5 Maths Gems #194

Welcome to my 194^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. 1st Class Maths 

It's great to see more A level resources from 1st Class Maths. There's now a full collection of excellent exam style questions for the statistics content of AS level maths, and now he's started to add mechanics exam style questions too. Unlike collections of exam questions on other websites which are often just made using ExamWizard, these questions are totally original and carefully thought through, meaning this is an excellent resource for use in lessons or for homework or revision.

I've added these to my Mechanics resource library. 

Also check out the accompanying videos which are very high quality and well explained as always.

2. Dr Austin

Thank you to Dr Austin for continuing to add incredibly useful resources to her website. Recent additions include multi-step trigonometry problems and a Pythagoras Pile Up.

There are also some new resources for congruency proofs, a topic that has always been under resourced. 

Dr Austin also continues to grow her A level collection. Recent additions include resources for binomial expansions and trigonometry.

3. Circle Theorems

Dan Lewis' post on Bluesky about angles in the same segment got me thinking about how I don't provide enough non-examples when teaching circle theorems (see Task 2 below). 

4. M4TH5
The website m4th5.co.uk has been redesigned. It features a number of free resources including a free and easy to use calculator emulator, interactive A level maths flashcards, an AS Further Maths Starter generator and a 100-mark A level exam paper with worked solutions (which is free, but only if you create an account). 

5. RISPs
Many of you will already be familiar with Jonny Griffiths' RISPs - a collection of open-ended investigative activities aimed at A level students. Jonny has updated the collection and created a new RISPs eBook which can be accessed at risps.co.uk. Thank you Jonny!

Update

TMUA

I have a number of students taking TMUA in January so am very grateful for the resources that have been shared for this. @andrewmaths1 has posted an excellent set of questions in a blog post and @etzsmc has shared another set of TMUA notes and exercises on TES: this time for TMUA Paper 2 on Logic and Proof. 

Conference Dates

Complete Maths conference dates for 2026 have been published. #mathsconf40 is on 7th March in the South, #mathsconf41 is on 6th June in the Midlands and #mathsconf42 is on 17th October in the North. As always, I'll attempt to attend all three if I can afford to.

The MEI Conference takes place on 2nd and 3rd July 2026 at Keele University. I'm speaking on the Friday so will be there then, and may also attend on the Thursday, depending on my timetable and school commitments. If I can't get the Thursday off school then I will still endeavour to attend the conference dinner on the Thursday night (a free bar sponsored by Casio is not to be missed!) Have I mentioned that I absolutely love the MEI Conference? I highly recommend it.

Subject Associations
No doubt you're aware that the long-awaited merger of maths subject associations has now happened and the Association for Mathematics in Education (AMiE) has been born. Congratulations and well done to everyone involved in this lengthy process. It's going to be great to have a single body representing maths teachers in the UK.

News from me

My latest post 'Things I assumed you knew' went down well, with a lot of readers getting in touch to say that they learnt something new from it (particularly the quick way of using equation editor).

I'm looking forward to reading Tom Briggs' book 'The Mathematicians' Library: The Books That Unlocked The Power Of Numbers' which my husband kindly bought me for Christmas. 

Thank you to Jamie Frost for hosting drinks at his house followed by a meal at his local pub just before Christmas. As always it was lovely to catch up with this brilliant bunch of maths teachers.

Finally, I'll leave you with this brilliant 3D printed tool for drawing trig graphs from @thechalkface.bsky.social.

Happy New Year everyone! All the best for 2026.

Things I assumed you knew

I'm writing this post at the request of a colleague. To explain what happened, I need to start by explaining what Solution Bank is. 

If you teach Edexcel A Level Maths or Further Maths and you make use of the Pearson textbooks, then your students are probably very familiar with Solution Bank. It's a set of PDFs that have full worked solutions to every question in the textbooks. Solution Bank is incredibly helpful for students to check where they went wrong or to point them in the right direction if they're stuck on a question. As I set a fair amount of textbook homework at A level, I tell students about Solution Bank in their very first lesson of Year 12. It's available directly from Pearson though it appears on various other websites too - a lot of students access it through Physics and Maths Tutor because that comes up first on Google.

Last week my colleague (who mainly teaches A level) found out about the existence of Solution Bank for the first time, through a student. He's been teaching A level maths for two years and no one ever had ever mentioned it before! He has been making his own worked solutions to every textbook exercise, which took many hours of unnecessary workload. I feel terrible, but when he joined my school in September I never thought to tell him about the existence of Solution Bank, and they didn't think to tell him at his last school either. He said that a blog post about Solution Bank would have helped him immensely when he first became a teacher, and might be useful to other A level teachers who don't know about it. 

