Mathematical Miscellany #48

From the BBC see this article on Learning at Home, including their latest schedules for Primary and Secondary Lockdown Learning.

On television programmes for primary pupils are on CBBC between 09:00 and 12:00 each weekday and for secondary school pupils on BBC Two, between 13:00 and 15:00.

Additionally programmes are available to catch-up, on-demand on iPlayer.

This coming week, commencing 18th January features Mathematics strongly, with three of the 13:00 slots including Maths and every afternoon at 14:00 we have Dr Hannah Fry.

BBC Lockdown Learning

This article including the schedule links has been added to this Maths at Home post.

This post can also be found on the Featured Posts Menu on the right hand side of this blog.

Chris McGrane – Starting Points Maths

Chris McGrane’s Starting Points Maths is highly recommended, note this announcement regarding these wonderful curriculum booklets. Several are already available, including the first Algebra booklet which looks excellent.

Looking at the Algebra booklet Order of Operations exercises it struck me that Graspable Math would work well for checking such exercises.

I have mentioned Tim Brzezinski’s brilliant GeoGebra book of Open Middle themed problems before, this collection continues to grow. Many problems in the GeoGebra book are exact digital analogues of those found on Open Middle’s site, with other problems characteristic of the Open Middle theme. This collection is included in the GeoGebra series of pages under Investigations and Problems.

I always keep an eye on Tim’s collection of GeoGebra resources and particularly like his recent Angle Sketching by Estimation and also this Open Middle Definite Integral Problem.

Tim Brzezinski – Angle Sketching by Estimation
Tim Brzezinski – Definite Integral Problem

I then found his recent extension, Open Middle: Definite Integral Problem (2) which should certainly keep everybody busy!

There is much to think about here, to investigate this what should we keep the same, what should we vary? I started playing around with Desmos to investigate further.

Open Middle Definite Integration Problem

A recent happy discovery, thanks to Jane Hart’s Top Tools for Learning 2020 is featured on the Ed100 list, the digital tools voted for by educators and students in colleges and universities, ilovepdf. ilovepdf is a free PDF convertor and editor, many tools are all in one place. I have not tried many of the tools yet but certainly have successfully and easily used the Merge and Compress functions several times and have been very impressed.

I note from the analysis that the tools predominately reflect the situation in higher and adult education, only a small proportion of votes came from schools. The lists certainly seem to reflect the unprecedented times we are currently living in.

David Millward – PowerPoints

Seeing PowerPoint right up there on the list, I have noted from my blog statistics that still popular downloads, years after I uploaded them are David Millward’s PowerPoint collection. In fact I can see from the comments that it was 2012 when I uploaded these!

Excel Resources

Mike Hadden – Excel Files

On the new Updates page, you will find featured posts as well as any which have been updated. A featured post currently is Excel Resources – Mike Hadden. There are some excellent demonstrations here for GCSE and A Level Maths and Further Maths.

If we look at the A/AS Statistics files we see BinHyp.xls, the notes clearly describe this resource.

Mike Hadden – A/AS Statistics Files

We can illustrate this with a question from Edexcel’s sample Statistics paper (Paper 2 question 5):

Edexcel Sample AS Statistics Paper
Mike Hadden – A/AS Statistics Files

The resources include several illustrations for the Further Mathematicians also, including resources on Complex Numbers and Matrices.

Mike Hadden – A/AS Pure Files

Also on the Updates page I have featured Maths at Home which is being regularly updated and checked. I have included Jack Brown’s extensive library of videos which is available on his website,; these are excellent for independent study. Also added to this post is Oxford University’s Oxford Online Maths Club; the session from Thursday’s livestream is available on their YouTube channel.

Also on Updates, you can see a new page, Investigations and Problems for the GeoGebra series and John Tranter’s lovely  Algebragons and Fractionagons on Transum Mathematics; both have been added to this post on Arithmagons which has a large collection of resources on Arithmagons, including a lesson plan from Colin Foster.

Transum Mathematics – Algebragons

Maths At Home

Having written several Maths At Home posts since the first school closures, I thought it would be useful to provide a compilation post for these resources. All resource links have been checked and new resources added.

Daily Lessons provides a closer look at the daily lessons from White Rose Maths. These lessons are available for Early Years through to Year 10.

Perimeter - White Rose
Algebra KO extract Nicola Whiston

Also – a wonderful complement to these resources we have Nicola Whiston’s amazing collections of Key Stage 3 Knowledge Organisers (see also Knowledge Organisers – Mathematics) which follow the White Rose Schemes of Learning. She is sharing the collection here, via Dropbox. These are really attractive and I think will appeal to students. For consolidation and review these are perfect.

White Rose Assessments

For more resources from White Rose Maths, see for example Secondary Schemes of Learning and Assessments for End of Block or End of Term.

Oak National Academy Online Classroom

From the Oak National Academy Online Classroom, an extensive collection of lessons is available. The lessons cover Primary and Secondary KS3 and KS4 for many subjects. For Maths, see KS3, KS4 Express Maths and KS4 Maths, note that various levels are available. These video lessons include activities for students.

