of their booklets comes in two levels: core and support. As always with MathsPad resources, their tasks are very well designed and their booklets include lots of lovely activities for challenge. Here's an example I shared in Gems 175 - these algebra puzzles can be found in the booklet Year 10 Foundation Chapter 2: Algebraic Expressions. These puzzles have six levels of difficulty and would work well with any year group.

And here's another example. This is from the Year 8 booklet on Area and Volume, from the section 'Writing expressions for circles'. At the top of the page we have an explanation:

And following this there are some practice questions. For some reason I never explicitly teach this skill, so this page has inspired me to make a tweak to my teaching of this topic.

Another source of booklets worth checking out is OAT Maths. The team, led by Jemma Sherwood, have been busy creating and sharing their own maths curriculum project. This includes a carefully sequenced curriculum and well designed booklets which feature high quality tasks, for example those of the late Don Steward.

For more good examples of maths curriculum booklets, check out this one on diagonals in quadrilaterals from @AMercerMaths and this one on calculations with standard form from Nathan Day.

Artificial Intelligence

2024 was the first time that AI has really been on our radars in education. As a profession we're rather sceptical about it. Teachers are increasingly encouraged to look to AI for workload-saving measures but I'm not convinced... Given that I don't even like using other people's PowerPoints in the classroom, I'm hardly going to start using AI to plan my lessons. And if I want to write a letter, it would be just as quick for me to write it myself rather then input a load of prompts into AI.

Maths teachers are even more sceptical than others because our initial attempts at using AI for task design using simple prompts like 'give me ten wordy questions on sharing in a ratio' have produced some rather dull tasks and a whole load of maths errors. However, there are two uses of AI worth keeping an eye on:

1.  @DGRAIMaths has created a website aimaths.weebly.com to share his tasks designed with AI. There are some great ideas in these tasks so they are well worth a look.

2. Take a photo of an exercise from an old maths textbook and AI can instantly turn it into a perfectly presented digital exercise. See my post on Digitising Old Maths Textbooks for more on this. Here's an example - I took a photo of an exercise on index laws from Elements of Algebra (Carson and Smith, 1914) and MathPix converted it into a Word document for me. These questions weren't written by AI - they were written by maths experts - but AI digitised them for us in seconds.

New Resources

We are fortunate in maths education to have a constant flow of new resources. I often feature these my gems posts and link to them in my resource libraries, which provide a quick way for teachers to find quality tasks for their lessons. Here I feature some of the most prolific publishers of new resources over the last year.

Dr Austin is an absolute superstar who makes resources for her own students and very kindly shares editable versions on her website draustinmaths.com for free. Her collection of resources is huge and grows all the time. These resources are very easy to use in lessons - I particularly like her 'fill in the blanks' tasks which incorporate both scaffolding and challenge. 

Nathan Day designs very clever tasks packed full of challenge and shares them through interwovenmaths.com. There's a wide variety of resources to check out on his website, including these lovely 'snake' tasks.

Oak National Academy is a DfE-funded initiative which provides fully resourced curriculums in every subject. It launched during lockdown when it quickly became clear that there were massive gaps in the ability of many subjects to deliver content remotely. Since then it has grown rapidly. For maths, Oak provides curriculums for Key Stage 3 and 4, plus sequences of lessons for every topic. These lessons include videos, PowerPoints, quizzes and tasks. 

Last year Dr Frost employed a team of writers to develop his original PowerPoints and expand his collection of resources. As a result there's been a steady stream of new and improved content shared on drfrost.org, including significant updates to his A level maths and further maths PowerPoints. Follow @DrFrostResource to keep up-to-date with the new resources published.

Everything Else

There's always something new being shared in the maths teaching community. Here are a few more things you may have missed over the past year:

• Craig Barton has continued to produce maths education podcasts. My most recent one was on 'Ten ways to get amazing GCSE results' - I was pleasantly surprised by how much nice feedback this received!
• Rob Southern and Susan Whitehouse published the book Teaching A Level Maths.
• New website Maths Advance is full of very challenging extension questions, perfect for high attaining classes.
• LUMEN launched their Key Stage 3 curriculum: learn about it here.
• @StudyMaths continues to add new features to mathsbot.com. My favourite recent additions include Find the Primes and Prime Factory. 
• @cclay8 shared a set of calculator guides for the new Casio model. I have found these really useful in ensuring that I'm familiar with all the functions and menus on the new calculators.
• PolyPad continues to develop its fantastic range of virtual manipulatives. 
• @MattTheApp made hundreds of developments to Maths White Board over the last year - it's packed full of games and activities for students.
• My favourite maths education tweets of the year have been from @catrionateaches who often shares really creative ideas to help improve the way we explain things. 
• My favourite blog posts have been from @MrDraperMaths. His thoughts on task design are always worth reading.

