5 Maths Gems #155

Welcome to my 155^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers. Loads of great stuff has been created lately and I haven't been able to keep up with it, so today I'm bringing you a double feature - this post features ten gems instead of my usual five. 

1. GCSE Resources

@gcse_math has shared an enormously helpful resource that must have taken a huge amount of time to pull together. He has collated all GCSE maths questions from June 2017 to November 2020 for Edexcel, AQA and OCR. These are organised by topic. This resource has already saved me a lot of time - it's so useful having questions from three different boards in one place.  

Other helpful new GCSE resources include a set of topic-based revision booklets from @taylorda01 and a page packed full of resources relating to this year's GCSE Advanced Information from @Corbettmaths. 

If your students are currently preparing for their GCSE and don't yet know all their key facts and formulae, don't forget that you can bulk buy my Knowledge Quiz books directly from John Catt at a discount. Students can use these to self-quiz either at home or in the classroom. They repeat the same quiz multiple times until they are consistently scoring 100% - this is a tried and tested technique to memorise facts. Having instant recall of facts and formulae then frees up students' brains to focus on reasoning and problem solving.

2. Number Puzzles

I now do the daily Nerdle puzzle every morning without fail, so I'm pleased to see increasing opportunities to bring this much-loved puzzle format into the classroom.

Numble was made by Olivia Gibson, who is a Year 12 Further Maths and Computer Science student at Manchester High School for Girls. She is a big fan of Wordle and had the idea of creating a similar game that involved guessing a 3-digit multiple of three (a ‘Numble’). Olivia's game was shared by her teacher @mathsDJ on Twitter where it was very well-received by maths teachers. It took Olivia two weeks to make Numble using JavaScript and in her own words 'she had a lot of fun making it'. The aim is to try and guess as many ‘Numbles’ as possible to build up a streak. @mathsDJ's school held a Numble competition with their Year 7s and the best was 27 in a row! It's a fantastic game for building understanding of divisibility rules, as well as logical problem solving. Well done Olivia!

Nerdle itself has now launched ‘pro Nerdle’ which is designed for schools in response to feedback from teachers. The game allows teachers to focus on a specific topic or skill, for example by removing multiplication or division or by adding additional symbols such as brackets and decimals. Another new Nerdle feature is the ‘Challenge Zone’ page, which provides a variety of pre-built pro challenges designed for learning or practice. Great stuff from Nerdle!

3. Mathematician Profile Cards
@Amplify has shared a lovely set of free mathematician profile cards. Each card highlights the life and accomplishments of a mathematician. There's also an activity: give each student a card and have them read the profile. When they’re done, students should find the two individuals holding cards that match the clues on the right-hand side of their own cards.

This would be a great activity for a maths enrichment club.

4. If I Could Tell You One Thing

The Mathematical Association has published a new book: If I Could Tell You One Thing, which is edited by @edsouthall. You can purchase a copy from the MA Shop at £14 for non-members or £9.80 for members. A free digital download is included. This book is packed full of great advice and pedagogical insights. I look forward to reading it over the Easter holidays. I hope people like my chapter, which is called 'More depth, less speed'.

5. GCSE Statistics
@karenshancock shared a definitions testing tool for GCSE Statistics. It contains 135 definitions and can be used for quizzing in class or at home.

Teachers of GCSE Statistics will be pleased to see that @HelenScott88 shared a thread on Twitter which lists a number of resources for this course. This includes the helpful website statsacademy.co.uk.

6. Circle Theorems Task

Thanks to @rodrigotweets1 for sharing a circle theorems task. I've added this to my resource library.

The design of this task is based on a very similar task I made for angles in parallel lines, which I explained in my Angles in Parallel Lines in Depth CPD. The idea is to get students thinking about all the reasons they used to solve a Don Steward angle problem (quite often they only write down one angle fact, when they have actually used multiple facts). Also, they compare answers with others and realise that different approaches can be used. By ticking boxes instead of writing out reasons, they can get more practice done and focus on the maths instead of the writing.

7. Backward Faded Maths
@taylorda01 has launched a new website: Backward Faded Maths. You can read about it in this thread or watch Dave's video for an explanation of what it's all about. There are currently eighteen worksheets on the website, with more to be released. Here's an example of a task for a contextual area of a semi-circle problem:

8. Pi Day Relay
Everyone loves Chris Smith's (@aap03102) relays, so it's great to see he has published a new one! This time the theme is Pi Day. Thank you Chris!

