5 Maths Gems #164

Welcome to my 164^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Worked Examples
@JakeGMaths shared a large bank of worked examples. It's free to use and contains over 400 examples. Each one is several slides long, guiding students through a method in a series of steps. Then there's a printable part for the students to complete, then the solutions. The PowerPoint has clear instructions on how to use these resources in lessons. Here are a couple of examples of the student tasks:

If you haven't yet read it, I recommend Michael Perhan's excellent book Teaching Math with Examples which inspired this work.

Also check out Jake's other projects which I blogged about in Gems 158.

2. Operations with Negative Indices

I really like this set of questions from @karenshancock. It's a good idea to do something a bit different with negative indices, to help develop fluency whilst interleaving other skills like fraction arithmetic.

Karen kindly typed this up and shared an editable version here. I've added this to my resource library under indices. 

3. Gif Generator

@PiXLMattTheApp continues to develop his website with an incredible range of features. His latest addition is a gif creator which allows teachers to very easily create a recording of a modelled example.

I wrote about opportunities to use animated modelling in my post The Power of Modelling and Exemplars.

4. Bearings

Thanks to @DrPMaths for sharing a task linking angles in triangles with bearings. This is a building block which prepares students to be able to answer trigonometry problems with bearings - something that students often struggle with. His resource includes a few example-problem pairs and a set of practice questions with solutions.

5. Starting Point Maths

@ChrisMcGrane84 has published loads of excellent new resources on startingpointsmaths.com recently. I featured some in my last gems post, and here are a few more. 

First, a task to try before learning how to differentiate: Developing Indices Skills for Calculus.

Second, a task which has a mix of linear equations, quadratic equations, equations which look quadratic but are linear, and a sneaky cubic. Mixed Linear and Quadratic Equations is all about strategy selection, so students become better at spotting quadratics.

And finally, Odd & Even Numbers – Additive Structure - a lovely task which might be useful in primary or secondary. Read Chris's description of the task to see how he used it.

Update

At school we've all been unwell lately - it's that time of year - and our Year 11s have been in mocks so we've been doing lots of invigilation, which is pretty dull. On a more positive note, I've been teaching some of my favourite topics: Year 7 have been learning about prime numbers which is always a joy, Year 8 have been solving equations, and Year 10 have been doing quadratics.   

I'm delighted that #mathsTLP made a return last Sunday. It was an absolute pleasure to behold an hour of teachers enthusiastically sharing resources and teaching ideas. Don't forget that this now runs every Sunday at 7pm, hosted by @MissNorledge and @BrookeEHunter. You're very welcome to join in: see my blog post about how to get involved.

Here are some things you might have missed:

• The MA is calling for submissions to lead a session at the joint subject associations conference next Easter. This two day conference at Warwick University will be the highlight of the year for maths teachers. If you're an experienced teacher with something to share, please do consider speaking. I particularly encourage female speakers, who are always underrepresented at maths education conferences. Complete this form by the end of November to offer a session.
• Realising my Equating Coefficients in Identities task ramped up in difficulty too quickly, I made a revised version of this resource which is shared on TES. 
• @MrDraperMaths wrote an excellent post about transformations of functions which featured a really interesting approach that had never occurred to me before.
• @sxpmaths shared an excellent summary of the different sampling techniques covered in A level maths.
• @missradders shared a lovely Teacher Treasure Hunt that could be used during Maths Week.
• Everyone loves the classic Standards Unit resources from the legend Malcom Swan. The 'Traffic' program was originally written in Java as part of the Standards Unit but @MathsTechnology has recreated it in GeoGebra.
• @nathanday314 shared some of his excellent starter activities plus a thread that explains how he uses them. The thread is well worth a read. 
• @draustinmaths continued to add new resources to draustinmaths.com, including this new task on forming quadratics which I've added to my resource library.
• The wonderful mathematical magazine Chalkdust published Issue 16 - you can read it online or order a paper copy.
• Did you catch my recent blog posts? I wrote a methods post called 'Easy Multiples' and I wrote 'Some Things We've Tried' where I described some of the things I've been up to at school since I became Head of Maths. 
• La Salle shared the dates and locations of its next three in-person conferences:

I'll leave you with this tweet from @dodecahedra about different ways to prove the sum of a geometric series. I'd only ever thought about one way of doing this before, so I enjoyed seeing the alternatives.

