5 Math Gems #199

Welcome to my 199^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Trimension

Following on from the release of Vectorama (Gems 197) and Graphiti (Gems 196), Neil Kendall has completed a third project 'Trimension'. This tool allows the construction of 3D models to help illustrate 3D Pythagoras and trigonometry problems. The key feature is the ability to extract internal triangles into a flat diagram. Neil has included four pre-built examples from past GCSE papers to illustrate what it can do (just go to add > examples).

This is a fantastic tool for teaching 3D Pythagoras and trignonomety - thank you Neil!

2. Interwoven Maths

Nathan Day (‪@nathanday) has made some updates to his excellent website interwovenmaths.com, including a new page of small tasks and a contents page showing all the resources and ideas now available on the site.

There's loads to explore on Interwoven Maths including this Quadratics Always Sometimes Never.

Nathan also shared Class Duels - a maths game featuring over fifty topics from across Key Stage 3 to 5. It can be played in two-player mode (split screen, which can be done on an interactive whiteboard) and single-player mode. 

3. Exam Countdown

Nathan Day also shared a newly updated Edexcel Exam Countdown page which includes both GCSE and A level (including Further Maths) and shows dates for 2027. Interestingly, there are two GCSE papers before half term next year, and A level Paper 1 is before half term too.

4. A level

@andrewmaths1 posted a link to a website that I've not seen before. mathstutorneri.com is great for students aiming for an A*. There's a booklet of challenge problems and a set of exam papers.

It's nice to have another website we can use for high challenge. We've always directed our A* students to MadasMaths which I first blogged about in 2016. This week's Edexcel A Level Paper 1 had two questions that were very similar to MadasMaths questions, so clearly it's a good idea to use this website! If you're not familiar with MadasMaths, there's IYGB practice papers for maths and further maths (don't ask what IYGB stands for...!) and there are also booklets by topic. I often use questions from these booklets in my maths and further maths lessons (tip for new users: zoom in on the PDFs to see full worked solutions hiding in the booklets). 

5. Tasks 
There's been a number of new tasks and resources shared on Bluesky and Twitter in the last few weeks.

Here's a nice task from ‪@4301maths on equations of parallel lines. 

@dalechapman shared a couple of tasks: one on simultaneous equations and one on constructions.

@canning_mrmaths shared a Quadratic Graphs Venn task designed for learners to think deeply about different features of quadratic functions. The task has four variations levelling up in difficulty.

@giftedHKO shared some distance time graph questions.

And @draustinmaths.com shared some new resources for simultaneous equations.

Thank you to everyone who shares resources!

Update

We're halfway through external exam season (for my department, eight exams down and eight more to go!). This is what we've had at my school so far:

• AQA GCSE: Paper 1 was nice! I thought Paper 2 was difficult on both Foundation and Higher Tier. On Higher there was a question where students had to draw a two way table and some of them said they didn't know what that was!  Eek, there goes four marks. Yet if they'd been given a two way table to interpret or fill in the gaps they would have had no problem. So we must get them drawing more two way tables in lessons! There were two questions on Foundation requiring equating coefficients - we need to change our Foundation scheme of work to ensure this is explicitly taught in future. One paper to go!
• Edexcel A Level: Paper 1 was difficult. There were some tough questions, fiddly answers and a few questions where students would be unable to do part b without managing part a which is frustrating. Some of our students have lost a bit of confidence but hopefully Paper 2 will give all students the chance to show what they know. The Further Maths (Core Pure) papers were both ok and I'm looking forward to Further Statistics 1 this Friday (my favourite module!).
• AQA GCSE Statistics: We switched to AQA this year and our students were pleased with Paper 1. We entered Year 10 for the first time (see my post about our Option Block Experiment) - they were terrified going into the exam, but all smiles coming out! 

For 'best guess' papers please continue to check Adam Creen's dropbox which includes GCSE (maths and statistics) and A level.

My recent post aimed at Heads of Maths Tasks for the Summer Term went down well - I've had lots of emails asking for advice and resources. I'm always happy to help but bear with me at this time of year when there's so much going on at school - I will always reply within a week!

I'm looking forward to the MEI Conference next month - always one of the highlights of the year! I hope to see lots of you there. I will leave you with this fantastic present gifted to Emily Rae by a student - I love this!

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.

5 Maths Gems #178

Welcome to my 178^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Inverse Proportion
I really like this tweet from @catrionateaches. When teaching inverse proportion I always talk about constant products but then I head straight into the formula y = k/x. Catriona suggests a subtle change in method. 

2. Graph Transformations

MathsPad has published another brilliant interactive tool for the Higher GCSE topic graph transformations. It shows how points on the original curves map on to those on the transformed curves. There is a separate section for quadratic graphs, which is particularly useful for relating completed square form to graph transformations. 