This led me to think about other things that we might assume all maths teachers know. So here goes - for many of you everything in this blog post will be obvious, but even if just one teacher benefits from this post then it's worth writing.

Equation Editor
I can't take any credit for this one, and if you've been reading my blog for a while then you'll already know about it (I first mentioned it in Gems 70 in 2017). If something is written in normal font in Word or PowerPoint and you want it to be formatted mathematically, highlight the text and press alt + =.  It will turn it into an equation.  You can also use keyboard shortcuts to write powers, fractions etc without having to click on the equation editor tools. This makes it very quick to create equations for lessons, assessments and resources. For example, to type 4³ just press alt and = together to enter equation mode, then type 4^3 <space>. I use this literally every day. Dr Frost has a helpful guide Equation Editor with Office for those of you who want to know more about this.

Excel Basics
I once worked with a newly qualified teacher who said, "It took me ages to input my test scores to the tracker last night because I had to go through the whole year group and find the names of all the students I teach". This made no sense to me until I looked at the tracker and saw that someone had sorted the whole year group alphabetically, and this teacher didn't know how to sort or filter by class. That's when I realised that I should have spent some time explaining how to use the tracker when this teacher joined my team. It was wrong of me to assume she knew how to use Excel, in the same way we shouldn't assume that new staff know how to use the photocopiers.

Everyone has their own ways of doing things in Excel but here are a few basics. 

If you're new teacher who has never used Excel before and you are being asked to regularly input data to a tracker, then I suggest you ask a colleague to talk you through it, or watch some tutorials on YouTube.

Having worked as an analyst in banking before training to be a teacher, I'm good with Excel and am always happy to support colleagues across the school with formulae and formatting. I think all schools should offer Excel training, at various different levels of expertise, to upskill teachers and leaders.

Here are a few other teacher IT basics that I always assume everyone knows but sometimes they don't:

• Press ctrl+f to search a document (e.g. if leadership send out a staffing timetable and you want to find your initials)
• If you have a screen or board that connects to a PC in your classroom, press the windows button and the letter p to change the projection settings (e.g. when someone uses your classroom and changes it to extended desktop when you prefer duplicate mode)
• The snipping tool is incredibly useful  - I use it every single day to pull extracts from resources into my lessons. 

Answers

Most resources are provided with answers these days, but sometimes we want to use a set of questions that doesn't come with answers. When I first started teaching I used to work them out on paper and then lose the piece of paper and have to do exactly the same thing the following year. Now we have better solutions to cut workload.

Instead of working answers out on paper, work out the answers by writing directly onto a Word/PowerPoint/PDF document, then save this document for use in subsequent years. Many people use a tablet or graphics pad for this. I do it on the screen in my classroom - I just write answers onto PowerPoint with the PowerPoint writing tool and save the ink annotations. You can also write directly onto PDFs and save what you've written (open the PDF in Edge to do this) - this is great for making model solutions for exams. If it says you don't have permission to write on it (e.g. it's a GCSE paper) then you can create an unprotected copy by printing it to PDF. 

I'm not a fan of AI at all but I have to admit it's a time saver for working out answers. I spoke about this in my recent presentation about Don Steward's wonderful resources. For example if I use Don's task cancel algebraic fractions in a lesson, I can put the screenshot into an AI tool and ask it to work out the answers for me.

We all know the AI isn't great at doing maths, so we have to check any answers generated by AI. With this surds simplification task ChatGTP did a good job except on Question 19.

Exam Board Resources

Last year I attended some A level training on Edexcel's large data set, and half the teachers in the room said they had never heard of Emporium. I almost fell off my seat in shock. How can you teach A level Edexcel (or any Edexcel for that matter) and not use Emporium? I use it all the time. The same goes for the other exam boards - they all have websites packed full of useful resources. Ask your Head of Maths how to get access. 

While I'm talking about A level, I should mention Adam Creen's collection of errors and corrections for the Pearson A level textbooks. This is very useful to check if you think there's an error in a textbook question.

UKMT

I've always assumed that every school offers students the opportunity to do UKMT challenges, because every school I've worked in has run them. It is surprising to meet maths teachers who don't know about the existence of these challenges. All the information is here. I know that many schools enter all their 'top set' students and run the challenges during the school day. We give every student the opportunity to enter (students sign up on an online form a few months in advance) and we run the challenges after school. I know some schools run lots of preparation for these challenges but we don't have capacity to do that, so we point students towards independent preparation resources (past papers and mathsaurus courses). If you're interested in other challenges and competitions, I have a slightly out-of-date post here that might be helpful.

