9 January 2021

Tools for Online Lessons

I've been reluctant to write a blog post about teaching online lessons because I am far from being an expert on this matter. In the first lockdown I mainly set work on Hegarty Maths. I don't believe in reinventing the wheel. With good quality videos and tasks at my disposal, I was very happy to use them. This time round my school has changed its approach in order to improve the student experience and (hopefully) maximise engagement. So now I do some live lessons (we run these as Microsoft Teams events, which are recorded for students who need to watch at different times). We will shortly be introducing asynchronous practice lessons in maths too, for which I will mainly be using Hegarty Maths.

So compared to many other teachers I'm relatively new to live lessons. Thankfully the expertise of maths teachers on Twitter is already immense. Tweets about live lessons are constant and amazing, with teachers all over the world giving each other practical advice and inspiration. I thought it might be helpful to share some of that advice here for my readers who aren't on Twitter. I'm not featuring the well-known websites here - we are very lucky that there are absolutely loads for maths (Hegarty Maths, Dr Frost, Corbett Maths, MyMaths, Mathigon, MathsWatch, MathsPad, White Rose, Times Table Rockstars, Desmos and so on). Here I'm featuring tools and websites that might be less well-known. This should give you a starting point to investigate further if you are looking for a particular solution for your online maths lessons. 

1. If you use Google Classroom...
I don't work in a Google school but if I did then I would make use of @Philmaths314's free Self Marking Google Sheets. As the name suggests, these are sheets that mark themselves. ⁦‪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. I featured this resource in Gems 131.

The sheets can be downloaded as spreadsheets too, so can also be used outside of Google Classroom.

The other thing that Google users might want to explore is flippity.net.

2. If you want online exercises without logins...
In the first lockdown there were times when I wanted to set my students an independent practice task at the end of a topic, but they had already done all the tasks for that topic on Hegarty Maths. One option was to set them an exercise from a website like Corbett Maths, asking them work on paper and mark their own work. Another option was the use the free interactive tasks on the CIMT website. These tasks look a bit dated but still work beautifully. I love it that examples are provided before the exercises, so support is built-in for students. No login is required so access is quick and easy. The exercises are self-marking so students get instant feedback. The other thing I like is that there are no adverts. I can't stand it when there's advertising on student-facing websites. Here are the links:

There's also interactive material for Years 3 to 5 here.

3. If you want to use mini-whiteboards...
Teachers who are heavy users of mini-whiteboards in their normal lessons might be interested in the various online mini-whiteboard tools that are now available, allowing you to see your students' work in real-time. There's been a lot of tweets about whiteboard.fi this week. Read the threads for more information:


The online whiteboard tool on drfrostmaths.com is also very popular.

Apparently Teams at my school has a built-in function call NearPod which has whiteboard capabilities but I haven't explored it yet. 

4. If you want to quiz students through Teams...
Each of my live lessons ends with a short online quiz to check what students have learnt. Because I work in a Teams school I use Microsoft Forms to conduct these quizzes, stealing most of my questions from diagnosticquestions.com. I schedule the quizzes in advance to pop up as an assignment near the end of the lesson. These quizzes are massively informative, guiding my planning of the next lesson and allowing me to give whole-class feedback and address misconceptions. It's like a self-marking exit ticket, which is awesome. 

In case you happen to be teaching rounding, here are four of my rounding quizzes from this week that you are welcome to borrow. I will add lots more quizzes to this document over the coming weeks. If we all start sharing our Forms quizzes, we will eventually have a big bank of them that we can all borrow and adapt, which will save a lot of time.

From Twitter I can see that many other teachers are using Forms quizzes very effectively in their Teams lessons. Here are some tweets that might be of interest.