Four takes on how to teach/discover/prove/understand summing the terms of a geometric sequence. pic.twitter.com/TaYTITpaWF

— William Rose (@dodecahedra) November 11, 2022

 

#MathsTLP Relaunch!

Back in the day, Ed Southall and I used to run a weekly Twitter chat called #mathsTLP (TLP stood for Twitter Lesson Planning). We launched it in March 2015 with a simple aim: to support maths teachers who were planning lessons. We would happily answer any question, but the main focus would be on finding suitable resources for upcoming topics. We mainly aimed to support new or non-specialist teachers, but everyone was welcome to join in. Ed and I would offer our own advice and suggestions, and other teachers would offer ideas too. So basically it was teachers helping teachers. 
 

Here are some examples of previous #mathstlp questions so you get an idea of what it looks like in practice:

#mathstlp was a considered a big success by the teachers who regularly got involved. And sometimes it reached beyond the chat participants - for example I summed up the discussion we had about teaching Foundation GCSE classes in this blog post which has since been read by over fourteen thousand teachers seeking the same advice.

I've been looking back through the #mathsTLP threads from 2015 - they show that some things have changed in the last seven years. These days there's a lot of love for rich tasks, intelligent practice and clever interweaving. Preferences and styles were a bit different back then, with lots of requests for games and 'fun' stuff. Either way, #mathsTLP will be as helpful now as it was back then.

Now - drumroll please. Here's the exciting news: 

#mathsTLP is officially back!

It will be run by the brilliant new co-hosts Christine (@MissNorledge) and Brooke (@BrookeEHunter), starting at 7pm on Sunday 6th November.

Join in or just watch it all unfold. You can read the tweets without any obligation to tweet yourself. But if you want to join in (we hope lots of you do!), just make sure you include #mathstlp in your tweets so that Christine or Brooke spot them in the feed and make sure they get a response. You are invited to either ask a question yourself or offer an idea in response to someone else's question.

One thing to be aware of: if your account is protected (you have a little picture of a padlock by your Twitter handle) then remember that no one can see your tweets unless they follow you! And even if they follow you, they will not be able to retweet you. So if you want to take part in a Twitter chat then please unprotect your account first.

*****

We're all working towards a common goal so let's help each other out. Please join in on Sunday 6th November to make #mathsTLP a success.

Easy Multiples

In 2018 I decided to write a series of short posts about approaches or methods that teachers might not have seen before. When I share these posts, I am well aware that there will be many people who already know the thing I'm blogging about, but I figured that it's still worth sharing even if it's only new to a handful of people. My first post in this series was about using vectors for enlargements and my second post was about factorising by inspection. I then got really busy writing my book, and didn't add to this blog post series for four years! Oops. So today I'm relaunching the series with a very simple little 'trick' (not a trick at all, just maths).

My Year 6 daughter has recently learnt long division. To be clear on what I'm referring to, long division looks like this:

Whereas 'short division' looks like this (this is sometimes colloquially referred to as a 'bus stop method'):

The only difference between the two methods is that in short division we work out the remainders in our head and jot them down in the dividend, but in long division we work out the remainders on paper in a more structured format. If your divisor is greater than twelve (for example if you're dividing by 28) then it might be tricky to work out remainders in your head, so that's typically when the long division format might be preferred. But they're essentially the same method, just with a slightly different structure for processing the calculations.

