5 Maths Gems #161

Welcome to my 161^st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Mathematicians Display

@nathanday314 has updated his excellent Famous Mathematicians From Around the World Display. This features 82 mathematicians from 53 countries. 

The original inspiration came from a display by @DrStoneMaths and @MrYoungMaths which I featured in Gems 132. 

For more classroom and corridor displays for maths departments, see my displays page. 

Do make sure you follow Nathan on Twitter if you don't already. He has been sharing loads of great resources over summer including tasks on simultaneous equations, bounds and indices. For example I love the task below, which is an adaptation of @karenshancock's indices task.

Speaking of @karenshancock's resources, I also love this sequences fill in the gaps task. I've added it to my resource library.

2. Vectors Task

It's always great to see new content on my favourite website MathsPad. They have now completed their curriculum booklets for all of Year 7, 8 and 9. These booklets are full of brilliant tasks - I use them all the time.

I also love their new free Vectors & Quadrilaterals Worksheets. The idea is to work out which type of quadrilateral will be formed if you follow a sequence of vectors. This provides practice working with vectors whilst prompting thinking about whether pairs of vectors are equal in length, parallel or perpendicular, and encouraging mental visualisation. There are two levels of difficulty.

I've added this to my resource library.

3. Certificate in Further Maths Resources

In my last post I mentioned that I've set up a new page linking to Certificate in Further Maths resources. This can be accessed from the main menu at the top of my blog. Since then, I've added three additional resources to this page:

• Content list for pupils from @mathshysteria. This handy student-friendly checklist may also be helpful for teachers' planning as it shows which topics are covered at GCSE and which are specific to Certificate in Further Maths.
• Certificate in Further Maths questions from A Level papers from @tm_maths. This will be a helpful source of challenging questions.
• Videos and exam questions by topic on an excellent new website from @1stclassmaths.

4. GCSE Revision 

In the Autumn term @MrsEVCartwright gives her Year 11 students a revision sheet per week on a topic covered so far in the course. Each sheet contains a recap of the main ideas and techniques, followed by some questions to complete for homework that week. You can download this resource from TES.

Back in Gems 155 I shared another GCSE revision resource - PowerPoint files containing GCSE maths questions by topic for OCR, Edexcel and AQA. I subsequently awarded it a Gem Award for 'Most Useful Resource' because I use it all the time in my GCSE lesson planning. @gcse_math has now shared this resource on its own website - gcsemathsquestions.co.uk. If you missed this earlier in the year, do check it out.

5. Place Value

Thank you to @Scott_Math83 for sharing some new resources. I like these place value tasks using fractions and decimals.

 

And this rounding problem is great.

Resource Libraries

If you're new to teaching then you might not know about my resource libraries which contain listings of resources for Key Stages 3 to 5, organised by topic. I use these libraries every day when planning lessons as they provide a quick way to browse quality free resources. 

I try to keep my Key Stage 3 and 4 libraries updated on an ongoing basis, and when I start teaching A level again next year I'll do some work on my A level libraries too. Links sometimes get broken when people move or delete their resources - if you find a broken link then do let me know! 

I also add new resources fairly regularly. For example I've recently added more links to resources from Dr Austin Maths including tasks for indices, standard form, factorising quadratics, inequalities and graphs.

The quickest way to access my resource libraries when you're planning lessons is using the menu across the top of my blog.

Update

I've mainly been doing DIY over summer and am now a bit fed up with painting. My house is in disarray (I currently don't have a bedroom!) so I'm looking forward to returning to school on Thursday. I had a really lovely break though, which included a very sunny family holiday in a cottage in Cornwall, and a great night out with maths teachers at Jamie Frost's house (thanks @nkl_17 for the photo!).

I'm looking forward to meeting my new classes next Monday. I'll be teaching Year 7, 8, 10 and 11, plus I have a Certificate in Further Maths class who will have lessons after school. My school first opened four years ago, so Summer 2023 will be our first ever GCSE results. It's a big year for us! This year we'll also be setting up our new A level courses ready for next September. In a couple of months we'll be advertising for a Key Stage 5 Coordinator to join our maths department - watch this space if you're interested in applying!

Good luck to everyone starting in new schools this week, particularly ECTs, and good luck to those of you embarking on teacher training. September is such an exciting month.