5. If you are using PowerPoint...
My online lessons are the usual mix of explanation, modelling examples, questioning and practice tasks. They are pretty similar to my normal lessons. Apart from my quizzes, everything else I do in my lessons is in PowerPoint - and apart from a pen mouse so I can write on my slides, I don't use any special technology or online tools. The only thing I want to mention is the timers that I use in my PowerPoints. To minimise faff during my live lessons, I make use of the lovely transparent timer gifs shared by @DrStoneMaths. They're just so easy to use: I put a task up on the PowerPoint, the timer starts automatically, and the students start working. Easy! I featured these timers in Gems 134.

Just bear in mind, when you see teachers on Twitter using loads of fancy interactive tools, a simple PowerPoint containing examples and a series of tasks works really well when presented by an enthusiastic and confident teacher. Sometimes we see other people doing different stuff and assume we're not doing enough. Let me reassure you - if your students are getting clear explanations and regular opportunities to practise then you're doing a great job.

I hope that this post is helpful. I know there are dozens more tools and ideas that I haven't featured - I'm trying to avoid overwhelming people.

Feel free to add your own advice in the comments. 

My husband works in a hospital so when I'm not in school looking after keyworker children, I'm home alone trying to homeschool my six year old and nine year old whilst simultaneously teaching lessons, responding to hundreds of messages and attending dozens of online meetings. Stressful is an understatement! Many teachers are struggling at the moment, so it's more important than ever that we support our colleagues during this difficult time.

Well done on surviving a killer first week. It will get easier!

1 January 2021

5 Maths Gems #140

Happy New Year! Welcome to my 140th 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).

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.

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.

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:

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

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!

30 December 2020

Victorian Arithmetic

Last term I received an email from Peter Elliott, the great grandson and biographer of Sir Thomas Muir (1844 to 1935). Thomas Muir was a renowned Victorian mathematician, principally associated with the Theory of Determinants, on which he wrote copious volumes. He was also Superintendent General of Education of the Cape Colony in the early 1900s. Muir wrote A Text-Book of Arithmetic for Use in Higher Class Schools in 1878, when he was the mathematical master in The High School of Glasgow. An online copy of the textbook can be accessed here on Google Books. 

Readers of my blog will know that exploring old maths textbooks is a hobby of mine. I have a page full of links to old maths textbooks here, and I own a large collection of physical books dating from the mid-1800s to the late 1900s. I have blogged about old textbooks numerous times, including in the following posts:

Extracts from old textbooks also feature heavily in my book, A Compendium of Mathematical Methods.

I promised Peter that I would have a look at Muir's textbook and share my findings with my readers. The book is rich in content and gives us a wonderful insight into how maths was taught 140 years ago. I strongly recommend that my readers take a look through the textbook themselves. In this post I have picked a few highlights, to give you a taste of the kind of thing you can expect to find in a textbook from this era.

As is typical of textbooks from the 1800s, the explanations are set out in prose. Modern mathematics textbooks tend to explain concepts and procedures by way of annotated examples, as opposed to heavy paragraphs, so the wordy nature of old textbooks comes as a surprise to us. The exercises are also rather different in style to what we are familiar with. Interspersed throughout each chapter, the challenge level in these exercises is high. To give an example, in the first chapter ('the nomenclature and notation of integral numbers'), we are presented with the following tasks:
Everything is taken to a far greater extreme than it is now. Check out the length of the numbers that students are asked to say out loud. They seem almost comical to us now.

Later in the book, we have a similarly amusing set of addition questions. In the days before calculators existed there were certainly some jobs - in the counting house for example - which required such lengthy manual additions. Just imagine the monotony of performing such arithmetic. 

One thing that makes Muir's textbook slightly different to comparable textbooks from the same era is his inclusion of 'real-life' example, as we can see here:
Muir also presents us with sets of questions that, apart from the seemingly cumbersome numbers chosen, would not be out of place on variationtheory.com.

The vocabulary in this textbook is similar to other textbooks from this era. I have previously presented at conferences on the evolution of maths vocabulary. One example is the interchangeable use of the words cipher, nought and zero. Another example is the language associated with powers:
These days it is rare to hear this language (i.e '4 power 3' for the third power of four. We are more likey to say 'four to the power of three'.). Also, note that this book pre-dates the time in which textbooks started to incorrectly and confusingly claim that the index can also be referred to as a power. 

