5 Maths Gems #188

Welcome to my 188^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1.  Mr Chapman Maths
Thank you to ‪@dalechapman.bsky.social for sharing some great new scaffolded resources.

The first one is a backwards faded task for recurring decimals. The scaffolding makes the topic highly accessible - this task could be used before students start constructing full recurring decimal proofs from scratch. 

A downloadable PDF and editable PowerPoint are available on mrchapmanmaths.wordpress.com - I have added this link to my resource library. 

Another of Dale's new tasks is on calculating pie chart angles - again, there's some excellent scaffolding here. I've also added this to my resource library.  Thank you Dale!

2. 3D Trigonometry
I really like these 3D Pythagoras and Trigonometry tasks produced by @tiredoldcliche.bsky.social. The triangles draw students' attention to what's going on in these questions and encourage careful thinking. 

These tasks can be downloaded here and here. I've added them to my resource library. 

3. Year 6 Knowledge Organiser

Year 6 teachers (and parents of Year 6 children like me!) will find this helpful - @missjessrennie has shared a high quality Year 6 Maths Knowledge Organiser, including a quizzable 'fill in the gaps' version. 

4. Sequences

Arithmetic sequences are full of opportunities for reasoning. I like this set of questions from @catrionaagg.bsky.social‬. 

5. A Level Resources

Thank you to @draustinmaths.com‬ for sharing some new Year 2 mechanics resources for teaching moments at draustinmaths.com/a-level.

Colleen Young's most recent blog post about A level revision resources pointed me in the direction of Swinton Maths where I browsed through some great resources. For example there are some tricky Venn questions, a hidden quadratics fill in the blanks and some Further Maths practice papers. Thank you @mrsmaths.bsky.social. 

On the subject of A level - our Year 13s will get their mocks back next week and I'd like to give them a few minutes of quiet reflection once they receive their papers. I used to use a '5 Minute Mock Paper Analyser' with Year 11 (for more about this read these posts from many years ago: Y11 Post Mock Exam #5minplan: Pupil Self Evaluation and 5 Minute Mock Paper Analysis). Based on this idea I decided to make a Year 13 Mock Exam Reflection on Canva. I'm not the best at design and it's far from perfect but Canva is super easy to use for things like this.

This is how it might look when completed:

Job Vacancy

All the job vacancies I've advertised over the last six years have existed because we're a new school - naturally we've needed to recruit every year as the school has grown. We're a happy team and my school is a great place to work so we've had no turnover in the maths department. But now one of my teachers is leaving us for an adventure (teaching overseas), and this presents an exciting opportunity for a maths teacher to join my lovely team. This opportunity is open to anyone from ECTs to experienced teachers. It starts in September and it's based in South London. If you want to chat about the role please get in touch. We're looking to appoint before Easter so apply quickly!

I'll leave you with this which was tweeted by @MathMatize. How would an integral symbol wear a tie...? My children were discussing a similar question regarding a giraffe wearing a bow tie recently.

#mathsconf37

Yesterday I spent the day at #mathsconf37 in Sheffield. I've attended over thirty of La Salle's Saturday conferences since September 2014. They are regular fixtures in my diary (they take place in October, March and June) - I always make the effort to attend when I can. I think it's massively important that I keep developing my teaching skills throughout my career, and actively take steps to improve my subject knowledge and keep up-to-date with what's going in in maths education. I genuinely think that attending these conferences makes me a better teacher and a better Head of Maths. I also like the social aspect. Having made a few friends from attending mathsconfs over the years, I always enjoy catching up and chatting about maths teaching with them (shout out to Megan who I often share train journeys with, and David who very kindly gives us lifts). #mathsconf37 was definitely one of my favourite mathsconfs. Even though I live far away in South London, Sheffield is a great location (a straightforward two hour train ride from St Pancras and plenty of cheap hotels to choose from), and the school itself worked really well (I marvelled at the wide corridors, well maintained toilets and double size classrooms). Thank you to Head of Maths Ben Rapley for hosting.

I used to write blog posts about every conference I attended, and back when Craig Barton used to attend, I sometimes did post-conference podcasts too. I haven't done that for a while, but I wanted to write a quick post today to share a couple of things from yesterday's event.

I enjoyed all four sessions I attended. In David Martin's session on Platonic Solids I learnt an interesting fact about the colours on Rubik's Cubes - if you add or extract yellow from any side you get its opposite (more on this here).

white + yellow = yellow
red + yellow = orange
blue + yellow = green

I loved Rob Eastaway's session where I learnt loads of interesting stuff about the Elizabethans' use of numbers. And in Sam Blatherwick's session on Magic Multiplication Squares I did a lot of fun arithmetic and thought hard about grids, ratio and factorising.