9. FDP Booklet
MathsPad subscribers will already be familiar with their growing collection of outstanding topic booklets. A recent addition is on fractions, decimals and percentages. @MathsPadNicola has tweeted a couple of examples of tasks from this booklet.

10. Tips for Teachers
Craig Barton (@mrbartonmaths) has launched a fantastic new website tipsforteachers.co.uk. Craig wants to build a free, extensive and diverse collection of ideas that teachers of any level of experience, teaching any subject, any age-group, and from any country might find useful and be able to apply to their own teaching. 

This website features tips in both podcast and video form. So for example some teachers might listen to the tips on their way to work, and others might show the videos in a department meeting and follow up with a discussion. 

This is a brand new website but already features lots of tips - from Craig, Adam Boxer and myself - and the collection will grow rapidly over the coming months.

Here's an example of one of my tips:

Update

Thank you to everyone who attended #mathsted22. I held this event at my school and it was great that so many local maths teachers attended. Thank you to Steve Wren from Ofsted for travelling down from Yorkshire to speak at this event, and to AQA for the sponsorship which meant I could run it for free. 

Since then I've been working on my keynote for the MA Conference, which is fast approaching. There are two online days plus one in-person day in Stratford-Upon-Avon. Tickets are available from £15. 

I have news. I've been Assistant Principal at my school for three years and have now decided to do a bit of a career u-turn and take on the Head of Maths role there in September. I have so many ideas and I can't wait to get started. I'm really lucky I'll get to lead a fantastic team and focus on the thing I love most - maths! If you're interested in my yo-yoing career path, which has had an unusual number of twists and turns over the last twenty years, I wrote about it here.

Finally, I'll leave you with this lovely Pi Day idea from @mathequalslove. Instead of writing a Haiku which has the structure 5 - 7 - 5, why not challenge students to write a Pi-Ku?

5 Maths Gems #153

Welcome to my 153^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Digitisers

Jonny Griffiths has shared a new collection of resources called Digitisers. These puzzles are aimed at late GCSE/early A level students. Topics include sequences, circle theorems, quadratics, differentiation, logs, trigonometry, simultaneous equations and surds.

2. GCSE Statistics
I’ve never taught GCSE Statistics but I know that teachers of this course often lament the lack of resources. So they’ll be pleased to hear that Ben Hamilton has started sharing a resourced scheme of work for Edexcel GCSE Statistics. I know that many teachers will be really grateful to Ben for sharing this.

Fully resourced SOW for @PearsonEdexcel GCSE Statistics under development:

Unit 1: https://t.co/VxIEp96seC

Unit 2: https://t.co/Avfn7CKhRy

Unit 3: https://t.co/P4sXcc4R75

More to follow: Preview of resources below 👇 pic.twitter.com/0Rw9ax9syW

— Ben Hamilton (@MrBenHamilton) July 7, 2020

3. Sequences Wordle
Wordle has been a big craze since Christmas and social media is filled with posts where people share their results. I have seen a number of excellent maths versions (like this one and this one). My favourite is this times table sequences version from MathsPad. It’s free to use and you must have a go to see how good it is. I played it with my ten year old and she really enjoyed it.

4. GCSE Booklets

Thanks to Richard Morley for sharing a very helpful collection of GCSE Revision booklets.

📢New resource alert!🎉

Been a bit quiet on the site recently, but I've collated all notes jotters so that they can be printed as a booklet, grouped by Foundation, Crossover and Higher, then by topic, download them at https://t.co/UD5GPGsLCM @mathsjem @missradders @Just_Maths pic.twitter.com/HL3VUjOf4U

— Richard Morley (@MrMorleyMaths) January 17, 2022

5. Tasks

Loads of great tasks have been shared on Twitter lately, including...

This task from @giftedHKO (I used this with Year 8 last week!). Students have to work out which shapes have the same perimeter.

Here's an interesting task from @SegarRogers which can be downloaded from @ChrisMcGrane84's wonderful website. It's fascinating to look at the range of questions here and how they can be classified.

@draustinmaths continues to share great resources, including this scaffolded task on rationalising the denominator.

