5 July 2020

5 Maths Gems #131

Welcome to my 131st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Self Marking Sheets
Phil Rhodes (@Philmaths314) has shared a free set of Self Marking Google Sheets. As the name suggests, these are sheets that mark themselves. ⁦‪You can assign your class these Self Marking Google Sheets in Google Classroom. The site is very easy to use: choose a sheet, create your own copy and then assign to your pupils. When they input answers, they get an instant score.

2. A Level Knowledge Organisers
I am quite often asked about A level knowledge organisers, so it's great that there are now some available for teachers who wish to use these. 

Thank you to @Lucyjc1612 for sharing knowledge organisers for mechanics and statistics.
And thanks to @misschakera for sharing knowledge organisers for pure topics. 

I have now added these to my A level resource libraries and my Knowledge Organisers page.

Thank you also to Jake Goodman and Rachel Mahoney who emailed me some Key Stage 3 and 4 knowledge organisers for inclusion on the Knowledge Organisers page. 

3. Pedagogical Prompts
@DanielPearcy has published a new website danpearcy.com containing collections of tasks, prompts and resources.
Dan introduced his Pedagogy Prompts at the Seneca conference yesterday. These are designed to prompt discussion amongst maths teachers, to help develop teachers' pedagogical content knowledge. Dan suggests that discussion of these prompts might form the first ten minutes of a maths department meeting.
For the above prompt, Dan suggests the following questions:
1. Which formula do you use for the cosine rule? A formula that isn’t listed above?
2. Why might you stress the importance of number 2?
3. Is there a context in which you would consider teaching number 3? Is it a problem that this doesn’t appear in textbooks or formula books?

I found this really interesting. When I teach the cosine rule I always verbalise it only using the third formula, but have never seen it written down like this.

4. Planning Tool
Thank you to @timdolan who has created a planning tool to help maths teachers think through a topic or series of lessons before they plan in more detail. 
5. New Resources
Here are some new resources and activities that have recently been shared on Twitter:

Blog Posts to Read
  • My favourite maths blogger @Mr_Rowlandson has shared a brilliant new blog post about posing questions in different directions.
  • Check out @jnovakowski38's blog post summarising the best places to go for different sets of virtual manipulatives, along with presentations and articles to support the use of them. I have featured most of these websites in my gems posts over the years but it's great to have them all in one place. The only thing I'd add to this list is the wonderful MathsBot.com

  • @InteractMaths shared a post with a range of carefully thought out median and range tasks.

Complete Mathematics Conference
Thank you to La Salle for sharing all the recordings from #mathsconf23 on their website. If you want to keep track of what you've watched, this session tracker shared by @MrWilliamsMaths is very helpful.
The ATM has been publishing short CPD videos on its website. One example is The Words We Use with Jenni Ingram which is a seven minute exploration of the use of language in mathematics and how small changes can alter meaning. 

Senenca Conference
I really enjoyed the three hour Seneca conference on Saturday morning. It was a great length and format. The short talks were a fantastic way to showcase new speakers and - in a very rare thing for a maths conference - there was a good balance of men and women speaking. I spoke about Lowest Common Multiple - this was a mini-topics in depth presentation. You can watch it here, along with the other excellent presentations. 

Do check out the Padlet shared by Emma Bell (@El_Timbre) during this conference.  This will be of particular interest to teachers who teach GCSE re-sit. Emma shared her incredible work on 'The Focused 15' - fifteen interconnected topics to focus on with re-sit students.

Also check out the If The World Were 100 People video that Emma showed during her presentation. I have blogged about a few '100 people' resources in the past but this one was new to me.

My CPD Videos
The Order of Operations Topic in Depth presentation I recorded with Craig Barton back in February has now been published by TES. You can find it on my CPD Playlist, alongside all my other CPD videos.

Two weeks left! I can't wait for the summer holidays. It has been a challenging term all round. 