Other vocabulary that has fallen out of common usage in schools include 'measure':

There's a bit more on the word measure here, and the alternative 'sub-multiple' is offered:

For prime factor decomposition, modern textbooks almost always feature prime factor trees. Old textbooks tend to feature repeated division. Interestingly, this book has a slightly different approach:
The author acknowledges that for large numbers, the process of finding the prime factors can be laborious. The example given is 9211, which resolves into 61 x 151.

I admit that I hadn't realised there was a difference between a denomination and a denominator. As far as I know, the term denomination has fallen out of use in the context of fractions.

I like it that mixed numbers are properly defined in this chapter. The attention to detail in definitions and notation is something that has been lost over the years. These days, too much is assumed.

Interestingly, the author refers to improper fractions as 'sham' fractions with an 'integer in disguise', and tells us that we should express them in their proper form (i.e. as mixed numbers).

The fractions chosen for the fraction addition exercise fascinate me. I like question five - the powers in the denominators seem to be a clever task design strategy, drawing attention to sensible denominator choice.

In all my journeys with old textbooks, something I haven't seen before is the idea of approximate simplifications of fractions.

This is interesting. At first glance I thought this was totally pointless. But I get the idea - if we want an idea of the magnitude of a fraction, we don't need to be exact.
Here's an exercise on this:

The author goes on to say, "There is another mode of finding approximate simpler forms of fractions which is in itself more important and more interesting than the above.' He then delves into continued fractions, which represents a massive step up in complexity compared to the rest of the book so far.

Victorian Contexts
There is a large section of the book dedicated to mixed 'practical examples'. It is often these contextual examples that provide the most amusement and intrigue: they give us a glimpse of what Victorian life was like. Here are a few examples, featuring disease, quills, boys doing arithmetic, and wine.

I hope you enjoyed this little tour of a Victorian maths textbook. 

If you wish to learn more about the life of Sir Thomas Muir, do check out Peter Elliott's recently published book Thomas Muir: ‘Lad O’ Pairts’: The Life and Work of Sir Thomas Muir (1844–1934), Mathematician and Cape Colonial Educationist

18 December 2020

5 Maths Gems #139

Welcome to my 139th gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

Well here we are, at the end of the most gruelling term of our lives. I'm sure we are all incredibly relieved to have made it to end of term in one piece. We should all feel proud that we've continued to fill our students' lives with the joy of maths, and we will continue to do so, no matter what gets thrown at us. Thankfully we now we have a short respite - from the physical exhaustion of pandemic teaching, if not from the anxiety. Throughout the Christmas break many of us will be steeling ourselves for January, when the level of challenge in schools and colleges will be ramped up even further. I wish I could offer words of encouragement and solace, but to be honest I am totally lost for words. I just hope that you all manage to have a safe and peaceful break over the festive period.

Perhaps on the first day of the holidays we all need to switch off from maths teaching, but I know some of you take comfort in browsing through teaching ideas and resources. It can be a cheerful distraction from the sadness that surrounds us. So, on with the gems.

1. Tasks
Thank you to @SegarRogers for sharing this brilliant speed, distance, time task. I love this. I've added it to my resource library so I remember to use it next time I teach speed. 

Thanks also to @ashtonC94 for continuing to share his expertly written tasks, including these on standard form and this interesting take on recurring decimals.

Here's another excellent set of tasks from @giftedHKO. The focus here is pie charts - a great topic which links nicely to proportional reasoning. 

2. Teaching Tools 
Thank you to @123lots for sharing @mathforge's handy Make Your Own Axes tool.

Also, I'm not sure whether I've featured this site before - thank you to @jemmaths for the reminder about @tesseralis’s website tessera.li. This website features a beautiful polyhedra viewer which teachers might find useful.

3. Website Updates
@MathsDunbar has completed Version 3 of his Trinity Maths Programme for the new National Curriculum. Matt has made ten of his best interactive topic files available as free downloads, which are macro-enabled Excel spreadsheets.