It was funny to see my daughter learning long division as it's something that I literally never teach in secondary school. I was pleased with myself for remembering how it works. For many students it exists in Year 6 alone, never to be seen again. A typical Key Stage 2 SATs question might look like this:

But something like this is highly unlikely to come up at GCSE. Students do sometimes have to do divisions by hand in their non-calculator GCSE exam (an example is shown below, from the Foundation tier), but I think most students would choose to use short division.

Some people argue that the long division algorithm is used again when students learn algebraic division in Year 12. This may have been the case ten years ago, but I think that most(?) A level teachers now prefer more intuitive methods of polynomial division, like the factor method shown below for example. 

So for the most part, long division resides solely in Year 6. And my daughter, who is in the 'middle' group for maths, was coping fine with it, but she told me that she finds it tricky to write out the multiples at the start. For example when she's dividing by 28, she's been told to begin by writing out some multiples of 28. She finds this time-consuming, a bit tricky, and rather dull.

But don't worry, because there's a really simple way to write out the multiples of 28. My colleague Sian showed me this - she picked it up a few years ago from her daughter's Year 6 teacher. I showed my daughter, who loved it - she was then able to master long division as she'd found a way round the tricky bit.

To quickly and easily write out the multiples of 28, just write the multiples of 20 and the multiples of 8 and add them together:

As long as the child knows their standard times tables fairly well, listing the two sets of multiples is straightforward. And the addition is pretty straightforward too, as they are always adding to a multiple of ten.

Here's another example: multiples of 17.

This may already be really widely used by Year 6 teachers. But in case anyone hadn't thought about this super simple way of listing multiples, I thought it worth sharing here. As I've always said, even if it just helps one person then it's worth taking the time to write about it.

Some Things We've Tried

In my last blog post I said I'd write something about the stuff I've been doing in my new job. I've been a Head of Maths before - in a truly excellent maths department - but that role was only maternity cover. I've also (briefly) been a consultant, advising Heads of Maths in various schools. But this Head of Maths job is different. This time I have lots of opportunities to do new and creative things.

My school opened four years ago and has added a new year group every year, so we now have our first Year 11 cohort. This is a really important year for us - we're likely to have our first Ofsted inspection, and we're also going to have our first ever GCSE results next summer. I'm confident we'll do well on both counts. Next month we'll also be running our first ever Sixth Form Open Evening and setting up our A level structures and curricula, ready for the opening of our new Sixth Form next September. Starting A level provision from scratch is something none of us have done before, in fact only a few teachers in the school have experience of teaching A level, so this is a really exciting challenge.

I'm very lucky that I have a fantastic maths department (twelve excellent maths teachers and still growing). I'm hoping to advertise for a Key Stage 5 Coordinator to join my team next September (if you're interested, get in touch!).

I've spent the last three years putting my heart and soul into building this school as a member of the senior leadership team, and I've made the decision that it's the best place for my own daughter to attend from next September. I care deeply about ensuring that the school is highly successful, and a brilliant maths department is a vital component of that success.

There are a lot of Heads of Maths who have been doing the job for decades and are much better placed than me to give advice on 'how to be a Head of Maths'. So I won't do that. But I will share a few things I've done during my first seven weeks in the role, because for a long time now I've been a huge advocate of teachers sharing practice with other schools. I wrote a similar post 'Some Things I've Tried' exactly seven years ago today. When you read the ideas below, it may be that you already do all of this at your school, or perhaps you don't want to do any of this. But even if just one school borrows one idea from this post then I think it's worth me taking the time to share it.

1. Papers Society

I first launched Papers Society six years ago when I was an LP at another school. It's a simple idea - motivate students to do more exam preparation by providing printed past papers, a place to revise, and snacks... I explained the rationale in this blog post. I used to have around twenty Year 11 students attend between February and May and I thought it was hugely successful. When I launched it at my current school - in the second week of September - I had over thirty students turn up in the first week alone. I quickly realised I wouldn't be able to run it in my classroom, so the next week we relocated to the canteen. I now have between 70 and 90 students attending every week, and this is likely to grow. My team of Year 11 teachers circulate to help while students complete GCSE papers. Students attend from every maths class - both Higher and Foundation tier. 