My school is running our annual personal development week next week - this means I haven't had to set any maths work, but there's lots of other stuff going on including a virtual Sports Day and a Discovery Day, where I get to run a live lesson teaching students a load of fascinating stuff about banknotes (my chosen topic, which I know a lot about from my previous career). In the last week of term the maths lessons are back on but we also have our students coming in for end of term tutor group assemblies, which is really exciting. We're also doing end of year reports (consisting mainly of form tutor comments) which I have whole school responsibility for, so that will keep me busy. 

My own children have a lot going on too. Neither of my daughters (Year 1 and Year 3) have been back at school (the little one goes to an infants' school which couldn't accommodate Year 1), but their schools have planned some lovely end of term stuff, so they're happy. In terms of their maths, my Year 1 daughter is still doing the daily White Rose lessons, as well as using a few apps like Hit the Button and DragonBox. My Year 3 daughter does the White Rose lessons too, as well as Times Tables Rockstars. I recently realised that the Bronze 5-a-Day sheets from Corbettmaths Primary are perfect for her too (I don't know why I didn't think of that earlier!) so that's a late addition to our daily routine.

I will leave you with this fantastic video 'The Story of the Vinculum' from @jamestanton. It's brilliant. 

21 June 2020

5 Maths Gems #130

Welcome to my 130th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

I'm writing this post the day after #mathsconf23. This huge online conference was a great success and I'll say a bit about it at the end of this post. 

1. Quadratic Formula
Andy Lutwyche (@andylutwyche) shared a new resource for teaching the quadratic formula. Note how the questions change - in the last few, students are asked to work backwards.
The idea was based on this exam question that was shared by @MontaigneMaths

2. Primary Goal-Free Problems
I originally saw the idea for goal-free problems in Craig Barton's first book. If you're not familiar with them, the idea is to remove the 'question' from a maths problem, making the problem more open and accessible - the approach is explained very clearly in Clare Sealy's post here.

Thank you to Jean Knapp (@MissJK24319629) for sharing a blog post on primary 'goal free' problems where she reflects on the last sixteen months of use and innovation trials. The post includes a big accompanying resource for Key Stage 1 and 2. 

3. Calculated Colouring
Thank you to Claire Clay (@cclay8) for sharing a set of calculating colouring activities that she has made, covering a range of topics from angles to algebra.

4. Squares
Sudeep from Boss Maths (@boss_maths) shared a problem that I found really interesting. Although the answer can be worked out mentally in a few seconds at a fairly young age, older students (and often teachers!) can totally over-complicate it. Don't read the replies under the tweet before you've looked at the question!

On the subject of squares, check out this blog post from @blatherwick_sam which has a great sequence of questions on squares.

5. Templates
Thanks to Nathan Day (@nathanday314) for sharing a lovely set of free editable templates based on Craig Barton‬⁩'s book Reflect, Expect, Check, Explain and online courses. This includes templates for retrieval starters, example-problem pairs, low stakes quizzes, intelligent practice, SSDD problems, diagnostic questions, and UKMT questions. Check out this thread to see the examples.

Bonus Lockdown Resources
  • Textbook publisher Elmwood is currently providing free access to its Key Stage 1 to 5 maths textbooks until the end of August. I signed up for Key Stage 3 and got online access to textbooks and homework books for Years 7 - 9. 
  • MEI is currently running Calculator Crunch 2020 - check out the hashtag #CalculatorCrunch for the daily questions, aimed at students in Year 6 and Year 7.
  • Emily Fleming from the charity SAMI sent me an email about a new A level Bridging Course aimed at Year 11s planning to take A level maths in September. This is free and looks amazing. Check out my tweet about this for more information.
  • Thank you to the ATM for sharing a series of free 'Maths Snacks' videos for children to use at home during lockdown. They are a mixture of tasks, puzzles, challenges, and games, selected to support and enrich the mathematics taught at school. Many can be accessed by very young children, with a little bit of adult support, and all of them are relevant to pupils across the whole school age-range. You can tell a lot of expertise lies behind these carefully crafted activities. 