@MrMorleyMaths has completed and published Phase 2 of his website mrmorleymaths.co.uk. Every topic now has a starter activity of questions, with answers, testing prerequisite knowledge.

4. GCSE Revision Resource
Thank you to @Billyads_47 for sharing a GCSE revision resource.

Don't forget that my GCSE Revision Resources page is absolutely packed with excellent revision resources for your Year 11s.

5. Multiplication Tool
Thank you to @mathforlove for sharing these visual flash cards for multiplication that he has produced in conjunction with @MathigonOrg. This is a brilliant free online tool for children learning their times tables.
I know it's too late for me to share Christmas resources, but in case you want to use them next year...

@Ayliean shared some lovely maths-themed Christmas cards.

This snowflake dot-to-dot activity shared by @giftedKHO is really nice. 

And @DrBennison shared his annual A Level Calculated Colouring, which is always fantastic.

I do have a page of Seasonal Resources. I didn't even get time to look at it myself this year, but it is there if you are ever after a themed maths activity. 

I recently published another 'Dose of Don' post from Anne Watson - do check it out if you haven't already.

I have also created another set of warm-up booklets for my classes. These are specifically designed for the curriculum my school - each week we cover three different retrieval topics - but feel free to borrow and adapt if you like. In the most recent set, most questions were taken from CIMT resources. 

There are a number of online maths conferences coming up in the Spring term. See my conference listings for details. I will be speaking at two of them - #MathsConfMini on Friday 22nd January and the WRM Secondary Maths Brunch on Saturday 30th January. 

Don't forget to check out Marvellous Maths 2 - an entire online training course for maths teachers.

Congratulations to Craig Barton on the fifth anniversary of his incredibly successful education podcast. You can read his reflections on five years of podcasting here.

Finally, I should mention that as my own school continues to grow (we will have Year 10 for the first time next year) we will be recruiting a new maths teacher in the Spring term, to start in September 2021. If you are interested in coming to work with me and want to get a flavour of what the school is like, check out our Open Day video and our Christmas video, and get in touch if you want to have a chat about it.

I'll leave you with this video, shared by @berniewestacott, which features Douglas Clements speaking at the White House on early childhood maths education. It's under five minutes, and well worth a watch.

Have a very merry Christmas, maths teachers. Time to get some rest. x

13 December 2020

Straight Lines

This is the second article written by Anne Watson in the 'Dose of Don' series. She posted it on her blog here and I have replicated it word for word. For the background on this series, please see my previous post Lines and Angles on Square Grids. My thanks go to Anne for giving me permission to share her writing here.

Dose of Don 2: Straight Lines
This is the second of an irregular series of writings in which I (and, I hope, others) delve deeply into the collection of tasks on Don Steward’s blog and pull out threads about key ideas in mathematics that run through several of his tasks. Where possible I give you a direct link to the tasks; where I have extracted part of a task I direct you to the ‘parent’ from which it came.

Don was very generous with his tasks and I hope that you will return this generosity in the way he requested before he died, namely to donate to justgiving.com/fundraising/jessesteward.

In Dose of Don 1 I focused on a particular feature of Don’s work on grids. I think of this as ‘that little triangle’ – a right angled triangle that, nestled up to a straight line on a grid, can be used to define angle, gradient, tangent, direction, distance between two points, rate of change, ratio, instantaneous change and so on. I am sure I will come back to this triangle again. For now, the multiple roles played by ‘that little triangle’ made me zoom in on expressions of the form ‘mx + c’ or ‘kn + c’ where the common use of x is for continuous variables and n for discrete variables. One thing I realised is that an expression like kn + c can be seen as a member of a family of multiples of k with remainders. For example, any whole number can be written as 4n, 4n + 1, 4n + 2 or 4n + 3. Any whole number is either 0(mod 4), 1(mod 4), 2(mod 4) or 3(mod 4). The parallel lines y = 4n + c are all the same line translated vertically according to remainder c when dividing by 4. The ‘undoing’ of 4n + c can be understood as ‘subtract the remainder to get back to the multiple, then divide by 4 to get back to n’, which is the same as saying  that the equations: y = mx + c and x = (y - c)/m are equivalent, which of course you know but the context or resurrecting a division from its whole number and remainder parts seems to be a good context for thinking about transforming equations (finding equivalent ways to express the same relationships) rather merely going through some manipulations to solve something.