So every Thursday after school, almost half of Year 11 come to the canteen to eat and chat and do maths papers together. Amazing. If they continue to come every week until June, they will have done at least thirty extra GCSE practice papers by the time they sit their final exams. 

Moving Papers Society to the canteen had a few unexpected benefits. Because there's loads of space, students who want to chat and help each other are welcome to, while students who want to work independently can sit at a table at the quieter end of the canteen. The other benefit is visibility: students in other year groups can see what we're doing because we're not hidden away on the maths corridor. Year 7s to Year 10s tell us they want to join in: they are keen to sit down with their friends and do some maths while they eat biscuits! Seeing Year 11s working hard, and happy to spend their spare time doing maths, is very positive for the culture of the school.

Article from our school newsletter

2. Support

Most schools run some kind of drop-in maths support. At my school we only introduced a maths clinic for the first time last year and it was a slow start - some weeks we only had one or two students attend. This year we re-launched it with a lot of publicity, and it seems to be going well so far. It takes place in my classroom every Tuesday lunchtime - this is the day I'm not on lunch duty, which means I'm able to run clinic for the whole of lunch. I've drawn up a rota so the other maths teachers take turns supporting me. Most students who attend bring their exercise book and ask for further explanation and practice on something they struggled with in class. My classroom has a large stock of textbooks - we don't use them in lessons but they are very helpful for providing extra practice in clinic. 

We've had a good number of Year 10 and 11 students attending clinic so far, but it's open to all year groups and we've barely had any attendance from Key Stage 3 students. I have a feeling that the presence of the older students might put younger students off. Also, a number of students from my Year 11 Certificate in Further Maths class have been attending to practise their Further Maths - this is great, but I know the presence of the best mathematicians in the school is putting off some of our Foundation tier Year 11 students. So to increase attendance across all year groups, I think we need three separate lunchtime clinics: one for Higher GCSE, one for Foundation GCSE, and one for Key Stage 3. And next year, I will need one for A level too. I just want to make sure everyone feels comfortable coming along to ask for help, and that anyone who attends a clinic gets plenty of one-to-one support while they're there. But I just can't staff all these lunchtime clinics. I do a lot of lunchtime duties so I don't have capacity to run more clinics myself, and my busy team need the opportunity to rest and eat between their Period 4 lesson and tutor time. 

So in summary - clinic is going well, I just wish I had the capacity to expand our provision.

3. Communication

One of the first things I did in September was write to all parents to introduce myself and provide information about maths at my school. This is partly a workload-saving move for me (so I don't spend all year answering the same queries from parents). I also did it because I think transparency and clear communication are vital for good relationships with parents. It helps me get parents on board so we can work together to support their child's maths education. We all know that parental engagement is incredibly important in maths, and even if just 1% of parents read my letter, it was worth sending. It was nice that some parents got in touch afterwards to say they found it helpful. If you want to see what I wrote, here's my Key Stage 3 letter and here's my Key Stage 4 letter.

I also put a lot of thought into how I communicate with my team. We don't have a department meeting every week so I send a weekly email to all maths teachers on a Monday morning with a quick summary of all the key things happening that week. I praise them regularly - if a member of senior leadership says something positive about maths, I pass it on to everyone on the team. And when I do get to host a department meeting - around three times in every half-term - I try to limit it to ten minutes of information and admin, with the rest of the meeting focused on developing the team. For example my next meeting comes just before Year 11 mocks so I will talk about revision strategies and I'll deliver some GCSE marking CPD, drawing on @Teach_Solutions's excellent thread on this. The subsequent department meeting will take place just before our Year 11 higher classes cover circle theorems and functions. As most of my team have never taught these topics, it's a great opportunity for me to run some topic-specific CPD.