Last week I was interviewed live on YouTube by Tom Manners (@Mannersmatics). I had the opportunity to talk viewers through some of the lesser known features of my website (there's a lot that people don't know about!). You can watch the interview on Tom's website
TES also released the fourth Topics in Depth workshop that I recorded with Craig Barton. It's on the Order of Operations. It's not on Youtube yet but can currently be watched for free on Craig's CPD Platform.

I very much missed seeing all of my usual conference buddies in person yesterday, but La Salle did an incredible job of hosting an absolutely brilliant online conference. The sessions on offer were all top quality, and it was great that the conference reached such a wide audience, include a large number of international delegates.

I strongly believe that maths teachers benefit from CPD on how to teach specific topics, so I delivered a session on teaching exact trig values. In this session we looked at the GCSE specification (including the rationale for the inclusion of this topic in the 'new' GCSE), how this topic is assessed, and how to structure and deliver the teaching of this topic. Thank you to everyone who attended my workshop, and particular thanks to @arzzax who was listening from Australia and shared the popular 'half-square' idea in this tweet

If you missed my workshop then you will be able to catch up on it when La Salle shares the whole conference online.

Do have a listen to the post-conference podcast, which I recorded straight after #mathsconf23 in a Zoom call with Craig Barton. 

If you enjoyed #mathsconf23, or you missed out, then do check out Seneca's three hour maths conference on 4th July. My next task is to write my workshop for that!

I will leave you with these puzzles, shared by @MathigonOrg. There are loads like this on Philipp's beautiful website.

6 June 2020

5 Maths Gems #129

Welcome to my 129th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Induction Booklet
Miss H (@MissJHE_) made a induction booklet for Year 6 which she shared here. It includes loads of activities for her new joiners to do over summer, plus an introduction to the maths teachers in her department. Inspired by this, I created my own version - I have used loads of Miss H's ideas, so she has saved me a lot of time - I am very grateful to her for sharing this on Twitter.
2. Distance
Richard Perring (@LearningMaths) shared a lovely question, and @MathyMahdi replied with a brilliant gif:

3. Learning Journeys
A few big pieces of curriculum work have been shared on Twitter recently. They must have taken absolutely ages to produce, so thank you to these teachers for sharing. 

@MrPatFerrers149 shared his school's Maths Learning Journey which can be viewed here.

@JaggersMaths shared editable learning journeys to accompany her massive five year scheme of work which she has recently made freely available for other schools to borrow and adapt. 

This was produced using @nathanday314's editable template.

@GemmaHeald made a curriculum map for her students which is available here

4. Slow Reveal Graphs
Thanks to this post by @benorlin I discovered the website slowrevealgraphs.com by @jennalaib. First read Ben's post, then check out the website. It's packed full of data literacy resources that are perfect for those 'what do you notice?' discussions.

5. Tasks 
@ChrisMcGrane84 has shared some excellent tasks on his blog startingpointsmaths.com that are well worth a look. Here's an example: a task on multiplication and division by multiples of 10 (see the blog post for the full task).

Chris has a book on mathematical task design coming out this summer.

Upcoming CPD Opportunities
  • Tom Manners (@Mannermatics) has announced a new series of interviews named '#ResourceFULL' which focus on maths resources. He has a number of guests lined up. I will be appearing on this at 8pm on 17th June.
  • La Salle's virtual #MathsConf23 will take place on 20th June. There's a great line-up of speakers and some really interesting sessions planned. It's now sold out (three thousand delegates!). You can buy your raffle ticket for this event (and support Macmillan Cancer) here.
  • Seneca will be running a free mini-maths conference on the morning of 4th July. Book your place here.

Don't forget that my YouTube channel is full of free CPD, and the Seneca course for my book - which has so far been completed by over 1300 people - is also totally free (if you enjoyed it please buy my book, and leave me a nice Amazon review!).