Apologies if I have missed something big here. Keep an eye on my monthly gems posts - I try to cover everything in those!

Social Media

This summer, tweets by Elon Musk angered teachers so much that it sparked a mass exodus to other social media platforms (mainly Threads and BlueSky - though amongst maths teachers, it seems that BlueSky is the preference). Teachers are setting up new communities there where we can enjoy chatting about maths education without our feeds being full of racism and hatred. I already had accounts on both BlueSky and Threads so you can find me there if you wish (mathsjem), though I am still very hopeful that Twitter will come out the other side of all this. Hopefully the Musk nightmare is temporary.

Events and Conferences

If you're looking to attend events with other maths teachers, there are always a lot to choose from. 

Last year Craig Barton and I ran three one-day maths CPD courses 'Marvellous Maths 3' (the online version is still available to buy) and I also hosted the book launch for Matt Parker's new book Love Triangle.  

I'm planning to have a year off hosting events myself, but there are plenty of conferences and events in the upcoming school year that are worth checking out. I have listed some of these here to give you a taste of what's normally available, though most dates have not yet been published. If you've not attended before, why not give it a go?

• Complete Maths usually run three in-person conferences throughout the academic year. These take place on Saturdays in October, March and June at various locations in England. The next event is #mathsconf36 which is on 12th October in Sheffield.
• Big Maths Jam is a wonderful 'recreational maths' event taking place on 2nd - 3rd November 2024. It's not about teaching - it's about maths. There are also smaller monthly MathsJam events for maths enthusiasts to get together in a pub and share puzzles, games and problems. They normally meet on the second-to-last Tuesday of every month in locations around the world.
• Maths Hubs run loads of professional development opportunities throughout the year - get in touch with your local hub to find what's on offer.
• The maths subject associations (including the MA and ATM) offer a range of CPD opportunities. This usually includes a big residential conference in the Easter holidays.
• The MEI Conference typically happens at the start of July.

Subscribe!

If you enjoy reading my blog posts then you can sign up to receive them by email. You'll only get a message when I publish a post, which is normally around once a month. And if you're interested in what you've missed since I started blogging ten years ago, check out my blog archive for access to all 486 of my published posts!

Enjoy the rest of your summer break.

Digitising Old Textbook Exercises

I have a pretty extension collection of old maths books. They’re very cheap to pick up in second hand bookstores, and the only thing stopping me from buying them all the time is the lack of space in my house!

I was browsing through ‘A New Course in Algebra’ this morning. It’s from 1959, so not particularly old compared to some other textbooks in my collection. It’s full of long algebra exercises with tonnes of challenge. I’m not suggesting we use these exercises in their entirety (I may be old fashioned, but even I draw the line at giving my students fifty sets of double brackets to expand!). But they do provide some nice ideas, particularly for extension questions.

I've blogged about the treasures I've found in old textbooks many times before (for example in my post about Elementary Algebra for Schools), and once I even had a team of teachers type up some of the exercises. I also have page on my blog where teachers can access online versions of old textbooks, going back to the 1500s. 

Today I thought I’d try something different. I took some pictures of exercises and tried converting them to PDFs using mathpix.com.

I didn't really know what to expect, but the quality of the output blew my mind! 

I randomly took some photos of pages from the textbook on my phone. I uploaded them to Mathpix and it instantly converted them to very high quality electronic versions. I'm shocked that it was able to read the pictures so well! Below are my initial attempts (note that I was randomly taking photos of various pages in the book, hence these aren't full exercises).

Here's the first photo I took:

And here's what Mathpix gave me. It is spot on.

I tried something which I thought might be harder to read (the indices in the textbook are a bit blurry):

But it had no trouble with this at all (this is an extract from this exercise - I have rearranged it in Word. I love these questions...)

I wondered if it could cope with surds and the answer is yes. 

This exercise on expanding double brackets came out clearly too. 

Compare this exercise with equivalent exercises in modern textbooks. So much thought has gone into it. I suspect that many modern day Key Stage 3 'top set' classes just practise the basics of expanding double brackets and then move on, instead of being given the opportunity to really strengthen their algebraic fluency by attempting questions like these.

And one final example - solving quadratic equations. 

Again, Mathpix converted it perfectly. Again, there are some great questions in this exercise.

Just as I got very excited about all this, I realised that Mathspix limits me to only ten free snips, and I used them all very quickly...

But it's so interesting to see that there's huge potential here to make very useable versions of some these old exercises. And yes - the answers are at the back of the book! So they could be converted too.