Grade Boundaries

A colleague recently asked me where to find maths GCSE grade boundaries because her Year 11 students had asked to see them. I told her I always use MathsBot for this. MathsBot has many useful tools for maths teachers so is worth exploring.

Gradeboundaries.co.uk is also a great place for both A level and GCSE maths grade boundaries.

Resources

Recently a colleague told me she'd never heard of Corbett Maths 5-a-day - it reminded me that I shouldn't assume that everyone knows these classics. For many years I've made good use of Corbett Maths 5-a-day for Year 11 retrieval and I assumed these resources were widely known, along with other websites that I use all the time like Dr Austin and MathsPad.

I also often meet teachers who aren't familiar with Don Steward which always surprises me as I've blogged and tweeted about his resources hundreds of times. 

Here are a few old blog posts that you might useful for resource basics:

• Classic Resources (including CIMT and Standards Unit) 
• A level resources 1 (an old post but still relevant. This features Solomon worksheets - I still regularly use questions from these in my A level lessons) 
• A level resources 3 (a more recent post featuring the brilliant madasmaths) 
• GCSE revision resources 
• Displays for classrooms or corridors

And finally - some more old blog posts that some of you might find helpful:

• Common subject knowledge errors
• Words to avoid (I could add 6-7 to this!)
• Maths teacher FAQs (all the Twitter stuff in this is a bit out of date now)

My full blog archive is here with over a decade's worth of information for maths teachers.

If you found anything in this post helpful then please comment below or on social media so I know it was worth writing! 

And if you have any other basic tips that you want to share with teachers, please feel free to add them below too.  

Thanks for reading!

5 Maths Gems #193

Welcome to my 193^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. 1st Class Maths 

I'm always happy to see new resources from 1st Class Maths. The latest is a set of exam style questions (in both AQA and Edexcel style) on reverse percentages.

Resources for compound interest and loci are coming soon.

2. Certificate in Further Maths

AQA's Certificate in Further Maths is a very popular qualification - I have a page dedicated to it here. I like Andy Lutwyche's latest resource: a Further Maths topic list with examples of questions for every topic. There are two versions: one with Sparx Codes, one without. This is a really helpful revision resource for students. Thank you Andy!

3. Dr Austin

Dr Austin has published some new percentages resources including Mixed Percentage Change Fill in the Blanks.

And for A level, there are new resources for graphical inequalities, algebraic fractions and algebraic division. 

4. Quadratic Inequalities

@AddvanceMaths published a booklet for teaching quadratic inequalities. It starts with prerequisite skills (solving quadratics, drawing inequalities on number lines and sketching quadratic graphs). It then has examples of how to solve quadratic inequalities, loads of increasingly difficult practice questions, and some problem solving.  Answers are provided too.

5. Circle Theorems

@MrLevMaths created a great set of questions which interweave circle theorems and trigonometry.

Update

• Maths teacher Peter Browne emailed me about his website IGCSEMathsTutor.com which has impressive online practice sheets like this one on Changing the Subject of a Formula. 
• Hannah Kettle continues to build her collection of cover resources at hannahkettlemaths.co.uk/cover.
• Paul Rowlandson published a new blog post 'Thinking About Perpendicular Bisectors'.
• Stephen Cox shared some really useful resources for TMUA preparation.
• Good news! AQA have made Maths ExamPro totally free for AQA Centres.
• Did you catch my recent post about adapting worksheets? It was nice to get some comments on this post and a few teachers even sent me their scaffolded resources which was fantastic.

I had a great day out at #mathsconf39 in London a couple of weeks ago. It was very well attended. I presented on Don Steward's resources. Loads of people told me they'd never heard of Don Steward - this made me sad, and I realised how important it is to keep sharing his tasks and make sure that new teachers joining the profession are made aware of everything he so generously shared. 

Read Atul Rana's blog post for a great write up of #mathsconf39. As always happens in October, this mathsconf was the day after an Inset Day for me, so I had the pleasure of attending maths conferences two days in a row. Here's a photo of part of my team at Inset Day on the Friday, and a photo from the pub after #mathsconf39 on the Saturday. 

Finally, I'll leave you with this video from Mitchell and Webb which made me laugh.

