5 Maths Gems #196

Welcome to my 196^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Make it Full Marks

@acutelearning shared a great resource called 'Aiming for A*: Make it full marks'. This is an A level resource made using AQA papers but is relevant for other exam boards too. 

In this resource students are presented with partially correct answers. Each answer is worth some or most of the marks. However, in each case there's at least one error or missing component that means the answer will not receive full marks. Students have to find the error and correct the answer to make it full marks. This is a lovely revision resource to use in a summer term lesson with A level mathematicians. 

You can access the resource here and the answers are here. 

@acutelearning has also shared some other useful resources:

• hypothesis testing revision
• alternating exercises (covering topics from KS3/4/5) - with PPT and answers

2. Mr Hardy Maths
@jim-hardy has shared his website mrhardymaths.co.uk which contains question banks for GCSE, A Level and A Level Further Maths. There's a search box to help you find relevant questions:

Opening one of the topics let you practice this skill on screen with students:

Clicking print gives you a worksheet with answers:

3. Graphiti
Maths teacher Neil Kendall has developed a free resource Graphiti to easily demonstrate calculus concepts graphically. As well as functioning like Desmos you can very easily use interactive tangents and normals, calculate definite integrals, illustrate area between two curves and show numerical integration interactively - switching between trapezium, Simpsons and mid-ordinate methods. It will work with cartesian (implicit and explicit) as well as polar and parametric equations. It works on desktop, mobile and tablet devices.

Here's a short video demonstrating many of its features:

4. Mr Chapman Maths

@dalechapman has shared a number of new features on his website mrchapmanmaths.com. He's made Large Data Set Flashcards for the Edexcel Large Data Set. This is a fantastic revision resource for students studying Edexcel A level maths.

There's also a fun game called Target 1000. You randomly generate a digit and place it in the column addition with a target of 1000. Have a go!

There are also a lot of resources on this website for teaching Decision Maths.

5. Dr Austin Resources
@draustinmaths continues to share fantastic new resources. Recent additions include Hyperbolic Functions for Further Maths, Exponentials and Logs and 3D Vectors for A Level Maths, and Volume and Surface Area of Compound Shapes.

Update

Calculators

I've enjoyed playing with the new Casio Classwiz+ which is a massive improvement on the previous model. The brilliant company Science Studio very kindly sent me both a 85 and 991, engraved with my name, and Casio sent me one too. What lovely people. I've been using my old White 991EX since 2016 and my dependence on the SD button has made me reluctant to transition to the 991CW. But now I have a 991CW+ I've finally stopped using the old white model. The 991CW+ is my new first choice calculator. 

MathsPad

Have you seen the latest update from MathsPad? As well as new resources in their 'Building Blocks' series, which are aimed at students with big gaps in foundational knowledge, they've also started a new collection of cover resources. These are free to access. Also, Nicola has written a useful explanation of the logistics of using booklets in lessons.

Exercise Books

A teacher on Bluesky asked a question about treasury tagging books and I made a quick video for her (I recorded it in a rush before school, so it's not the best thing I've made! Please don't judge...!). In this video I show the layout of our A4+ exercise books and the way we set up our treasury tags. I know a lot of teachers complain that their exercise books are a mess so you might be interested in what we do. 

Conferences

You may have seen that mathsconf40 has been announced for Saturday 18th April. This is a first - mathsconfs have always taken place in March, June and October. A mathsconf at the start of the summer term has taken me by surprise. It's great to see that these conferences are still running. It looks like some people will be staying at the Premier Inn Derby South but for some reason that's £111 for a room so I'm not quite sure what to do about that - it takes the cost to well over £200 for train fare and hotels. I remember when I used to spend £40 on conference hotel rooms! Those were the days.

The MEI Conference is now taking bookings. This takes place in term time (Thursday 2nd - Friday 3rd July) but it's after exams when lots of teachers have gained time so hopefully doesn't involve missing too many lessons. I recommend asking your school to fund your attendance at this - there's no harm in asking! Schools often have untapped CPD budgets. It's a brilliant conference that I highly recommend. 

I attended an Inset Day last week where I went to three excellent sessions: a workshop on the CG100 which was delivered by Simon May from Casio, a workshop on A level marking delivered by Isobel Oakley from Pearson, and a workshop on university admissions tests delivered by Alexandra Hewitt from MEI. I've been to so many conference in the last twelve years it's sometimes hard for me to find sessions that are relevant and useful that I haven't been to before, but on this occasion all three workshops were genuinely helpful. Alexandra said something in her session that really struck me - she talked about who we should encourage to do maths degrees and it occurred to me that I only think of maths degrees as being suitable for the very best mathematicians. But a student could be on a Grade B or C in A level maths and it's their strongest or favourite subject, and maybe one day they'd make an excellent maths teacher. These are the students that I should be encouraging to take a maths degree. I don't do enough of this. This gave me something to think about.