Finally, it has recently come to my attention that some teachers are not aware of a couple of excellent websites that have been around forever - if you're new to teaching and your training provider didn't tell you much about where to get resources, please check out my old post Classic Resources. In particular, it's worth knowing that CIMT has a load of interactive materials for Year 7, Year 8 and Year 9 (examples and exercises with no login required) that teachers might find helpful when setting remote learning. 

I'll leave you with this word search from Frank Tapson's Teacher Resources on Line. Can you follow the maths words though this maze?

23 May 2020

5 Maths Gems #128

Welcome to my 128th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Secondary Ready Course
Thank you to the team at Sparx for making their Secondary Ready course freely available until September. I have seen a number of schools recommend this to their incoming Year 6s - given the current gap in education, I'm sure many families will appreciate this support. My school is planning to mention it in our induction pack for Years 6s who will be joining us in September.

I like the certificate idea suggested by this school:

2. Colour the Pattern
Here's another nice idea from Miss Konstantine (@giftedHKO). In her 'Colour the Pattern' activities, students colour the boxes with the stated properties, which produces a pattern.
3. L Shaped Perimeters
I enjoyed this tweet from Segar Rogers (@SegarRogers) which takes a critical look at perimeter problems presented in secondary school textbooks.

4. A Level
Some great resources for A level teachers have been shared in recent weeks:

  • Joe Berwick (@BerwickMaths) has been working on diagnostic questions and whiteboard exercises for every single subsection in the A level Edexcel textbooks. He has already done all of Year 13. Check it out on BerwickMaths.com.
  • Jack Brown (@TLMaths) has launched a new look TLMaths.com which features videos on A Level Maths, Further Maths and Core Maths. His excellent videos cover AQA, Edexcel, OCR A, OCR B (MEI), WJEC, Edexcel International, Cambridge International and more. 
  • @BicenMaths made a “memory page” for everything he wants his Year 13s to know by ️heart. This one focuses on trigonometry and calculus, and there’s a blank version so they can self-test. 

5. CPD 
Craig Barton has launched a new range of online CPD courses. So far he has published 'Formative Assessment and Diagnostic Questions' which features over 80 videos and 40 links and resources. The cost of accessing the course is only £30 per person. He has also published 'Making the Most of Worked Examples'.

I have had a look at both courses and they are excellent - if you've ever been on a course run by Craig then you'll know how good these will be. Craig has also turned my topics in depth workshop on angles in parallel lines into an online course which is totally free. If you have time for CPD during lockdown, do check these courses out.

After two months of expecting the next mathsconf to be moved online, this week there was an announcement to confirm that this is indeed what will happen. On 20th June, #MathsConf23 will be hosted virtually and will be free to attend. This will attract delegates and speakers from all over the world. Lots of people who are normally unable to attend conferences on Saturdays will be joining, so it's going to be huge! It will be an unusual experience for us all. There's already a fantastic selection of talks on offer - book now so you get a place. Thank you La Salle!

Speaking of CPD, don't forget that there is now a free Seneca course covering a couple of chapters from my book A Compendium of Mathematical Methods. Lots of teachers have been completing this in recent weeks.

You'll also be pleased to hear that there will be a virtual Maths Inspiration show (aimed at Year 10s in particular) on the afternoon of July 9th. It will feature Matt Parker, Ben Sparks, Zoe Griffiths and Rob Eastaway, so it's guaranteed to be brilliant.


I'm still shocked by the death of Don Steward. I encourage you to read this tribute from his friend Graham at the SHaW Maths Hub. Many people have asked me how they can send flowers or make a donation. You can email any insightful memories about Don to shawmathshub@tpstrust.co.uk and they will be passed onto his family. There's also a link in this news article to leave messages. And if you wish to donate to Don's chosen charity, you can do so here. Thank you to everyone who has contributed to the hashtag #donsteward. It has been wonderful to see so many of his resources shared, and I know that our community will continue to share and celebrate his resources for years to come.