In Gems 151 I featured @nathanday314's new website Interwoven Maths. Since then, Nathan has added more tasks to the site including tasks which interweave rounding with fraction and decimal arithmetic. 

 

Updates
There's lots going on!

I made free tickets available for #mathsted22 and all 120 of them went in two days. I'm really looking forward to this event! I had a few demands that I stream the Oftsed talk but I don't have permission from Ofsted to stream it. If people want to run a similar event in their own area, they can request an Oftsted speaker here. 

Yesterday I ran a 2.5 hour workshop on curriculum and depth at the MA/ATM London branch. Thank you to everyone who came, and thank you to the IoE for hosting and Japleen Kaur for organising. The ATM and MA have branches all over the country which provide free/cheap CPD for maths teachers, so do check out your local branch.

I also did a talk at #mathsconfmini about maths department improvement. It focused on the recent feedback that schools have received from Oftsed (and 'mocksted') inspections under the new framework. The recording is available to conference attendees here. 

I'm looking forward to presenting at the MA conference in April. I'll be speaking online on the first day. Tickets are available here.

Here are a few more things you may have missed:

• My video 'What secondary teachers should know about the Key Stage 2 maths curriculum' went down well - lots of departments have watched it together in their department meetings. 
• Mathematical Education on Merseyside has been running take-home maths competitions in February half term since the late 1970s. They attract about 2,000 entries annually, with Challenge aimed at Years 7 and 8, and Senior Challenge aimed at Years 9 and 10. Their 2022 competition is live now - visit their website to enter your students.
  
• Dan Draper - one of my favourite bloggers - wrote about circle theorems. 
• The Liverpool Maths School is running on-demand CPD for maths teachers, with a focus on enriching GCSE lessons with Key Stage 5 content. Information is here.
• On Twitter I shared some examples of exercises from my old post 'Equations Exercises' where I got a team of volunteers to type up parts of an algebra textbook from the 1950s. This set is a good example of interweaving two skills: expanding double brackets and solving linear equations:

I'll leave you with this problem from The Art of Problem Solving which was shared by @rinaldi6109. Find the value of k.

MEI Conference 2019

I was fortunate to have the opportunity to attend the MEI Conference from Thursday to Saturday last week. I normally only attend conferences at weekends and in the holidays so getting permission from work to attend a term-time conference was a rare treat. The last time I attended the MEI Conference was in 2015 - I blogged about it here.

Residential conferences are a very different experience to one day events. There’s more time in sessions to discuss ideas and do maths, and there’s more time outside of sessions to socialise, meet new people and chat about teaching. At lunch on Friday I sat with Ben Sparks plus Christopher Rath (@Rathematician) and his colleagues - they showed me cool maths stuff that I'd never seen before. So much fun. Since I got back I've been showing everyone my new tricks! Literally every time I see Ben Sparks he blows my mind with some clever maths magic. He did the same in his workshop on Saturday morning where we played a poker game in which I genuinely thought I had a full house – until I realised he’d rigged it. How does he do that…?

It was wonderful to stay for all three days of the conference - I loved every minute and felt incredibly relaxed hanging out on a university campus in glorious sunshine. The evening entertainment was top quality - the after-dinner speak Harry Baker was absolutely wonderful. Everyone was blown away by how lovely he was. Watch this video to get an idea, but go see him perform if you can (I first shared this video back in 2015 in Gems 26 so it was cool to actually meet him in person!).

I’d always assumed that the MEI Conference is aimed mainly at A level teachers but I found that there was a wide range of sessions to appeal to all secondary maths teachers. It had a bit of an academic feel to it in parts - particularly the first two plenaries. The first keynote was by Dr Eugenia Cheng (she’s my new hero) and second keynote was delivered by Professor Alison Etheridge – she delivered a fascinating lecture on genetics which made me feel like I was back at university! I love the high expectations that the organisers have of their audience - it’s wonderful to be immersed in intellectual challenge every now and then. Craig Barton’s keynote on the final day was brilliant, as always. He also had the coolest clicker I've ever seen. Did I mention that I’m running a course with Craig in October? You can book your place here.

One thing I like about the MEI conference is that there's a very different range of speakers from the events I usually attend so I get to hear lots of new perspectives. I recorded a conference podcast with Craig Barton on the Friday night (after a few glasses of wine…) so have a listen to that to hear some reflections on a few of the sessions I attended. I didn’t get a chance to speak about every workshop. In this blog post I’m just sharing a couple of things that I didn’t mention in the podcast that I thought teachers might be interested in.