Here's a photo of part of my team on the way home from our post-conference drinks. There were eight of us earlier in the day but we forgot to take a picture. I love my team - a group of absolute legends who support each other every day and work incredibly hard to make sure every child succeeds. 

I wish all of my readers a restful half term break.

5 Maths Gems #184

Happy New Year and welcome to my 184^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Dr Austin

Thank you to Amanda Austin for continuing to share fantastic free resources for Key Stages 3 to 5. I've been adding these to my resource libraries. Recent additions include Simplifying Expressions True or False, Parallel or Not Parallel Activity and Drawing Line Segments with a Given Gradient, plus lots of A level mechanics tasks. 

2. MathsPad

MathsPad have recently published some really lovely new resources for subscribers including significant figures puzzles that involve a lot of reasoning and worksheets on 2D and 3D Shapes. They have also published new textbook chapters for Year 11 packed full of fantastic tasks including chapters on area and volume, real life graphs and measures, inequalities and rounding and estimation. 

There's also a new interactive tool for exploring the triangle inequality. 

3. 1st Class Maths

Another one of my favourite websites is 1stclassmaths.com. I use this a lot when teaching AQA Level 2 Certificate in Further Maths, and we also direct our Year 11 students to it for GCSE revision. The videos and resources are all really high quality. Our students also find the topic frequencies page fascinating! And I will definitely be using the A level resources when I teach statistics this term. 

Recent additions to the GCSE revision page (which has both an AQA and Edexcel version) include questions on volume and area, sequences and fractions. I have added all of these to my resource libraries.

4. Things to Memorise

Since Formula Sheets were reintroduced at GCSE we've had students asking whether we have a list of facts and formulae that they still need to memorise. I've finally got round to making something for the students at my school. I've tried to make it succinct and it's certainly not an exhaustive list of everything they need to learn, but it does provide a summary of the key facts that they can get parents or friends to test them on. Students need to be fluent in all these facts so they can focus their efforts on reasoning and problem solving.

You can download these for both Higher and Foundation tier (including editable versions) here for your Year 11 students. I was a bit unsure about sharing these documents because I didn't make every image myself - I just found things on Google images that I thought were particularly clear. Apologies and thank you to the creators of the pictures I have used. If you spot any mistakes, please let me know.

5. Integration 

I very much enjoy Catriona Agg's posts on Bluesky. A nice example is her recent post about integration using trigonometric substitutions. I'm using this with my Further Maths class next week.

I also loved her recent post about graph sketches. 

I also like Catriona's topic map for trigonometry, which really helps students get a sense of where their learning fits with what they've done before and what's coming next.

I do something similar in my lessons - for example here's a slide I show when I teach factorising to Year 10:

Updates

Here are a more few things you might be interested in:

• I received an email from Head of Maths Ben Plowman about a daily puzzle based on the 'Knight's Move' in chess. Ben's son made this clever little game. I think my readers will enjoy it: knightpuzzle.com.
  
• Tom Francome's team has been busy digitising Don Steward’s paper notes and they are now available on Don's wonderful blog. Read Tom's post about this here. I've really enjoyed reading Don's notes - they are full of treasures. New teachers who have not yet discovered Don Steward's tasks - please drop everything and explore them now. 
• OCR have recently published some posts that will help teachers develop their A level curriculum knowledge. In Amy Dai's post A Level Maths and Further Maths: the importance of accurate vocabulary in statistics there's really helpful information on where candidates go wrong in exams. And Steve Walker has written a great post on Show That questions. These posts and more can be accessed through OCR's website.
• Paul Rowlandson published a new blog post: 'Taxing Tasks with Turtles' which looks at a selection of geometry problems and investigations that can be explored by using a small amount of coding.
• The Joint Conference of the Mathematical Subject Associations takes place in Loughborough on 14th to 16th April 2025 - check out futureproofingthecurriculum.org.uk for information.

Vacancy

Come and work with me! I will have at least one vacancy for September and I'll definitely need someone who can teach Year 13 mechanics. We have a fantastic uptake for A level Maths and Further Maths and I have a brilliant team teaching it, but we need one more A Level maths teacher to join us. I will be advertising soon - hopefully in January - so watch this space. We are located in South London. Behaviour and attitudes are excellent so our students are a pleasure to teach - this year our Maths Progress 8 score was 1.22 (data available here). Here's a picture some of my lovely team of maths teachers enjoying our Christmas party! If you're interested in joining us, please get in touch.

An apology for my absence
You might have noticed that I don't blog anywhere near as much as I used to. This is constantly on my mind. I really want to keep blogging, I just struggle to find the time and inspiration these days. My job grew this year and although I love it, it can be all-consuming at times. Plus parenting busy daughters in Year 6 and 8 doesn't leave much time for hobbies like blogging!