5 Maths Gems #143

Welcome to my 143^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

1. Place Value Tool

When making the CPD course Marvellous Maths 2 I struggled to find a virtual manipulatives tool that really effectively conveyed the relative sizes of tenths, hundredths, thousandths and so on. Luckily James and Nicola from MathsPad watched the course and this prompted them to go off and make one!

What they have produced is incredible. Freely available to all, this tool gives you the opportunity to fully explore place value with students to really deepen their understanding. 

Do have a play with it. It's awesome.

James and Nicola have also started publishing their Curriculum Booklets which are packed full of brilliant activities. Read their latest update for more information about their excellent booklets. 

2.  Powers

I really like the ideas explained in this Twitter thread from Sam Blatherwick (@blatherwick_sam). When teaching fractional powers, he gives his students a power chart like this:

Students can use these charts to answer questions like this:

Read Sam's thread for the full description of how he uses this chart to develop understanding. 

I really like this. It reminded me of my favourite indices resources - Mental Mathemagician from yummymath.com, and 3 Power Line and 5 Power Line from Don Steward.

3. New App

I don't often feature resources that aren't free but this one caught my eye. The Arc Maths app (@ArcMathsApp) has been developed by a maths teacher and looks rather good. 

It's aimed at students aged 11 - 16 and gives users a highly personalised experience. Schools with access to iPads can subscribe and make use of this app in the maths classroom, in tutor time or in intervention. 

I don't know many state schools with class sets of iPads, but it's worth knowing that parents can subscribe to this app for their child at a cost of £3.49 a month. This may be something that schools can advise parents to invest in if they ask for ideas of how to help boost their child's maths grade.

4. CPD

The collection of free CPD videos from the Loughborough University Mathematics Education Network is brilliant. Maths teachers looking for CPD for either themselves or their department would benefit from exploring the videos on offer. The latest addition is Improving Language Use in Maths by Dani Quinn.

5. Simple Linear Graphs

As I mentioned in Gems 141, Dan Draper (@MrDraperMaths) has published loads of great blog posts lately. His post 'x=a, y=b: When?' looks at curriculum and concept development through a series of well-designed tasks.

Update
I enjoyed the first day of the MA conference. Delegates who attended my session can download my slides here. And you can listen to the post-conference podcast with me and Craig Barton here.

Did you see my recent blog post? I wrote about the The Power of Modelling and Exemplars.

If you enjoy my blog posts then you can subscribe here. You will only be emailed when I publish a new post, which is normally once every three or four weeks.

I'm very glad to be on my Easter break after a crazy Spring term. As well as attending the three-day MA Conference, my holidays will mainly consist of hanging out with my lovely daughters, and completing endless Only Connect style puzzle grids from the website puzzgrid.com (which I am a bit addicted to). I'm trying to keep work to a minimum this Easter because I desperately need a rest, but I do have a few things coming up over the next two weeks:

• I'll be reading Michael Pershan's book 'Teaching Maths with Examples' which looks excellent.
• I'll be recording a podcast with Ben Orlin, chatting about bygone maths symbols
• I'll be attending #GLTBookClub on 13th April. We'll be talking about Chapter 18 (angles in polygons) from my book A Compendium of Mathematical Methods.

I'll leave you with the news that Tarquin are now taking orders for empty protractors. I spoke about this idea in my Angles in Depth CPD. A lot of the mistakes made in measuring angles come from students relying on reading scales on protractors (which they often misread) rather than using reasoning. Protractors without numbers help students think logically about the measure of turn. 

This is exciting! @TarquinGroup now have the Empty Protractor and teacher resources available to order https://t.co/C1jJ9Lit3H alongside some of my practice tasks. @LboroMEC @mathsjem @boss_maths @MathsPadJames @mrbartonmaths @edsouthall #mathscpdchat pic.twitter.com/XVoDwPtvuO

— Tom Francome (@TFrancome) March 30, 2021

 

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

 

5 Maths Gems #112

Welcome to my 112^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Classic Errors
I like this activity suggested by James Tanton (@jamestanton). James asks 'Would taking classic and tempting errors "head-on" be a worthwhile classroom activity and discussion?'.  It's worth reading the responses in the thread. In it Cathy Yenca‏ (@mathycathy) recommends the classic resource 'Algebra Atrocities' which is worth a look.
2. Geogebra Percentages
Thanks to Mark Horley (@mhorley) for sharing some helpful Geogebra applets created by ⁦‪@orchiming‬⁩ .