The final point I want to make on communication regards the consistency of the messages our students receive in lessons. If there's something I want all teachers to tell their students, I create a slide containing that information, to ensure that every student is told the same thing. For example: I wanted all Year 11 teachers to issue a pack of practice papers for students to complete over October half-term. So to reduce workload for my Year 11 teachers and to ensure consistency of experience for students, I printed all the packs for my team and provided a slide to show in class. 

Another example: we use warm-up booklets in my department (a measure introduced for practical reasons during Covid but retained and developed because we love it) - so at the start of the year I provided a slide that teachers could show their classes on how to use warm-up booklets. I didn't mandate the use of this particular slide, but it's there if they want it, and it saves them the workload of making something themselves.

4. Enrichment

We started doing UKMT challenges a couple of years ago so this is now becoming well-established. I've always been adamant that 'being in top set' shouldn't win you certain privileges, as maths enrichment should be available to all. Many schools just enter their top sets into UKMT challenges, but we offer everyone the opportunity - it's totally voluntary. This year we've had 88 students sign up to do the IMC and 130 sign up to do the JMC. So that's around 20% of our students, which I think represents a good amount of interest in doing 'extra' maths. However, maths enrichment shouldn't be exclusively 'opt-in', as then you don't reach the students who love maths but don't realise they love maths! So we will run a Maths Week in May during which every child will benefit from extra-curricular maths enrichment in some form.

One thing I hope to do this year is take a group of Year 10s to see the GCSE Maths in Action lectures. I've only been once before, many years ago, but found them hugely inspiring, both for the students attending and also the teachers. I'm eagerly awaiting the trip's approval so I can make a booking. We'll probably offer the trip to the Year 10 students who signed up to do the Intermediate Maths Challenge.

One of my biggest personal challenges this year was being asked to create a short maths-focused literacy activity for our Year 11 students. This initiative is called 'Reading Scholars': every other week, Year 11s are given subject-specific reading to discuss in tutor time. This is a great idea to get students reading something beyond the curriculum that will challenge and engage them. I love any opportunity to get students doing some maths enrichment, so it was nice to be asked to make something for their tutor time. There are already loads of fantastic reading exercises for maths such as these lovely Guided Reading tasks from @JennyHillParker, these Reading Resources from vickyolive on TES, and an excellent set of Guided Reading resources shared by Nicola Whiston on TES. But I needed something a bit longer with a reading age of around sixteen, plus I'd been given a specific structure for the questions I had to write, so I was unable to use these resources. I found lots of great articles from NRICH and Plus Magazine, but most were a bit too long, so in the end I went for this engaging article "There are a zillion different names for big numbers" (from a slightly unusual source, but a good read!), and created the prompts below (the format of the slide is standard for all of our Year 11 Reading Scholar activities).

 

I think I'll be asked to create more of these reading tasks later in the year, and I have a few ideas: perhaps this piece on Women in Maths or an article about the work of a Fields Medal winner: Maryna Viazovska or James Maynard. If you can think of anything else that might work well, please let me know! I very much enjoyed this challenge - writing comprehension tasks is not something I've done before, so it was good to give me something that got me thinking!

*****

I'm very proud of my excellent team of maths teachers and I think we have really strong systems in place in the department, particularly the way we assess (I've spoken about assessment many times before so I haven't included it in this post!). I have lots of ideas for the department going forward and am excited about the journey ahead. You may already do everything I've written about in this post, but if not then I hope you found something helpful here. I might blog again next term about some other things we're trying. In the meantime, I would love it if other maths teachers would share some of the stuff that their department does. I'm always keen to learn from others.

5 Maths Gems #163

Welcome to my 163^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. The new school year has brought a flurry of activity on Twitter, with tonnes of great resources being shared over the last few weeks.