Football Loci
Rob Eastaway (@robeastaway) ran a session called 'What's the difference between a puzzle and a maths question?' which was partly about how to turn a dull question into an interesting one. Something that really jumped out at me related to loci. We often see really contrived scenarios in loci questions but he shared a fascinating scenario that I loved.

Rob showed us a set of football rules from 1891, when the rules of the game were evolving. It said:

"The goals shall be upright posts, eight yards apart, with a bar across them eight feet from the ground.

When the ball is kicked behind the goal-line by one of the opposite side, it shall be kicked off by any one of the players behind whose goal-line it went within 6 yards of the nearest goal-post..."

Show pupils this and ask them what it would look like. Where can the player stand to take a goal kick according to these rules? Perhaps ask pupils to try to draw a scale drawing of it.

They should end up with a couple of arcs rather than the six yard box we are now so familiar with.

Once they've done this you can show them a picture of the 1901 FA Cup Final when Tottenham Hotspur played Sheffield United. There are arcs! It's very cool. The Wikipedia page on goal kicks says "In 1891, pitch markings were added to define the six-yard radius from each goal-post".

In 1902, the term 'goal area' was introduced for the place from which the goal kick was taken - it assumed its modern dimensions as a rectangle extending six yards from each goal post.

I loved this workshop and I think that this lesson on loci and scale drawing would go down really well.

Fascinating stuff from Rob Eastaway, as always.

Circle Theorems Chase
Tim Honeywill (@honeywilltim) led a session called ‘Expecting the Unexpected’ where he shared a pack of problems which are suitable for IGCSE and A level pupils. I love angle problems and there were a few in the pack, including this beauty called 'Crazy Circle Theorems'.

Tim's pack of questions contained loads of nice problems. Here are a few more examples:

Very kindly, Tim has let me share the whole set of resources from his workshop here. Thank you Tim!

Sectors of Circles
I ran a workshop on resources in which I talked through the process of planning a sequence of lessons on sector area. I showed a large number of places we can go to get resources including some classics such as SMILE. I talked about different types of task and discussed how they meet different purposes.

For this workshop I made a new Fill in the Gaps task on sector area (extract pictured below) which is intended to be used as part of the initial instruction phase. The idea is that pupils develop an understanding of how to identify what fraction of the circle is required, and make connections between sectors of different sizes. I also decided that I wanted to get pupils more comfortable with sketching diagrams, so I included that in the task. If you use this resource, let me know how you get on.

There's lots more I could say about the MEI Conference but to keep this post to a manageable length I will leave it there. Thank you to everyone - speakers, delegates and organisers - who made it so fantastic. Well done MEI! Great work.

Hanging out with Chris Shore and Tom Bennison

The next residential maths education conference I attend will be the MA Conference 2020 which involves two nights away at a spa hotel in the Easter holidays – I’m looking forward to it already!

5 Maths Gems #51

Welcome to my 51^st gems post. This is where I share five teaching ideas I've seen on Twitter.

1. Exam Tips
The lovely Julia Smith (@tessmaths) works hard to support maths teachers in Further Education and raise awareness of the challenges they face. Since September 2015 she has been tweeting tips for GCSE resitters using the hashtag #gcseresit. She has now published those tips here. Do take a look - they're not just for resitters!

Top Tip 38 suggests "making revision bags for half terms, Christmas and Easter breaks - these are like party bags (only better) - containing sweets, exam papers and topic tests". I read a similar idea in John Corbett's (@CorbettMaths) post 'Revision: Christmas Presents'. At Christmas he put a selection of Corbettmaths Practice Questions in envelopes along with a pen, pencil, a small bag of sweets, a few chocolate coins and a revision schedule. His school posted these packages to his students at home during the holidays. Not only did John's students complete revision that they otherwise would not have done, but they were also really chuffed and more engaged in maths revision at school as a result of John's thoughtful gesture. This lovely idea would work well at Easter too.

2. Fun with Primes

Christian Lawson-Perfect (@christianp) has created a fun game isthisprime.com/game. Maths teachers beware - this is addictive!

3. Fraction Talks
Fractiontalks.com is an excellent website curated by Nat Banting. It provides lots of lovely fraction problems, like the examples below, along with suggestions as to how you can help develop students' reasoning skills.