There is also a section for trigonometric graphs, where transformations of the graphs of y=sin(x) and y=cos(x) can be explored.

It's great to see a new resource published for teaching graph transformations - I always find that this is the GCSE topic for which it's trickiest to find suitable resources, because many tasks still include stretches (these were removed from the syllabus back in 2017 - GCSE now just covers reflections and translations).

Do check out MathsPad's full range of interactive tools - some of them are free to use even if you don't subscribe (you really should subscribe to MathsPad though!).

3. GeoGebra

It's worth following @geogebra to see ideas for interactive GeoGebra maths resources that can be used for demonstrations in lessons or student activities. Here are a few recent examples:

⚖️ GEOGEBRA RESOURCE! 📏

Try this FREE GeoGebra Exploration resource to convert units within a given system of measurement. Check it out! https://t.co/RQuWgxlNTR#mtbos #iteachmath #math #mathematics pic.twitter.com/qbp4U8DIFj

— GeoGebra (@geogebra) February 27, 2024

📦🐭 GEOGEBRA RESOURCE! 🥡🐱

Try this FREE GeoGebra Practice resource to draw box-and-whisker plots from a set of data. Check it out! https://t.co/VsqOGblJ2P#MTBoS #iteachmath #math #statistics pic.twitter.com/GAz9gbyLAR

— GeoGebra (@geogebra) February 27, 2024

🦾 GEOGEBRA RESOURCE! 🎰

Try this NEW & FREE GeoGebra Exploration resource to convert a number from standard form to expanded form one place value at a time. Check it out! https://t.co/vAIXvL5g48#MTBoS #iteachmath #math #mathematics pic.twitter.com/UXSN3RHQ69

— GeoGebra (@geogebra) March 4, 2024

4. Pythagoras
@nathanday314 shared a clever set of questions on Pythagoras' Theorem. There's a lot of challenge here (check out Question 12). Question 3 is deliberately impossible, and note the subtle differences between Questions 3, 4 and 5.

5. Prime Factors

@StudyMaths shared a video showing how to use the interactive Prime Factor Tiles on MathsBot to find a lowest common multiple, and in response @MrCowardMaths shared this really lovely task.

Update
Here are some other things you might have missed:

• The NCETM continue to publish their set of secondary mastery professional development materials. Their first set of Key Stage 4 materials focuses on numerical structure. These materials contain lots of teaching ideas that are well worth exploring. 
• @1stclassmaths has shared GCSE Predicted Paper 1 for both Edexcel and AQA. After Paper 1 takes place in May he will publish Predicted Paper 2s, and after Paper 2 he will publish Predicted Paper 3s. These papers will be very high quality so I recommend following @1stclassmaths for updates.
• @cclay8 has shared some more of her excellent calculator guides for the new Casio model. 
• @MattTheApp continues to share numerous resources for GCSE preparation on Maths White Board including maths formula sheet familiarisation tasks.
• @AMercerMaths shared a fantastic example of a curriculum booklet on diagonals in quadrilaterals. 

My school is still seeking an A level teacher to start in September. I can offer 100% A level teaching, or alternatively I can offer a timetable with Year 11 - 13 (or similar) if that's more desirable. Our students are a delight to teach and my team is awesome. If you live in Surrey or South London, this is an amazing opportunity. Please get in touch (email resourceaholic@gmail.com) if you're interested - I'm very happy to arrange a tour or call.

I'm presenting at two maths conferences in the next four weeks. The first is #mathsconf34 which is near Bristol:

And in the Easter holidays I'm presenting at the Shape Up conference in Stratford-Upon-Avon:

Finally, it's been a while since I've hosted a social event so I'm excited about this... more information coming soon.

5 Maths Gems #167

Welcome to my 167^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Polypad

I've blogged about Polypad before, and used it myself in a lesson on nets last week. My students were suitably impressed! Recently there's been a series of tweets about some really cool stuff that Polypad can do - these are definitely worth a look. Click on the tweets below to see the animations in action, and check out @MathigonOrg's feed for more like this. I particularly like what you can do with factors.

It’s awesome how how Ss can explore greatest common factor of any set of numbers in @MathigonOrg #Polypad — especially when number fact fluency isn’t quite there yet. For many Ss, automaticity can develop through playful explorations like these! https://t.co/HgqAGlaGXg #MTBoS… https://t.co/Zk8W8FU5mG pic.twitter.com/wZ5QHE8HwV

— Tim Brzezinski (@TimBrzezinski) February 12, 2023

How does scaling a hexagon's side length impact the 4 animations on Polypad? What will stay the same? What will change?