1. Zeroes and Ones

@TickTockMaths shared a couple of nice tasks to prompt discussion about writing superfluous digits. 

The first task is Do we need that 0?:

And the second task is Do we need that 1?:

2. Frequency Trees

Thank you to @blatherwick_sam for sharing this lovely frequency trees and ratios task. 

3. Graph Axes

Thanks to @mrshawthorne7 for sharing a great task for finding the equations of linear graphs where there's variation in the scaling of the axes. Charlotte says there’s some nice discussion to be had around Questions 1 and 4 (they're the same equation but ‘look’ different) and Question 5 and 6 (they ‘look’ the same but are different equations). The full resource features a mix of positive, negative and fractional gradients and some questions where given the equation the students need to label the axes. It can be downloaded from sketchcpd.com. 

4. Nets
Thank you to @joann_sandford for sharing a feature of @MathigonOrg's Polypad that I didn't know about. You can use it to create and test nets of 3D objects. Check out the gifs below where I had a little go myself. In the second gif you can see what happens if you make an incomplete net. It's very easy and it's fun! 

5. Tasks

There have been loads of fantastic tasks shared on Twitter recently, including a number by @ChrisMcGrane84 which you can find on his website startingpointsmaths.com. Examples include this task on working backwards from volume:

And this one on substituting negative numbers:

I've also seen some excellent tasks on standard form from both @MrE_Maths and @nathanday314.

@MrE_Maths shared a thread with lots of tasks featuring both scaffolding and challenge.

And @nathanday314 shared a thread and resource showing his approach to teaching standard form, including his narrative on the history and usage of standard form.

 

Conferences

Somehow I ended up presenting at three conferences in four days, which was stressful and a lot of hard work, but brilliant. I do love a maths conference.

On Wednesday I was at the Pixl Conference at The Oval in London. I'm not a Pixl member so it was fascinating for me to get an insight into how Pixl supports maths teachers through high-quality CPD, apps, resources and assessment (for example they provide mock exams - the kind that students won't be able to find online! - and grade boundaries). It's a really good model. The conference itself was a bit different to usual - it was a series of very short sessions, which meant it was buzzy and high-energy with lots of quick ideas. I did a ten minute keynote on challenge. It was a fun day, and the lunch was absolutely delicious!

On Friday I was at the Harris Federation conference. I work for a Harris school - every year all Harris staff have an Inset in October at the Excel Centre, with well over 4000 people attending. In the middle part of the day everyone goes to a role-specific session. I was asked by the maths consultant team to run the Key Stage 3 maths room which had around 130 delegates in it for a 2.5 hour session. This is a long time to run a room by myself, so in the middle part of the session I had everyone spend time trying out some challenging Key Stage 3 tasks from mathsvenns.com, Don Steward, MathsPad and mathshko. Everyone got really stuck into these tasks which was great. It was ironic that I shared excellent Don Steward tasks when Harris Federation has blocked access to Don Steward's website in all Harris schools, and despite my requests they will not unblock it. Incredibly frustrating. Anyway, if you attended this session then thank you for your excellent engagement - if you work for Harris and you want the slides, the maths consultant team will share them after half-term.

On Saturday I was in Manchester for #mathsconf30. This was brilliant. With Rob Smith running a full tuck shop, it felt like a real return to the full pre-covid experience. I attended some excellent sessions and really enjoyed chatting to lots of teachers, many of who were at their first in-person conference. I presented on Area in Depth which seemed to go well, despite some weird projector problems! If you attended my workshop - thanks very much for coming - you can access my slides on my Topics in Depth page. After the conference, Craig Barton and I recorded a podcast at Piccadilly Station where we shared our top tips from the conference. It's a super-short podcast (under half an hour!) so do have a listen.

If you attended any of the three workshops I delivered this week and you want to say thank you, you can buy me a drink here or support me by paying £4 a month on Patreon. Many other maths websites have adverts that provide an income stream but I don't have any adverts to help cover the cost of hosting my website. So any donations are gratefully received. Thank you!