 

Tasks with Scaffolding

Every year I set a development priority for my department, and this becomes the focus of our 'DPD' sessions throughout the year (DPD is 'department professional development'). We focused on challenge in the past two years and I think we've done a great job with that - we got 17% Grade 9 at GCSE last year (we're a totally non-selective school and for comparison, the other comprehensive schools in our borough had an average of 6% Grade 9s last year). As much as I love talking about challenge, I think now is a good time to shift our focus to how we can improve the way we support our lowest attaining students. 

There are various strategies we adopt that are probably fairly standard (e.g. students are taught in sets, and we have very large top sets to ensure our lower attainers can be taught in smaller groups, normally with TA support). We also run Entry Level Certificate for our Year 10/11 students who are likely to struggle to achieve higher than a Grade 2 at GCSE. 

The focus in our DPD sessions is on what happens in the classroom, for example how we use techniques such as gradual release and example problem pairs and how we choose appropriate tasks for our lower attaining students.

It's been a while since I've taught very low attainers. Before my school had a Sixth Form, when I had capacity in my timetable to teach Years 7 - 10, I considered middle sets to be my area of expertise. In Year 11 I typically teach the 'borderline' GCSE group (the bottom group in Higher Tier - for us that's Set 5 out of 8, and my challenge is to turn their grades from 4s and 5s into 6s and 7s). The last time I taught very low attainers was five years ago. At the time I thought hard about the best approaches to take, and blogged about some of the strategies I tried (see posts like Five for Five and Classroom Reflections). But now that 'teaching low attainers' is our department focus, and it's me who has to lead the CPD on this, I'm keen to read all related research and hear what other teachers do. I was fortunate to attend an excellent session at #mathsconf39 called 'Unlocking Potential: My Experience Teaching Low Prior Attainers in KS4', delivered by Heidi Morris. Often sessions about teaching low attainers are solely about manipulatives so it was refreshing to hear a range of ideas in this workshop. Heidi talked about how she motivates her students and the techniques she uses to make topics accessible and memorable. For example, she talked about 'GCSE Fridays' when they do scaffolded and repeated GCSE question practice, rather than introducing new content when they're tired at the end of the week. 

Tasks with Scaffolding

In today's post my focus is on scaffolded resources. If you aren't familiar with the term scaffolding in this context and you want to read more about it, I recommend Jamie Clark's excellent one pager.

Maths teachers are so lucky to have an abundance of high quality resources to choose from when planning lessons. There are absolutely loads of tasks that are brilliant for middle and high attaining students, but if you're teaching a small class of Key Stage 3 or 4 students who are working at GCSE Grades 0 - 2, it can sometimes be difficult to find suitable resources. Teachers don't have time to make their own resources, but I feel this is something that teachers of the lowest attainers have to do fairly often. In this post I thought it might be helpful to showcase what's available and think about some design principles.

Factorising Quadratics For All

At my school all of our Key Stage 3 classes study the same curriculum. After half term Year 9 will be factorising quadratics. This is a topic that some lower attaining students actually quite enjoy as it's heavy on procedure and light on reasoning. But the big barrier to success in this topic is fluency in times tables and fluency in working with negative numbers.

I've attempted to design four tasks for this topic, each with a different level of scaffolding and challenge. 

The tasks shown below are designed for different classes, but they all practise exactly the same skill: factorising monic quadratics with positive numbers. The first two tasks are intended to be projected on the board (i.e. students copy each question into their exercise book), the second two would be printed (when teaching low attainers we don't want to add unnecessary challenge, and for some students copying from the board can be very difficult).

In this lesson on factorising positive quadratics, the teacher would model a couple of examples (known as the 'I do' phase of the lesson) and then in the 'you do' phase there may be some cold calling or mini whiteboards. The tasks below are designed for the 'you do' phase of the lesson where students do independent practice. Have a look at the difference between each task.

High attainers

Mid/higher attainers 

Mid/lower attainers

Lower attainers

In the first task above you can see there's lots of practice to develop fluency, bearing in mind 'top set' students would complete these very quickly (this is a short task - probably five to ten minutes). There are some questions at the end that are slightly different to the modelled examples, to get students thinking. After reviewing the answers and discussing methods for the more challenging questions, the teacher would probably move onto factorising with negatives in the same lesson.

In the second task above, which is designed for a 'middle set', the challenge questions are separated and an example is provided to remind students of the technique.

You can see how the amount of scaffolding increases throughout the tasks, which become increasingly more suitable for lower attainers. There are other methods for factorising quadratics (e.g. using grids) that might help too - but this post is about task design rather than methods.