Don poses a raft of questions about properties of any four consecutive numbers, many (but not all) of which can be proved by using expressions 4n + c. For example, if their sum is 130, what would the numbers be? ('4 consecutive numbers mixed questions'). The algebra associated with this question is of the same kind as finding expressions for perimeters.  On the same page he offers an enigmatic slide that combines mod 3 and mod 4 when the ‘n’ in a linear expression is itself a linear expression. I have a bit of a ‘thing’ about substitution when it is given as a pointless exercise which focuses on calculation rather than structure, so I enjoyed this slide because it needs the distributive law and would look good represented by cuisenaire rods or even two connected cogs (If 3n + 2 turns of one cog make a bigger cog turn once, then ….?).

So far, the use and meaning of algebra comes through the questions posed. How does he approach the more procedural necessities of working with linear expressions? The following two slides show a commitment to structure and meaning. My personal approach to algebraic expressions is to avoid doing anything to them unless I know it is necessary and can anticipate its use. So with these slides I did not start by ‘what should I do?’ but ‘what are these telling me?’. 

These are from 'algebra snakes and branches' in which much of the emphasis is on building and transforming expressions so that given expressions can be read with meaning.

I have offered these to various teachers and also young learners and there seem to be two reactions: one is to multiply out all the brackets, simplify and compare whole expressions; the other is to think about their constants and eliminate those that cannot have the right constant, then check the number of ‘n’s’ and eliminate any that cannot have the right number, then check by substitution e.g. 1 for n or d (do you need two values?). This approach uses the meaning of the distributive law and substitution can be used to find out what the effect on ‘-3’ is of subtracting 2 times it on one of the examples on the right hand side. However, asking ‘what are these telling me?’ reveals some care in devising these examples. I am not going to point out everything I observe but, for example, look at how (n + 2) appears in various guises in the left-hand example. Something similar lurks in the right-hand example. ‘Multiplying out’ loses those observations that would significantly reduce the work by recognising structures.

This ‘what is it telling me?’ approach to algebra has echoes throughout his collection of tasks.  Here are a couple of slides that embed the question: ‘if I know this – what else do I know?’

These are from a slides entitled ‘so, linear’. He says on the website that ‘legitimately going from one statement to another (is kind of what maths is about)’ [his brackets]. This is so deep but so understated.

The shift from thinking of linear form as the generalisation of ‘mx + c’ to ‘ax + by’ is one I need to explore more. I recognise that a graph that can be written as ax + by = c is a variation on x + y = 1, with the associated ease of finding intercepts on both axes. It looks as if Don had that in mind with his suggestions of substituting zeroes in the righthand slide. It also looks as if he had the requirement for algebraic solutions to simultaneous equations in mind with some of these transformations.

Here is another example of the need to recognise the algebraic format of linear graphs with a typically playful task: 'muddled rules and graphs'. Why has he chosen to use similar numbers in most of these? How might learners’ approach to this task vary if the axes were not similarly scaled? How many of these can be ‘seen’ as variations on x + y = 1?

Finally I find myself returning to a task I posted in Dose of Don 1 called ‘integer intersection points’. I return to thinking again about straight line graphs as representations of similar triangles, every pair of points on the line being the vertices of a right-angled triangle whose vertical and horizontal lengths are in a fixed ratio. Because my approach to these does not seem to match his, I am left with the intrigue of working out his train of thought and talking to myself about its equivalence to mine. 


21 November 2020

5 Maths Gems #138

Welcome to my 138th 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 (@ChrisMcGrane84book 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.

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:

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.