My inspiration for content is seriously lacking too. There was a mass exodus of maths teachers from Twitter over summer, and it's now pretty dead there in terms of posts about resources. There's a pleasant community of maths teachers on Bluesky, some of them sharing lovely ideas and insights on a regular basis using the hashtag #mathstoday, but for some reason I just can't get into it. I have tried. And it's not just social media providing few ideas for blog posts - this year I'm only teaching Years 11, 12 and 13 - I find that when I teach Key Stage 3 I have much more to write about. My timetable is mostly Sixth Form, but having had a seven year break from teaching A level, I wouldn't be so bold as to give advice about A level pedagogy. 

But I haven't totally disappeared. In the background I do still add resources to my resource libraries to make sure they are kept up-to-date. You can access my resource libraries here. And I often get emails from teachers and Heads of Maths asking for advice which I'm always happy to provide. And I do have some things I plan to blog about later in the year - for example I think there might be some interest in how we structure the teaching of our new option subject (which combines GCSE Statistics with Certificate in Further Maths) but I should wait until our first set of results are in this summer before I write about that! 

So in short - sorry for my absence from both blogging and social media. I am still here in the background, and I hope to see many of you at conferences this year. 

I will leave you with this lovely little puzzle from ‪@1stclassmaths.bsky.social‬.

Thank you for reading, and all the best for the start of the Spring term.

5 Maths Gems #140

Happy New Year! Welcome to my 140^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

1. Functions Puzzle

Thank you to @mathequalslove for sharing this lovely Evaluating Functions Puzzle. Sarah's blog post includes both a paper-based and interactive version.

2. Statistics Tools

Thank you to @DrPMaths for sharing a very useful histogram drawing tool. 

And thank you to @MathigonOrg for the new probability additions to the excellent PolyPad tool (I blogged about PolyPad in Gems 114).

Here are some new probability tools for Polypad:
🔄 customisable spinners and 🎲 non-transitive dice! https://t.co/HDEd7BNKaK pic.twitter.com/MqF3lUEGXj

— Mathigon (@MathigonOrg) December 26, 2020

3. Bad Calculators

Thank you to @TylerAuer for sharing his new puzzle app. Have a go at the puzzles on badcalculators.com - they're really fun. To give an example, in the puzzle below we want to go from one to one hundred using the operations +3, x4, +5 and x6 only. The challenge is to do it in a certain number of moves.

4. Mechanics Video

Thank you to @BicenMaths for sharing an excellent video and memory page summarising Mechanics for A-Level Maths.

5. MathsPad

@MathsPadJames and @MathsPadNicola have done it again! I've had a MathsPad account for a good five years now and have been impressed by every single monthly update they've ever published. Their latest resources are brilliant, as usual - including a clever 'greatest integer' activity that requires students to convert between fractions, decimals and percentages. They must work out the biggest integer that will make the statement true. The activity has two levels of difficulty.

They have also published a brilliant new tool to explore prisms interactively.

New for January: Explore Prisms Interactively - including Cross-section, Net, Explode and Layers modes.

Full January MathsPad update here:https://t.co/VuDmRGAstH pic.twitter.com/fgpVYm3sF4

— James Pearce (@MathsPadJames) December 31, 2020

Most MathsPad resources aren't free, but the subscription is well worth it (I use their resources literally every day!). They also have a huge range of interactive tasks that can be set for students working at home during periods of remote learning.

Update
It was unfortunate that I spent the entire Christmas holidays unwell with Covid 19. My poor husband caught it from me, so both of us were ill for Christmas. I am feeling better now, though my energy levels are low and I still have a bad cough. My sense of taste has also not yet returned to normal. This isn't a big deal, but it does mean I won't be able to enjoy a nice glass of wine on my 40th birthday on Wednesday, as wine currently has no taste whatsoever. I know I shouldn't complain about such trivial matters - I was fortunate to experience a relatively mild case. My heart goes out to all the teachers and their families who have been affected by Covid 19 in 2020. 

In case you didn't see them, I wrote three blog posts in December:

• Victorian Arithmetic
• 5 Maths Gems #139
• Straight Lines

And here are my five most popular blog posts from 2020, in case you missed them:

• Warm Up Booklets
• Remembering Don Steward
• Maths Teacher FAQs
• Catching Up?
• CPD for Maths Teachers

I'll leave you with these Function Composition memes, taken from this brilliant thread shared by @MrsStevensMath. The thread includes a set of slides explaining this assignment to students.

Happy New Year to all my readers, and good luck with the online teaching. Stay safe!

5 Maths Gems #138

Welcome to my 138^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers. I've got a bit behind on my blogging lately because school has been overwhelmingly busy, so here I'm trying to catch up by featuring ten gems instead of my usual five. 