I've put all four tasks on TES in case they're helpful. They can easily be adapted to include negatives too. I'm not an expert task designer - the purpose of me creating these tasks was to showcase different levels of challenge and scaffolding that are possible within the same topic.

Sources of Scaffolded Resources
There are some great websites which have scaffolded resources. Here are some examples:

1. Backward Faded Maths

Percentage Change by Dee Vijayan

Area of a circle by Alex Hughes

2. Mr Chapman Maths

Recurring Decimals to Fractions - Backwards Faded

3. Starting Points Maths

Solving Equations: Backwards Faded

4. Dr Austin Maths

Sine, Cos and Tan Ratios Fill in the Blanks

5. Gareth Evans

Standard Form Resources

What have I missed? If you know a good source of scaffolded tasks, please comment below.

Also, here's a challenge for you: it would be fantastic if some of my readers had a go at what I've done above for factorising quadratics. Pick a topic and design three or four different tasks that all practise the same skill but are scaffolded differently, for different types of students. Please share what you come up with!

5 Maths Gems #192

Welcome to my 192^nd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Hannah Kettle

Hannah Kettle is making worksheets and accompanying videos to review each unit of the GCSE Maths course. Unit 1 Higher (Number) is now on her website with the accompanying worksheet. Hannah has a great idea - these videos and resources would be brilliant for Year 10 or 11 cover lessons. Students make notes and review the first page while watching the video, before having a go at the second side on their own.

2. Durham Murder Mysteries

‪Hannah (‪@missradders) tweeted about how much her Year 8s loved the Durham Maths Mystery she used in an algebra lesson. 

This inspired @mrs-p-maths to post about using a Straight Line Graphs Maths Mystery with Year 10.

It's been a very long time since I've blogged about these resources and I suspect that a lot of new teachers won't have seen them before. If you like these check out Gems 96 where I shared some similar activities produced by Richard Perring.

3. MathsPad

MathsPad have shared some excellent new resources in their September Update including new chapters in their curriculum booklets. 

There's also new Arrange the Digits slides and worksheet and Proportion Tables slides and worksheet.

4. AS Level Tasks

Dr Austin shared some fantastic new AS level tasks at the end of the summer holidays. Check out her website draustinmaths.com for the full collection. 

Through the #mathstoday hashtag on Bluesky (this is where maths teachers post daily highlights from their lessons) I've seen a number of other fantastic Year 12 tasks this week.

From Catriona (@catrionaagg), an algebra task where students are pushed to articulate their reasoning...

... and a lovely lesson on graph sketching.

@MrLevMaths shared a really interesting task on intersections, thinking about sketching and the discriminant. 

Karen (@karenshancock) shared an index laws and algebra task with a good level of challenge.

Nathan (@nathanday) shared a lovely task on graph intersections and solving simultaneous equations.

Nathan also shared some Susan Wall tasks. When I first qualified as a teacher I went on a course on how to teach A level Maths and that's where I was introduced to Susan Wall's brilliant tasks - I'm a big fan. Here are some examples shared by Nathan:

I also spotted that Nathan has shared a helpful Edexcel grade boundaries tool for A level Maths and Further Maths where you can very easily see grade boundaries by module. 

5. AS Level Statistics

I'm delighted to see the recent additions to the A level resources at 1stclassmaths.com/alevelrevision. These are brilliant and incredibly helpful. I've added the links to my A level library. 

Update

I'm looking forward to seeing lots of you at #mathsconf39 in London next month. I'll be presenting on Don Steward's wonderful resources, and I'll be out for post-conference drinks on Saturday night.

It's great to hear that MathsWorld is opening a discovery centre in London - I was totally unaware this was happening until my mum sent me an article about it! I can't see anything on their website or on social media about this. Assuming the article is correct, this might be a future school trip destination for schools in and around London.

I'm so used to getting my maths news from social media, it surprises me when I see it elsewhere. Last week I also spotted an article about an Ada Lovelace statue being erected in Leicestershire. I'm a big fan of Ada Lovelace and will no doubt visit this statue one day when I'm in the area. It can be added to the list of mathematical stuff to visit in the UK, along with Turing's statue in Manchester, Ramanujan's plaque in Putney, the beautiful Penrose tiles outside the Andrew Wiles building in Oxford, Newton's house in Grantham...  as I write this list I realise that there are a great many mathematical things to see - perhaps there's another blog post in this.

Finally, thank you to Hannah @neechmaths for posting something on Bluesky that made me laugh out loud... These are genuine Casio fx991CW calculator reviews on Amazon.