In Matt Man's workshop I tried some lovely surds problems and also discovered some new places to find questions. I write a lot of Key Stage 3 assessments every year - it's one of the most time consuming things I do, but I do enjoy it! - and I often struggle to find interesting questions that students haven't seen before. For example for my highest attainers I want really challenging questions with lots of reasoning. And for my lowest attainers I want accessible questions with scaffolding. I use various sources to find questions but I always want more! Matt showed us that on Exam Wizard (which is free to use, as long as you have an Edexcel login) you can choose 'Awards' from the first drop down menu in 'Build a Paper' - there are a whole load of maths questions there that I've not used before. I was vaguely aware of Edexcel Award qualifications but I didn't think to look in a whole other section on Exam Wizard. 

They have everything from Level 1 Number and Measure which has plenty of questions suitable for Key Stage 3 assessments, to Algebra Level 3 which has lots of challenge. There are also loads of statistics questions (including topics such as binomial, normal, index numbers, moving averages etc), many of which will be useful for teaching GCSE Statistics where there's a serious lack of available resources to use in lessons. Here are some example questions from the various different awards:

Note that the last question here is not a surds question - this is just substitution so it's suitable for Key Stage 3.

Thanks very much to Matt Man for sharing this hidden source of questions on Exam Wizard!

At the end of the day I delivered a session on factorising. I shared some interesting questions and techniques from a 1914 textbook. Here are some examples of the kind of expressions we were factorising in this workshop:

The delegates really got stuck into these and I think the session was well received, so I might do a follow up at the next conference.

Thank you to La Salle for hosting a great conference, to Rob and Leonie for running a lovely tuck shop, and to all the speakers for their sessions. 

See you all next time.

Securing a Job as a Maths Teacher

The job market for maths teachers is particularly busy between January and May. Many of my readers might be in the process of applying for jobs and going for interviews. I sometimes get emails asking for advice so I thought it might be helpful to share some general advice here. I wish someone had told me these things in my first few years in the profession! 

Here's a list of fives dos and fives don'ts when applying for jobs in maths education.

Five things you should do

1. Do ask for clarification regarding the lesson

I once went for an interview where they simply told me to teach 'percentage change'. I fretted about what this could mean. Using multipliers to increase and decrease? Or working out the percentage by which something had changed? I didn't ask for clarification on the topic or the students' prior knowledge or anything else. On the day of the interview I taught a lesson on percentage change and quickly discovered that the students already knew how to do all of it. And even worse, all the tasks I had planned required a calculator, and no one in the room had a calculator...

I now know that it's totally standard to ask the school for clarification regarding the interview lesson. Most candidates email the school to ask for:

• Seating plan
• SEND information for the class
• Attainment levels, to help you pitch the lesson appropriately
• More information about the topic (e.g. if asked to teach a lesson on volume of a cylinder, ask whether the students have already studied volume of a prism etc).
• Equipment available, if relevant (e.g. whether students will have calculators, or whether mini whiteboards are available etc).

Some candidates ask for even more than this, and that's absolutely fine. I wish someone had told me earlier in my career that it's alright to ask for more information.

2. Do communicate formally

I know it sounds silly to say 'use capitals letters and punctuation on your application form and in emails' but you'd be surprised... If you're filling in an application form and you don't even capitalise the names of the schools you've worked in, it screams 'can't be bothered'. 

3. Do ask for a visit or a chat before applying

This isn't essential at all, but is totally acceptable if you're unsure about applying, particularly for big job changes where it's really important to get the right choice of school and understand the scope of the role (e.g. applying to be Head of Maths). And if you have questions about suitability, for example if a role has been advertised as full time and you want to know whether they'll consider a part time applicant, just email to ask.

4. Do ask about behaviour policies

If you're given a tour of the school on an interview day, look closely at the behaviour and attitudes of students in classrooms, corridors and playgrounds. In the interview, it's sensible to ask about behaviour policies and routines (depending on the school, I'd personally be looking for centralised detentions, sensible classroom escalation procedures, and a team of behaviour mentors or equivalent).

5. Do know how it all works

Teaching is a bit different to other industries. There are some fairly standard rules and procedures in recruitment.