Finally, if you missed it then you must check out the video of Tom Lehrer's That's Mathematics, sung by mathematicians in lockdown. Ed Southall was behind this idea, and he managed to make it happen with the help of Chris Smith and Ben Sparks. It is a delightful 2.5 minutes that will make you smile.

Stay safe, maths teachers. x

7 May 2020

5 Maths Gems #127

Welcome to my 127th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Maths Challenge Pick 'n' Mixes
Thanks to @Ayliean who has made a couple of absolutely brilliant Maths Challenge Pick 'n' Mixes. There are two versions: one is to encourage pupils who are really struggling to do anything at home right now - you can download it here.
The other version is for pupils who just can't get enough maths. You can download it here for the clickable links.

2. Websites
Jim Hardy is a maths teacher from Nottingham who has created the website mrhardymaths.co.uk. Each year he still finds himself scrolling through papers in search of exam questions to work through with students when they get to the end of a chapter, so he created this website to save himself time. The website contains exam questions for GCSE, Certificate of Further Maths, A level Maths and A level Further Maths. I like the uncluttered interface of this website.
Another website that I hadn't seen before is nagwa.com. This was shared by @SarahGarry9. It has content for Years 1 to 13. For each year group there are videos by topic and multiple choice quizzes.
Whilst on the subject of A level - another new resource that teachers might find useful is these 1-stop-shop PDFs containing exam questions and mark schemes for A Level Maths and Further Maths. These were created by @BicenMaths. The PDFs are easy to navigate, and hyperlinked when downloaded. They work well on students' phones or tablets. 
3. Code Breakers
Miss Konstantine (@giftedHKO) shared a set of 'break the code' activities that are working well for her students at home. Check out her post where she has shared these tasks for a number of topics.

4. Bridging the Gap
Thanks to @nicole_cozens for sharing the AMSP's new package for Year 11s to prepare for A Level maths. A MOOC will be coming later, but this package provides some help for Year 11 teachers and students.
5. Further RISPS
Jonny Griffiths (@therispguy) has now shared his 'Further Risps' PDF ebook for free. It contains forty investigative tasks for Further Maths A Level students.
It was the sixth anniversary of my blog last Monday and that means I should have published my annual Gem Awards, like I do every year at the end of April. The problem is, it takes ages for me to write a post like that, and I just haven't had time to do it yet. I'm normally great at multi-tasking, but managing my current school workload while being at home with my children all day is proving a bit much for me some days. I've been trying to help my daughters complete their school work while simultaneously answering a constant flow of messages from students and colleagues, and to be honest I'm finding it tough! So I missed the Gem Awards, but I will do it over half-term. Watch this space.

Here are a few things you might have missed since my last gems post:
  • The Topics in Depth CPD on angles that I recorded with Craig Barton in February has been published by TES. This free online CPD is suitable for teachers of Key Stage 2 to 4.
  • The Mathematical Association's April eNews, which I collate, was published last week.
  • A Seneca course for my book A Compendium of Mathematical Methods has been launched. This is free online CPD. It is bizarre to see things I've written translated into a training course. It covers the book's introduction plus two topics. I think Seneca have done a really good job of this! If you enjoy it, please consider buying my book.

Finally, I'm sure you've already seen the news that Don Steward passed away. I am shocked and incredibly sad, and so angry at this horrific virus. I blogged about my memories of Don on Wednesday, and have been comforted by so many teachers sharing his wonderful tasks on Twitter using the hashtag #donsteward. The responses on Twitter to the news of his death have been incredible - he touched the lives of maths teachers all over the world.

I'll leave you with one of the many Don Steward tasks that I have enjoyed over the years. Find the area of this triangle without a calculator. I just did this question, just to make sure I can remember how to do maths (it's been a while!), and did a little happy dance when the answer fell out so elegantly.
Stay safe, maths teachers. x