Update

At all three conferences people asked me how my new role is going. I'm really enjoying being Head of Maths. It's nice to do a role I feel so confident in. I'm lucky I get to work with such a great team. I might blog about some Head of Maths stuff over half-term. 

My brilliant colleague Morgan made an amazing door display with her tutor group for Black History Month. It's fabulous. She got the graphics from Twinkl. Nira Chamberlain, who is featured on the display, tweeted about it:

Dear @mathsjem . Can you personally thank your students and colleagues from me for including myself on such a wonderful #BlackHistoryMonth design maths poster door. I am touched and humbled. @Mathematical_A @ICMS_Edinburgh @aimafidon pic.twitter.com/Y24ak2qUfk

— Professor Nira Chamberlain OBE PhD HonDSc 🇯🇲 (@ch_nira) October 14, 2022

Over the last few weeks I've been attending Open Days at my local schools. We're choosing a school for my eldest daughter Maddie who is in Year 6. My nearest secondary school is a Catholic school which she won't get into. We live in a grammar school borough but we decided not to enter her for the selection tests, so that left us with four comprehensive schools to look at, including my own. All the schools we looked at had brilliant maths departments - it was so interesting to get the chance to look around! 

My school's Open Day tour ran as a self-guided route around the school. The maths department was set up in the canteen. This gave us tonnes of space so we put maths puzzles out on three big canteen tables, and I was delighted that all three tables were quickly full of Year 6 children and their parents doing maths together, assisted by our brilliant student helpers. The engagement in these puzzles was incredible.

Open Day today. Massive amount of engagement in the puzzles we put out. Loads of parents sat down and had a go with their children which was fantastic to see. Loved having a room full of adults and children doing maths together. ❤️ Source: https://t.co/9Cz0dvjL0o pic.twitter.com/TQVlXltnXB

— Jo Morgan (@mathsjem) October 1, 2022

My school is a fairly new building and we have tried to keep things uncluttered, so the maths corridor has plain walls and - until recently - nothing mathematical about it. One of the first things I did when I became Head of Maths was to add a bit of personality - we now have a lovely wall sticker. Sticking this up during a lunch break was very intense! 

Here are some blog posts and resources you might have missed:

• My favourite maths blogger @Mr_Rowlandson blogged about Pythagoras following his #mathsconf30 talk. I was gutted I couldn't attend this talk - it was on at the same time as mine. 
• @my_mathsticks blogged about how he uses etymology in his teaching. He has a book coming out next month called Mathematical Etymologia. This is exciting - I love this kind of thing and talk about it a lot in my lessons.
• @TickTockMaths published some new lessons including adding and subtracting decimals, solving linear equations with fractions, rounding and order of operations.
• @draustinmaths published more new resources including some for GCSE Further Maths and some for circle theorems.
• The Mathematical Association announced the dates of its next annual conference. It will take place at the University of Warwick on 3rd and 4th April. It's a joint conference with all the maths subject associations. Save the date - this will be great!
• With the return of the dubiously worded GCSE formula sheet, it's worth reminding ourselves of resources which might help students practise using it: Dave Taylor shared this resource in April and Mel at JustMaths shared this blog post.

I'll leave you with three nice problems for you or your students.

First, @mcnally_gerry shared a simple but lovely surds task that I really like:

Next, @mathsimpact shared a problem from an old Key Stage 3 SATs paper. These papers are always packed full of lovely questions.

Finally, here's a great puzzle from @aap03102's brilliant maths newsletter.

5 Maths Gems #162

Welcome to my 162^nd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Scaffolded Tasks
Thank you to @JaggersMaths for sharing a highly accessible Pythagoras task with lots of scaffolding.

And here's an extract from another task which is structured to make it both accessible and challenging. Thanks to @scott_math83 for this set of probability tree questions.