• For safeguarding reasons references are taken before interview. So you have to tell your current headteacher that you intend to apply for a job before you submit your application (both as a courtesy, and because they will find out when the reference comes through anyway!).  
• The recruitment process tends to work very quickly in teaching so if you're asked to come in for interview then you'll normally only be given a few days notice. You'll have a very busy time preparing for interview, planning your interview lesson and setting cover. Don't try to negotiate the day of the interview - your current school shouldn't be asking you to do this. Obviously the school you've applied for will have already planned out all the logistics of the interview day and will want to see all the candidates at the same time. You shouldn't demand a change to the interview date unless you have a really good reason (like you're going to a funeral, it which case it's totally reasonable to request a different date). 
• Offers are normally made same day, and the expectation is that you'll accept or reject the offer straight away. This is because the school is waiting to inform the other candidates of the outcome. Make sure you're ready to make the decision when the call comes in. Or, if needed, tell the school you need to talk it through with your significant other/parent/friend and then phone the school back as soon as you've made your decision. Don't mess them around - it's not fair on anyone involved. I once offered to a candidate who accepted and later changed her mind (because her school made a more lucrative counter-offer) - but at that point we'd turned down the other candidates. So she left us with no one and we had to start the process all over again.
• Time is precious in teaching. Don't go for interviews 'just for the experience' if you have no intention of accepting the job. It's not fair to waste people's time. And once you've formally accepted a job at one school, make sure you withdraw any outstanding applications at other schools. 

Five things you shouldn't do

1. Don’t feel the need to show off every teaching technique in one lesson 

To me the most important aspects of an interview lesson are:

• a well structured lesson
• clear instructions issued to students throughout
• clear modelling and explanation (this is probably the most important thing!)
• at least one well chosen task [be prepared! - make sure you've got something ready in case the students are much quicker or need a lot more challenge or a lot more scaffolding than you expected]

I'd also want to see some kind of assessment of students' understanding, but you don't need to show off multiple assessment techniques in one lesson! Bear in mind that mini whiteboards can be tricky with a class where you haven't embedded routines. 

You can't demonstrate everything you know about teaching all at once. It's hard to show your very best teaching with a class you've never met before. Unless there's a large number of excellent candidates, a solid lesson is all that's needed. 

2. Don't worry about behaviour being a challenge in an interview lesson

Depending on the school, you might have to use a few techniques to get students on task, but if you have the Head of Maths and Headteacher sitting at the back observing, students shouldn't be disruptive. And if they are, the members of staff in the room will intervene (obviously you won't be expected to give detentions or send students out during an interview!). Schools normally pick 'nice' classes for interview lessons, so don't stress about this.

3. Don’t use recruitment agencies

They charge schools extortionate fees. This money should be going towards children's education, not into agents' pockets. If you're applying for permanent teaching roles then go directly through the school or MAT, unless there's a good reason not to.

4.  Don't turn up unprepared. Or late! 

Make sure you've practised answering some standard interview questions (you can find lists of these all over the internet - I'd print some questions, write out possible answers and practise saying them out loud). And don't worry about arriving very early and waiting in reception for a while. That's way better than misjudging the journey and arriving late.

5. Don't be scared! 

If you're unhappy in your current school then go for it - apply somewhere else. For example you don't have to put up with a school where leadership do nothing to address poor behaviour. I promise you, there are schools where teaching is a pleasure. They do still exist. Applying for a new job is difficult and time consuming, and it can be a bit terrifying, but if you're unhappy at work then of course it's absolutely the right thing to do. 

I hope this is helpful! If you're going through this process for the first time, make sure you ask for advice if you're unsure about anything. And if you don't have colleagues you can ask, try asking on Twitter or Bluesky where I'm sure lots of teachers will be happy to help.

Good luck!

5 Maths Gems #187

Welcome to my 187^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Calculator Skills
I love the website gcsemathsquestions.co.uk, which I first featured back in Gems 155. It has PowerPoints of GCSE questions from three exam boards, sorted by topic. I find this really helpful. A new addition to this website is a calculator resource. It features GCSE questions that allow students to practise each calculator skill, including prime factorisation, ratio and mean from a table, and QR codes so students can see video explanations of how to answer each question using calculator functions. I plan to use this resource in a revision lesson with Year 11 in a couple of weeks. 

2. AI Updates

I've blogged about using AI in maths teaching a couple of times before: 

• in AI Maths Resources I wrote about the resources on aimaths.weebly.com which were created by @DGRAIMaths using AI
• in my post Digitising Old Textbook Exercises I wrote about how I used AI tools to instantly turn exercises from old textbooks into high quality electronic documents.  