These interactive tools help with explanations of percentages. For example the profit and loss applet shows really clearly how the calculation works.

3. Area Mazes
I know I've featured Area Mazes in my gems posts an number of times before, but I think they're really fun so there's no harm in mentioning them again. Have a go at this one -  it was tweeted by @Errs5 and is taken from the Area Quiz app which looks excellent.

4. Calculator Crunch
In my post about Year 11s lacking basic calculator skills I mentioned that MEI are running Calculator Crunch to encourage schools to get younger pupils using calculators. Aimed at Year 6 and 7, they are sharing a daily calculator challenge between 10th and 20th June. You can download all the daily challenges from the MEI website and use them at any time. They have also provided a Year 6 lesson plan and a Year 7 lesson plan that you can download here.

Check out the hashtag #CalculatorCrunch to see examples of pupils' work.

5. Place Value
Another great idea for using calculators is in a lesson on place value. Tom Francome shared this 'Place Invaders' task in a conference workshop - it's taken from the ATM book Practising Mathematics which he wrote with Dave Hewitt.

Grab a calculator and have a go and you'll see why this is a great task to use when teaching place value. I think that place value is one of the hardest things to teach in Year 7 so it's helpful to see a good quality activity for this. Tom suggested it would also work well with standard form.

Update
Exam season is nearly over, and it's been an unusually turbulent one this year. We've had questions that appeared to be copied from textbooks, a mistake in an A level, controversial contexts, a leaked exam and some surprisingly challenging A level papers. Never a quiet day in maths education!

I recently made a final set of GCSE revision resources which you can find on my GCSE revision resources page. You might find these resources helpful if you have Year 10s preparing for end of year exams.

I presented at ResearchED Rugby yesterday. My session focused on multiplication - first we looked at a range of multiplication methods and then I presented a critique of each of the reasons the Government gave for prescribing 'formal' methods at Key Stage 2. For the remainder of the day I attended excellent sessions in the maths strand. Rugby School has an incredible history so was a cool venue for a conference.

Next weekend I'll be presenting on the Evolution of Maths Vocabulary at La Salle's conference in Yorkshire. Read my blog post "Whatever happened to vulgar fractions?" to get an idea of the sort of thing I'll be talking about, and if you find it interesting then do come along to my workshop. I'll also be manning the MA bookstand for most of the day so do come and say hello if you get the chance.

Bookings are going well for the training course I'm running with Craig Barton in October. This course is open to all maths teachers and we have two dates available - a northern leg and a southern leg. Ask your school or college to book your place now if you want to come along.

At the end of May Ed Southall and I relaunched The Mathematical Association's eNews. This monthly newsletter provides an update of what's going on with the MA and also in the wider world of maths education. We now feature exclusive monthly puzzles for your students (written by Ed), and there are more new features coming soon. You can subscribe here to receive eNews from the end of June.

I've been kindly sent a couple of books by their authors recently. Kyle D Evans sent me a copy of 'Here Come the Numbers' which my daughters (aged five and seven) love as a bedtime story. It's both mathematical and lovely.

Mark Ritchings sent me a copy of 'GCSE Maths Challenge' which contains 40 GCSE style questions that are aimed at pupils who are working at a Grade 8 or 9. This short book might be helpful for a GCSE tutor, or possibly a top set teacher who needs a few extra ideas for extension questions to write on the board.

Maths teacher Richard Atkin (@RichardAtkin1) - whose uncle was a Trustee of the MA - very kindly delivered an enormous number of old maths books to my house. This will keep me busy for a while! I've already found lots of treasures that have taught me new things. I estimate that I now own at least 300 different maths textbooks dating from 1800 to 2000. I love this!

A group of us are going to Matt Parker's Humble Pi comedy show on 16th July in London (it's a preview of his Edinburgh Fringe show). If you want to join us, book a ticket here and let me know you're coming. There are similar comedy nights in London listed here, including one that features the amazing FoxDog Studios. FoxDog Studios will also be at Edinburgh Fringe and are doing gigs in various locations before then - dates are listed here. They are amazing.

I'll leave you with this great activity shared by Sarah Carter (@mathequalslove). You can download the full resource from her blog. This puzzle might work well in a first Year 7 lesson in September, along with the other tasks I listed in my post Year 7 Maths Activities.