Follow @FractionTalks for updates.

4. Orangier
Don Steward has been producing loads of fantastic resources lately. I particularly like the task 'orangier' for the development of proportional reasoning. Students are given various combinations of orange squash and water and they have to determine which ratios give an orangier mixture.

5. Pi Day

It's Pi Day next week. I know some people don't like Pi Day because in the UK we don't write dates in the format mmddyy, but it's nice to see many schools seizing the opportunity to get students talking about maths.

All countries that use the mmddyy
date format - from @amazinmaps

Clarissa Grandi (@c0mplexnumber) has created a lovely resource that you can use in the classroom even if your school isn't organising any school-wide activities: 'Do aliens know about Pi too?'. I like the crop circles featured here, they're really interesting.

I featured more Pi Day ideas in Gems 26 last year.

Update
Here are a few things that you might be interested in:

• The FMSP's list of upcoming Changes to AS/A level Mathematics. 
• Big Ideas in Primary Mathematics (draft) by Mike Askew - thanks to Simon Gregg for sharing this.
• Craig Barton's podcast with Charlie Stripp of the NCETM and MEI.
• My post about the gaps in my knowledge of primary school mathematics - there's been lots of interesting comments on this post.
• My post about #mathsconf6. Booking for the next conference is now open - it's on Saturday 25th June in Leeds.

I have a couple of new posts in draft, one about Year 10 assessment and the other about 'bad' resources, so watch this space.

I'm hosting #mathscpdchat at 7pm on Tuesday 15th March - we'll be talking about how our students use their exercise books. Please join in.

I recently featured in a totaljobs.com article 'Insights into teaching' that you might enjoy.

I'll leave you with this lovely activity 'Fold and Punch' that was shared by Mike Lawler (@mikeandallie).

5 Maths Gems #45

Hello and welcome to my 45^th gems post. This is where I share five maths teaching ideas.

1. Circumference
Don Steward has been writing lots of brilliant posts lately so do keep an eye on his blog. I love two of his recent posts - Pi Development and Circle: Introducing Circumference. The latter features animations such as this:

and a really nice set of circumference questions.

2. Pinpoint Learning
Causing quite a stir on Twitter over the last two weeks, @tom_quilter's new website pinpointlearning.co.uk provides students with personalised question booklets based on exam results. It's perfect for after a mock exam. You simply upload students' marks and the website automatically produces individual booklets featuring question on the topics that students need to work on. The website is free and is set up for Edexcel papers, so if you've recently done an Edexcel mock then do give it a go. I've seen many tweets from teachers who've already tried it and speak very highly of it.

3. Five Minute Mock Analysis
When you return mock exams to students you might like to use this excellent Five Minute Mock Paper Analysis from @MathedUp. The file is editable so you can customise it for your school.

4. C4 Integration
I'm teaching C4 integration to my Further Maths class at the moment. We've just done Volumes of Revolution and I enjoyed making use of props to explain the concept. Thanks to an idea from Chris Smith (@aap03102), I used paper decorations to demonstrate how a solid is formed when a plane is rotated around the x axis.

I used these alongside gifs such as those shown below.

I also enjoyed using constant characters for the first time. This is an idea from @edenspresence that I featured back in Gems 22. Students who forget the 'plus c' in their answers are asked to decorate a constant character. Hopefully this will encourage them not to forget again and will make an interesting display for the classroom wall. Here's a couple of examples of what my students came up with:

5. Snowflakes
These Star Wars snowflake designs are brilliant and even feature characters from the latest films.

Here's a video about how to fold them:



If you're planning to do some snowflake activities at school in the last week of term then it's a great opportunity to talk about fractals - read Gems 16 for more on this.

Snowflakes can be a bit tricky to make so you might like these Paper Snowflake Cutting Tips. And this video (shared by @WycHighMaths) from Vi Hart is awesome:

It's only one week until #christmaths15! How exciting. You can still buy evening tickets if you want to join us for the party. The party includes a maths quiz, puzzles, food and a disco - partners and friends are very welcome.

If you teach Year 10 then do check out my recent post about real-life graphs.

Right, I have mock marking to do and Christmas cards to write so I better get on. I'll leave you with this nice question from @OCR_Maths - what fraction is unshaded?