Oak National Academy Introductory Quiz

Looking at an Express Maths GCSE lesson, the introductory activity is a quiz. Feedback is provided where students submit incorrect responses.

From the BBC see this article on Learning at Home, including their latest schedules for Primary and Secondary Lockdown Learning.

On television programmes for primary pupils are on CBBC between 09:00 and 12:00 each weekday and for secondary school pupils on BBC Two, between 13:00 and 15:00.

Additionally programmes are available to catch-up, on-demand on iPlayer.

BBC Home Learning

From BBC Bitesize, home learning resources are available for Years 1 to 9. If we look at Year 7 Maths for example we see collections which include lessons with videos, activities and quizzes. Note the two week home learning packs, these include several of the excellent daily lessons published in 2020.

More Maths at Home – AMSP describes the excellent resources from AMSP which focus on target groups of students to support their progression from Year 10 to Year 13 (ages 14-18) and beyond.


Note the menus for Students and Teachers at the top of the page which help you find appropriate resources. Choose the Student menu, then the appropriate option for the level of study.

Dr Frost Maths is of course used by millions round the world. Amongst the extensive library of resources are videos for students age 8-18 explaining topics from scratch. There are longer Exam-topic videos, average length 10 minutes and shorter Key Skill videos which are about 2-4 minutes in length.

Dr Frost Maths – Videos

Free lessons from Colin Hegarty recorded on YouTube are available to help GCSE students prepare for A Level Maths.Hegarty A Level

An extensive library of videos from Jack Brown is available on his website, Jack has created thousands of videos covering the complete A Level specification; note also the impressive  Further Maths teaching videos and exam paper walkthroughs and a collection on bridging the gap between GCSE and A Level.

Pearson Edexcel GCSE Maths Lessons

From Pearson Edexcel comes a video collection of free GCSE Maths lessons. All around 50 minutes in length, there are 24 videos available.

From NCETM, we have lesson-planning and professional development resources for primary and secondary teachers. The resources include a set of Primary Video Lessons.

Mathematical Miscellany #41 includes You can read about the features here and follow News and Updates. There are now Basic and Premium plans but the free plan does allow a temporary whiteboard (2 hours) with a link provided so students can join; it is also possible to insert an image as shown below. See Pricing.

Whiteboard fi Diagnostic Questions - White Rose Algebra

Alison Clarke-Wilson shared this blog on Research-based Effective Online Teaching Strategies

Back to school at home… includes Home School Support from Maths Genie for students covering a range of abilities in three streams from Key Stage 3 (and high ability Key Stage 2) to high ability Key Stage 4.

Maths Genie Quiz

Maths Genie
The resources are available on the Maths Genie Home Learning – You Tube Channel. Videos are available on YouTube and at the end of each week a recap lesson, and a mini online assessment are available from Maths Genie’s Maths Grader. (@mathsgrader on Twitter)

This post also includes a reminder of Transum’s high quality, attractive resources. Given that there are an extensive number of self-marking exercises available, this can be a great source of activities for students to work on at home.


The Transum site is easy to navigate, there is a clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning.

Maths At Home – Nrich details some wonderful resources from Nrich who have  published features for Primary and Secondary. Both have numerous activities students can work on at home. The activities are categorised by age and within each collection you will find activities in various categories which are fully explained in the article for teachers.

See also – Coronavirus Update: How NRICH Can Help You

Nrich making a difference

Mathematical Miscellany #38 included a reminder of all the great resources on Jonathan Hall’s Mathsbot – there are so many activities which students can use whilst working at home; with answers provided for students to check, they are getting feedback as they work. Students could try for example Differentiated Questions or a topic ladder of their choice. A recent edition is the student version of Do Now.

Mathematical Miscellany #39 includes from STEM Learning, Home learning activities for families with resources to support primary students and for Secondary students, Maths, Science, Computing, DT and Post 16 resources are available.

STEM Learning - Maths Calendar

Looking at Secondary Maths, we see a collection of games, activities and puzzles that can be used to support children’s mathematical education from home. This attractive calendar links to resources for each day of the term; follow the guide, or choose appropriate activities. No account is required for the home learning resources linked to on the Maths Calendar.

A Level Mathematics, have you seen…? is on the resources from The King’s School, Chester.

Dr Frost booklets Kings School

The Mathematics Department have written chapter booklets to accompany Dr Jamie Frost’s presentations. The booklets have been designed to be used by students to fill in whilst studying from the accompanying Dr Frost presentation. The resources have uploaded to TES, see this TES search; alternatively this Twitter thread has a link to each set of resources on TES (you don’t have to be a Twitter user to access the link).

Bring on the Maths was the first post written in the Maths At Home series and includes several resources for students working at home including Bring on the Maths,

Bring on the Maths Logarithmic Equations

On CIMT there are interactive tutorials for Years 78 and 9.