1. Prime Factors Tool

Jonathan Hall (@StudyMaths) has published another new tool on the brilliant mathsbot.com. This lovely prime factors tool uses virtual prime factor tiles to help students make sense of prime factorisation, highest common factor and lowest common multiple. Click on the cells to toggle through blanks, products, and prime factors.

2. Certificate in Further Maths Resources

Teachers delivering the AQA Level 2 Certificate in Further Maths should check out Amanda Austin's (@draustinmaths) website which contains practice resources for this qualification. I like the format of her practice strips which are very helpful for sticking into books.

Do check out the rest of Amanda's website, which features a collection of KS3 and KS4 IGCSE and GCSE Maths resources ordered by topic. 

3. Tasks

Since Chris McGranes's (@ChrisMcGrane84) book on mathematical tasks was published and he started running courses in task design, there has been a flurry of excellent tasks shared on Twitter and Chris's blog. Here I share a couple of examples - check out his blog for more like this.

Fraction Stories (thanks to @limeswright for tweeting about this one - I think I will use it next week to assess prior understanding in my first fractions lesson with Year 7):

Simultaneous Equations (I'll be teaching this soon to a class who will really benefit from the  scaffolding in this activity):

4. GCSE Statistics
Thank you to Helen Scott (@HelenScott88) for sharing her GCSE Statistics Retrieval Roulette. Aimed mostly at Higher Tier candidates, the chapter references in this resource relate to the Pearson GCSE Statistics textbook. For guidance on how to use Retrieval Roulette, read Adam Boxer's blog post.

5. Volume

Thank you to @SegarRogers for sharing this cuboid volume task. He designed it for a class in which some students have trouble seeing individual cubes, requiring a gradual removal of the isometric grid, and other students are ready to try working backwards.

6. Recall

All the way back in Gems 87 (April 2018) I shared an example of a regular recall starter from @JaggersMaths (formerly @MissBanksMaths). Mrs Jagger has now updated her R^Infinity resource, which teachers can use to quickly create personalised four-question starters. Visit her website to download the resource and to find out how it works.

7. Sequences and Fractions Task

Richard Perring (@LearningMaths) recently shared two interesting tasks. The first is a sequences task in which students generate their own sequences.

The second task is based on a similar idea, but relates to fractions. I really like these tasks.

8. Number Sense Maths
Clare Christie (@Ms_Mathsteacher) got in touch about the website numbersensemaths.com. There are tonnes of free resources to get schools going on structured number fact teaching, and a full scheme of work for those who want to commit to it. 

This website will be of particular interest to primary schools, and I think that SEND departments in secondaries will find useful strategies and resources here too.

9. Place Value
@taylorda01 had a nice idea for a place value task. Present students with the following numbers and ask them how many times bigger the value of the red digit is than the value of the blue digit. Then ask how much bigger the value of the red digit is than the value of the blue digit.

10. Pictograms
Thanks to @giftedHKO for a new pictograms resource. I have linked to this in my data resource library.

Update

Last weekend I enjoyed spending the morning in Scotland (virtually!) for the Northern Alliance N5 Maths Conference. The workshops were excellent. I presented on teaching quadratics. I will present a similar workshop at La Salle's '#MathsConfMini' which is on a Friday evening in January.

Another event I'm presenting at in January is White Rose Maths Secondary Maths Brunch.

In case you missed them, I published two new blog posts in the last couple of weeks. They were:

• Lines and Angles on Square Grids (a post written by Anne Watson about a collection of Don Steward tasks)
• Zooming In (a post about a great teaching tool I recently used for the first time in a Year 7 lesson).

Another thing I was involved in last week was a discussion about Don Steward's tasks on Tom Manners' ResourceFULL channel. This is worth a watch if you want to see some outstanding examples of rich tasks.

Other things to check out if you haven't already:

• Marvellous Maths 2, which is a CPD course for maths teachers from me and Craig Barton. It's been great to hear of teachers using ideas from this course in their teaching this week.
• Ed Southall's new book, Geometry Juniors. This is aimed at 8 to 12 year olds. It looks great!
• The review of my book A Compendium of Mathematical Methods published in the MA's journal Mathematics in Schools. I loved this review and was very pleased to read an account written from the perspective of the book's main target audience (maths teachers!).
• I've had a few questions about intervention resources for Year 11s recently. Do check out my GCSE Revision Resources page if you're looking for this kind of thing.

I'll leave you with this wonderful pentagon tessellation tool from Mathigon.

Regular pentagons don't tessellate – but there are 15 other types of pentagons that do. We’ve collected all of them at https://t.co/PDYbPhRhMa. Can you fit them together? pic.twitter.com/a7I5Z32des

— Mathigon (@MathigonOrg) November 6, 2020