Learn about these new features in the latest "What's New" video at https://t.co/oSXzdL2Bq4@MathigonOrg @desmosclassroom @Amplify #iteachmath #mtbos pic.twitter.com/JAzZnsIJLM

— David Poras (@davidporas) February 17, 2023

Visually solving equations w/fractions as coefficients in @MathigonOrg #PolyPad. https://t.co/vgrvly7vVK @desmosclassroom @Amplify #math #MTBoS #ITeachMath #algebra pic.twitter.com/2bXs2Gk6fP

— Tim Brzezinski (@TimBrzezinski) February 17, 2023

2. Fingertip Knowledge
@mathsmrgordon has shared a set of fingertip knowledge documents for Foundation Tier GCSE. These are like self-quizzable knowledge organisers, similar to my Knoweldge Quiz books, but with calculations as well as factual recall. 

You can download these documents for algebra, number, ratio and proportion, charts and averages, probability and geometry and measure. Thanks Ben!

3. Standard Form
@nathanday314 continues to produce amazing resources. His Calculations with Standard Form Booklet is full of excellent tasks with loads of challenge. Here are a couple of examples:

Nathan also produced some Star Wars Pythagoras Challenges which I love:

4. Kinematic Graphs

I taught tangent to a curve and area under a graph to Year 11 a couple of weeks ago and spotted these two tweets about kinematic graphs. These are helpful for both maths and physics teachers.

I'm a sucker for a pretty graphic - and how pretty are these! https://t.co/epPwAsVG2j
So many fab comics on here for Mechanics and Physics #mathsTLP pic.twitter.com/R2q8KbvnpH

— Christine Norledge (@MissNorledge) January 29, 2023

Created this table fill for velocity-time graphs pic.twitter.com/fecWPsOCGW

— Miss E (@Miss_R_Em) August 25, 2022

5. Same and Different
Thank you to @KarenCampe for sharing her brilliant blog post 'Same and Different'. This post is about a thinking strategy Karen uses for discussion in her lessons in which she asks students to compare and analyse features of two mathematical situations. Here are a few examples.

The first shows two subtraction problems: 5 – 2 (top) and 2 – 5 (bottom).

And this one is for gradient and y intercept:

And here's one on simultaneous equations:

And one on notation:

There are loads more examples in Karen's blog post.

Update

My school finally had its much-awaited first visit from Ofsted. They did a deep dive in maths. I'm really proud of my wonderful team - they're all superstars. Here's seven tenths of my department celebrating the end of a challenging week:

Over half-term I was busier than usual on my blog, publishing three posts:

• Ten Videos for Maths Lessons
• Area in Depth (sharing an exciting new video from me and Craig Barton, sponsored by AQA)
• Ratio by Sam Blatherwick (a #doseofdon post)

I received two lovely parcels: David Acheson's excellent new book 'The Spirit of Mathematics' (with thanks to Oxford University Press) and a new Casio 991CW, engraved with my name (with thanks to Stephen at Science Studio).

Here are some things you might have missed:

• I discovered a website drolivermathematics.com which features numerous resources including condensed papers for GCSE, A level and AQA Certificate in Further Maths. This is great for reducing printing costs, and I like the way the solutions are set out.
• I made a Year 11 final stretch calendar for my team to help them plan their remaining time with Year 11. Feel free to download and edit this for your school if it helps.
• @draustinmaths has been creating loads of new resources including some for indices, similarity, trig graphs and recurring decimals. Check out her website draustinmaths.com to download her resources.
• @Arithmaticks shared a great blog post 'Year 11 Staple Challenge' about a clever way to use past papers with GCSE students.
• @MattTheApp shared an exciting new feature on his website: a blank whiteboard interface with a large range of tools. It has everything from a protractor to a number line to an onscreen timer.

As we head into Spring, there's loads to look forward to. #mathsconf31 in Bracknell will be great - I'm very much looking forward to presenting on Pythagoras which is one of my favourite topics. La Salle is still looking for presenters for this conference and I strongly encourage teachers to submit workshop proposals. I'll also be taking forty Year 10 students to Maths in Action on 7 March which will be brilliant. And I'll be going to the Christopher Zeeman Medal Lectures and Ceremony at the Royal Society on 22 March. The Spring term ends with the Joint Conference of the Mathematics Subject Associations at Warwick University. I love a residential campus conference! So there's lots of fun stuff coming up. On the flip side, over the next two weeks I'll have 127 Year 11 mock papers to mark, which is a bit less fun... I'm sure lots of you are in the same boat.

I'll leave you with a set of GCSE revision memes (first shared by Paul Collins years ago - and I've added some more). We've put a few up in the maths corridor in the run up to mocks to lighten the mood and get people smiling. Don't forget, if you're looking for revision resources for Year 11, there's an extensive collection here.