I thought it might be useful to use my gems posts to occasionally update readers about AI related developments in the world of maths education.

• @MattTheApp has created an AI maths chatbot called the Eden Project - check out this tweet to see the kind of thing he's doing with it. 
• Lots of schools are experiencing problems with students using AI to cheat on Sparx and other homework platforms - you can normally tell by the speed at which they complete their homework. There's a thread about this here. 
• @hartmaths tried using AI to help create a gap fill activity on volume. This is what it came up with:

3. A Level Statistics
@mrwhatleymaths.bsky.social‬ has generously shared his work on A Level Statistics. There are very few resources available for this qualification so this will be incredibly helpful for any school that runs, or is considering running, A Level Statistics. There's some crossover with other qualifications too.  Oliver's resources and scheme of work can be downloaded here. 

4. Vocabulary
@melissamaths's team have had a big focus on mathematical literacy and Tier 3 vocabulary this year and have created a bank of key words and command words across all three Key Stages. The words have student friendly definitions, alongside an image of the 'word in action'. You can download this word bank here.

5. Don's Patterns

‪@catrionaagg.bsky.social‬ posted about one of Don Steward’s tasks which has a pattern in the answers. This makes it easy to check, and students quickly spot the pattern so they can self-correct as they go, plus there's an instant extension activity in trying to write the next question. The task is for solving equations with an unknown on both sides:

This reminds me of one of my favourite Don Steward tasks - 'Expanding and Simplifying' - this also has a pleasing pattern in the answers:

It's a great idea to set a challenge task along the lines of  'find another expression that fits the pattern'.

Conference

It's only two weeks until #mathsconf37 in Sheffield. It's not too late to book tickets. There's a great lineup of workshops and I really encourage maths teachers to attend if they've never been to one of these conferences before. It's always a great day out.

I'll leave you with this... Thanks to ‪@emmathe37th.bsky.social for sharing The Polygon Song from Mr Walker on YouTube. This made me laugh!

5 Maths Gems #186

Welcome to my 186^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. 1st Class Maths

One of my favourite websites, 1stclassmaths.com, has published a new set of practice papers - Higher and Foundation Paper 1 in the style of both AQA and Edexcel. More papers will be added during this summer's exam season. 

I love the quality of all the 1st Class Maths practice papers and resources. The questions are all original - these are not just collections of past paper questions. At my school we always make good use of these resources in our GCSE revision lessons. 

To give you an idea of the quality of the 1st Class Maths papers, here are a couple of the more challenging questions from the AQA-style higher paper:

2. OCR Puzzle of the Week

Every Friday OCR share a maths puzzle on social media using the hashtag #OCRMathspuzzle. I last featured these in a Gems post three years ago (Gems 154). Here are some recent examples.

By the way, if you're new to my blog then you might want to take a look at my back catalogue of gems posts. These posts are packed full of inspiration for both new and experienced maths teachers - they feature over ten years' worth of resources and ideas.

3. Dr Austin

Thank you to Amanda Austin for continuing to share so many new resources on draustinmaths.com. Her latest resources include tasks for quadratic inequalities, set notation, algebraic proof, equations, completing the square and proportion.

4. Guess the Angle

Thanks to @StudyMaths for sharing a new angle estimator.

 

This is one of many useful tools available on mathsbot.com - there are lots to explore. For example I recommend using the Sports Day timer on a phone to record race times on Sports Day. The Blackboard is very helpful if you're live modelling and you need a timer and calculator to hand. I also make a lot of use of the GCSE Countdown and the Grade Boundaries. The customisable graph paper and axes are also very helpful. 

5. Lessons from Dr Frost 

The team at Dr Frost continue to work on upgrading the PowerPoints on drfrost.org. These PowerPoints and accompanying resources can be downloaded for free and cover a wide range of topics from primary through to A level.

My friend @PaulRodrigo2718 is on the team of authors - his excellent set of lessons on bearings was recently published. His slides are full of clever explanations and animations. This slide on airport runways does a far better job of explaining runway numbers than I've done in the past (download the resource so you can see the animations).

If you visit the Dr Frost resources page then you'll see a list of lessons recently published. Here are a couple more extracts: 

From Properties of a Number Based on Prime Factorisation

From Adding and Subtracting Numbers in Standard Form

A level resource

For use in my recent Year 12 lessons I created a booklet for teaching Binomial Hypothesis Testing. There's lots of scaffolding in this. You can download it from TES or find it in my Statistics Resource Library.