CIMT Interactive Material

MathsBox Quick Cover
Mathsbox is a subscription (excellent value) site but

Maths Box Skills Checks 2

Also, free for everyone Weekly Checks for Year 3 to GCSE. New checks are available each Monday.

Also have a look at these Quick Cover Lesson samples; each each lesson includes examples/methods with 30 to 60 questions with answers.

MEI are providing additional support during school/college closures; a package of free resources to support remote teaching is available.

Craig Barton has shared links to many resources and ideas in his post: Covid-19: School closures – free maths support, resources and ideas.


CK-12 Foundation has created a resource page with hand-picked lessons in math and science popular during the month of March.

ATM are providing some free resources at this time; note too ATM’s list of Activities for Home or School – suitable for Key Stages 2 to 5 – these have been suggested by ATM member and education consultant Mike Ollerton.

The resources for Key Stages 2, 3 and 4 include an extract with several problems with hints and suggestions from Forty Problems for the classroom.

A free resource for KS5 is a complete publication, The Proving Ground – an introduction to mathematical proof. This e-book offers forty easy to understand problems classified by one of three levels, level 3 has problems which have not been resolved. The book is very clearly structured, a notes page is provided for each problem, best accessed after trying the problem first. There are also Learning Pages which introduce different proof techniques. The home page is the contents page with links to all parts of the book.

From the introduction…

Hello, and welcome to this book, which offers you forty tricky, sometimes extremely tricky, mathematical
problems to think about. Twenty of these have been resolved by mathematicians, sometimes after many
years of work, but the other twenty at the moment remain unsolved, despite the attention of some
seriously clever people down the years. Will you be able to spot the difference?

For any students going onto an Undergraduate degree in Mathematics or are thinking about doing so then Oxford University’s Oxford Online Maths Club (free) will be of interest. This is a new weekly maths livestream from the Mathematical Institute of Oxford University providing free super-curricular maths for ages 16-18.

The sessions start on 7th January at 16:30 UK time.

The content will include maths problems, puzzles, mini-lectures, and Q&A. The sessions are all free and require no sign-up. The livestreams will be available on YouTube indefinitely.

Full details are available here, and you can see what the session on 7th January will include on the YouTube channel.

Happy New Year 2021

It’s that time of year again and we can play the 2021 NCTM Year Game in our January lessons. Full rules are here.

As I write there are still references to 2020, however note this statement “Student solutions may be submitted starting January 1, 2021, using the Web form linked on the side menu. We will begin to post student solutions after February 1, 2021.” 

Can your students use the digits in the year 2021 and the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100? This year, in a change to the rules, decimal points and double-digit numbers are allowed. The rules for 2021 in detail are here.

And so to number properties of 2021, 2021 is an unusual year in that it is the concatenation of two consecutive integers (20 and 21) and also the product of two consecutive primes (43 and 47). This won’t happen again for a while! Have a look at Numbers Aplenty for more on this and also many other number properties. Did you know that 2021 is a Duffinian number?

Alex Bellos also included this in his Monday Puzzles, you will find other puzzles there to keep you busy!

2021 is also an iban number – this has amused me for a long time (along with the eban numbers) – get your students thinking outside the box with the iban sequence: 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 100, 101…

Dave Miller – Spire Maths

On Dave Miller’s Spire Maths, you can read his recent posts for more on consecutive prime years, 2021: the product of consecutive primes, 2021 is an Extra Special Year and 2021 is a Special Year.

A lovely geeky number fact from Chris Smith

We can always check Tanya Khovanova’s Number Gossip site for properties of 2021. The common properties of 2021 are shown. All Number Gossip properties are detailed here.

How many ways can you write 2021 as a sum of squares? We can also look at WolframAlpha for further information on the number properties of 2021 including what 2021 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.

The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.


For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.

We could look back and use the excellent MacTutor History of Mathematics Archive from the University of St Andrews, Scotland. We could check today or any day for Mathematicians who were born or died on that day.

The site is searchable in several ways, including the comprehensive index of History Topics.

Teacher Resources on Line

On the subject of dates and the new year, from trol, Teacher Resources on Line, we can make a calendar for 2021. I do like the fold and tuck models – no glue required Scroll down the page.

Wishing educators and students everywhere a very Happy New Year.

Tidying Up!

A break is always a good time for tidying up and reorganising things!

Continuing the Use of Technology series of pages, the PhET Simulations, Standards Unit Software and Wolfram Alpha pages have been added to the series.

Edexcel GCSE GeoGebra Resources

Added to the GeoGebra series is a new page, GeoGebra Resources-Edexcel so all the resources for GCSE and A level Maths and Further Maths are available in one place.

A recent addition to the top menu includes Updates where updates to popular posts are noted. A further new page added today is Popular Posts and Links, just a small number of currently popular posts and/or files. I see that the file of legacy coursework tasks from Edexcel has proved very popular this year as has The Workers of Zen.