2. Number Etymology Video

@berniewestacott shared a lovely video 'Why is Eleven not called Oneteeen?'. This is a really interesting summary of some of the etymology of numbers. I love this kind of thing.

3. Angles
Teacher and task designer @SegarRogers shared a set of clever angles tasks designed to give students a deep understanding of complementary angles.

He tweeted his tasks here, here and here.

4. Indices

@giftedHKO shared an indices task that she used with her Year 10s last week. I'm also teaching this topic to Year 10 at the moment, so this was a well-timed tweet for me! She had them complete a grid with all the powers of two through to ten up to the fifth power. This supported them in completing fractional indices questions with larger numbers.

5. Fractions
@robertkaplinsky shared a challenge from openmiddle.com which might be suitable for Year 7s doing fractions. This lovely task is written by @IanKerr_math.

Update
I love September - teaching new classes is so exciting - but it's always manic and exhausting isn't it? I've been struggling with mixed feelings in my new role. I'm loving being Head of Maths again - I've done this job before so I feel very confident in the role, plus I get to spend all my time focusing on the thing I'm most passionate about (maths!). But at the same time it's frustrating for me to step down from the senior leadership team after three years of putting my heart and soul into building a new school. I know I'll get used to it. I must keep reminding myself of all the benefits of changing role - I no longer spend two hours a day on systems and spreadsheet work, because they've now hired a data officer to do these things. Instead, I've been swamped with Year 11s asking for help with maths at every opportunity (we've not had Year 11 in this school before, so this is a novelty for us!). So I'm still just as busy as I used to be, but I think my expertise is being put to better use now. I might blog separately about some of the things I've already done in my capacity of Head of Maths, and some of the things I've planned, as this might help support new Heads of Maths. Watch this space.

Another thing I'm massively enjoying this year is teaching AQA's Certificate in Further Maths GCSE. Six years ago, my timetable was mainly A level. I now haven't taught A level for so long, I'd forgotten how much I enjoy it. Certificate in Further Maths isn't A level, but I'm teaching stuff like Binomial Expansion and Trig Identities, which I love. I have a class of 31 keen mathematicians who meet after school every Wednesday. It's going to be a rush to get through the content - this week we were doing some work on exact trig values and I discovered that their fluency in working with surds isn't quite where I expected it to be - but I think I am going to absolutely love teaching this course.

Here are some things from Twitter that you might have missed in the last couple of weeks:

• @mathsaurus shared his free online course to help students prepare for the UKMT Senior Maths Challenge which take places on 4th October 2022
• @Ridermeister shared his problem solving booklet containing 151 problems aimed at Year 13s who want to prepare for a university interview in Mathematics.
• @PiXLMattTheApp shared a tool to create a bespoke maths newsletter in thirty seconds! With this tool you can create a newsletter that could be sent home to parents or used as a form time activity.

In other news, I loved wearing my new mathsy Popsy dress 'Marva' at school last week. I will wear it again on our Open Day in a couple of weeks. Colleagues keep asking me how many maths dresses I have. Five! One for every day of the week.

I look forward to seeing you all at some of the conferences coming up in the Autumn term. I'll be doing a new 'Topics in Depth' presentation on area at #mathsconf30 in Manchester on 15th October (I hope! I've booked a train to Manchester, but due to issues with the train operator, there are currently no trains home on Saturday or Sunday. This is stressful!). I'm also speaking at the Pixl Maths Conference at The Oval on 12th October. And if you work for Harris, I'm speaking about Key Stage 3 challenge at the Harris Federation October Conference at the ExCeL Centre on 14th October. While writing this I've realised that I've unintentionally agreed to do three conference presentations in one week! Oops - sounds intense! Luckily I will be on half-term the following week to recover.

I'll leave you with this surdic expression to simplify -  your GCSE students might enjoy this. This was shared by @mathisstillfun, a great account to follow for regular maths problems.