Mathsconf37

I'm really looking forward to #mathsconf37 on 15th March in Sheffield. If you've not been to a mathsconf before then this would be a great time to try it out. It's always very inspiring to spend the day with maths teachers. Come to my workshop 'Fun with Factorising' if you like a bit of algebra. 

Speaking of conferences, I attended the Harris Federation Maths Conference on an Inset Day last week. The excellent Emma McCrea did the keynote, and I enjoyed a session on A level problem solving with Sinead Vaughan from the AMSP and a session on the Large Data Set with Jocelyn Stockbridge from Edexcel. Here's a photo of me with the members of my wonderful team who attended the conference.

I'll leave you with this graphic, created by @elephanteating. I knew that a pie chart was a Camembert Diagram in French but I didn't know about the rest! I love this.

5 Maths Gems #185

Welcome to my 185^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Admissions Tests and A Level Resources 

Every year in the Spring Term ‪@ecrmaths runs a series of information sessions for her Year 12 students on the main STEM admissions tests (TMUA, MAT, STEP, PAT and ESAT). She has shared her slides for her 2025 sessions. This is incredibly generous and helpful of Emily - I need to run similar sessions myself but had nothing prepared. Her resources are excellent so this will save me a lot of time and really benefit my students. 

Speaking of A level, did you see the recent new resources on Edexcel Emporium? They have shared A Level Maths Exam-Style Topic Tests for Statistics and Mechanics.  These questions are new and have been reviewed by the examining team - they are not just collections of old questions. They have also published a set of Mock Papers for AS Further Maths - this was very much needed. 

2. Constructions Booklet

Thank you to Tom Riley for sharing his workbook for constructions and loci. 

Tom has also provided some words of wisdom on teaching this topic (see his Bluesky thread for more detail):

1. Start with lots of practice of just drawing circles with compasses.
2. Go into lots of depth on each construction before moving on so that students become familiar with the language early (e.g. shading, showing points, use of scales).
3. Interleave where possible (e.g in the booklet you see circles then perpendicular bisectors then circles with perpendicular bisectors).
4. Include tasks where students have to identify which construction to use (extract below).
5. Use a visualiser.

3. Literacy and Oracy

Oracy is a big focus for a lot of schools at the moment. At my school we have done loads of CPD on it for the last three years (!) but it continues to be something we need to develop across the school. 

‪MrLevMaths‬ helpfully shared a slide from discussions he'd had in department CPD about the link between student oracy, mathematical communication and understanding. How do you ensure students know which expression you mean when you are explaining? How do you explicitly teach them to talk about their maths?

 

Teachers all say these things differently. For C above, would you say the words "lots of" "multiply" "all over"? This is a really interesting thing to cover in department CPD. 

You might be interested in the 'Maths Pronunciation Project' video I made a few years ago. Even the way we say x⁴ differs between teachers.

4. Transum

I spotted a tweet from @Transum about their interactive circles parts vocabulary tool. It might help students appreciate the number of different shapes a sector can have, and prompt questions about major/minor and whether a segment can be a semicircle. 

Transum is full of lovely tasks and tools. For example check out Tim Honeywill's Indices Challenge. 

Transum has also added three more panels to their popular Refreshing Revision tool which can be customised by the teacher.

5. Congruency

@hartmaths shared some congruency questions that he used with his Year 11s. There's lots of interweaving here - these questions feature angles in parallel lines, properties of shapes and circle theorems.

Update

La Salle have said on Twitter that Mathsconf37 will be on 15th March in Sheffield. Tickets are not yet on sale but apparently they will be soon. I've prepared a workshop for this conference called 'Fun with Factorising' which I am very excited about. If you enjoy algebra, come along!

I have a vacancy at my lovely school - we're looking for a maths teacher to join us in September. We're a mixed comprehensive school in South London/Surrey. We have great behaviour and attitudes, happy students and excellent maths results (our first two maths P8s were 1.26 and 1.22. 50% of our students got a Grade 7+ at GCSE last year, and 94% got 4+). My team are friendly and brilliant and it's a real pleasure to work with them. We are particularly in need of someone who can teach mechanics at A level, and we can offer a timetable that is majority A level teaching if desired. But if you're considering applying and you're not an A level teacher, please do go ahead and apply as we can be flexible on this. The closing date is Monday 27th January so apply quickly, or get in touch this weekend if you have questions. We will interview over the next couple of weeks. More information here. 

Finally, don't forget to check out Dr Austin's new resources - they cover circles, ratio, averages and mechanics. I particularly like her Area and Perimeter of Sectors with Pythagoras Practice Grid.