Looking back…and looking forward

Looking back at 2022, last week I looked at some posts popular in 2022. Continuing the theme of looking back, from the Office for National Statistics, The Year in Numbers in which the National Statistician, Professor Sir Ian Diamond looks back on a year of notable statistics, and from Quanta Magazine, The Year in Math including notes on a bumper year for number theorists from a high school student throught to more experienced mathematicins.

I was interested to see the Top 10 OpenLearn courses of 2022, OpenLearn is the The Open University’s free learning site. The Top 10 includes Everyday Maths and also MSE’s Academy of Money, a course where The Open University joined forces with MoneySavingExpert to produce a course to help people master their finances.

For 2023, a very happy new year to all, I have created the annual look at number properties for the new year and links to NCTM’s year game to play with your students in January. I will keep this page updated with any new resources and ideas.

Tanya Khovanova – Number Gossip

Looking ahead to some new resources, recently created we can use for the year ahead, see the following:

I have often mentioned Wayne Chadburn’s monthly calendars. He writes these calendars to provide regular, varied practice – a little bit of maths each day. Three versions of each monthly calendar are available, Higher, Foundation Plus, and Foundation; answers are provided. Calendars for January through to May are now available.

Maths White Board

For another source of calendars, including the option to create your own, use Matt Woodfine’s resources on Maths White Board.

Fawn Nguyen has provided all her wonderful resources in one place, see Fawn Nguyen, for her new resources page which she plans to add to as time permits. The Collections include a selection for Elementary, chosen from her brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who have used visual patterns in their classrooms.

Visual Patterns
Visual Patterns – Fawn Nguyen

Jack Brown has recently completed his teaching video collection for A Level Further Maths, Mechanics a / Minor.

You can see the OCR B MEI specification for each section, with much in common between the boards, these are useful resources for other boards also; the differences between the exam boards are identified in the resources.

For Further Resources on Dimensional Analysis see this page in the Further Maths series:

Mechanics – Dimensional Analysis

For A Level Mechanics – see this post: Mechanics.

Staying with A Level, Mark Willis has updated his A-level Year 2 resources. Each topic now has the question with gaps for students to fill in whilst either trying the questions or watching the videos.

Note that IGCSE resources are also available on Mark’s site – included in the IGCSE resource collection.

The Doctor Frost Maths Key Skill Team remain busy, still on a Mechanics theme, here’s a recent addition to the Key Skills for Mechanics, K428c – equilibrium on an inclined plane, with an inclined force.

The Dr Frost Maths – Key Skills for Mechanics were included in this post highlighting resources for A Level Mechanics.

Checking Amanda Austin’s wonderful Dr Austin Maths – New, we see recent additions on Functions.

Peps McCrea is launching a weekly 5-min email for teachers who are keen to keep up-to-date with thinking and research around effective teaching. For ‘Evidence Snacks’, you can subscribe here.

I will finish with Jake Gordon’s Christmas present for all teachers! It will be really interesting to see developments on his resource – an infinite canvas to use as a whiteboard in 2023. See Jake’s YouTube Channel, Mr Gordon’s maths universe which includes an Introduction; the interface is very simple and intuitive to use.

I have mentioned Eric Curts before, for example see his introduction to Mathigon, a Control Alt Archive Workshop where he interviews Mathigon’s head of content David Poras.

His recent EdTech Links of the Week 1-2-23 features Jake Gordon’s Infinity Whiteboard.

2022 Popular Posts

A little problem for the holidays (a terrible misuse of the equals sign!)
Popular Posts and Pages 2022
Examinations Summer 2022 & Examinations November 2022
These posts written in 2022 include advance information for the 2022 Examination sessions; whilst those sessions are complete, both posts also include many resources which provide very useful GCSE revision resources for any exam session.
A little problem for the holidays
I wrote this post over 10 years ago in 2022 when my son sent me the problem you see illustrated above! People searching for a solution seem to find their way to my blog.
Knowledge Organisers – Mathematics
Written in 2019, this post with many knowledge organisers from KS3 to A Level and further reading references remains consistently popular.
Retrieval Practice
With many resources for retrieval practice and further reading, this page created in 2019 remains consistently popular.
A Level (16+) Resources
Initially created in 2017, this page has undergone many revisions to add new resources for A Level.
Venn Diagrams was first written in 2015 when we knew that the GCSE specification change would mean more problems on this topic, the original post has been rewritten 4 times with the latest written in 2021
Geoboard Activities
This page was first written in 2015 and has increased in popularity every year since then. Online GeoBoard tools and also activities are included in the post.
Further Maths A Level Topic Tests
Initially written earlier in 2022, this post included Edexcel’s Further Maths Topic Tests written as part od the support for the Summer 2022 examinations. Those tests are no longer available, however the post remians popular with other resources offering Further Maths questions by topic.
Simultaneous Equations
This 2022 post includes many varied resources for teaching simultaneous equations.
Worked Examples – A Level
First created in 2018, this page has undergone several revisions and has increased considerbly in popularity, the free Hodder resources provide a great collection of worked examples.
Misconceptions in Mathematics
A post on Misconceptions was originally written in 2013 and has undergone a major revision, Back in 2013, the Count On website existed and included a collection of misconceptions. In 22 sections, in each section misconceptions are given along with the correct version. Further explanations are also provided and also follow up exercises with answers. Happily, I downloaded the file at the time and have included it in on the page.
And look at this December 2022 update: Dan Meyer’s thought-provoking December 2022 post, “…students don’t have misconceptions.”
I wrote the original post on this wonderful site for A Level students from Dr Trifon Madas when one of my students discovered it in 2016. Sadly Trifon Madas passed away in September 2021. This website remains freely available in a static format for all its users, in his memory. See News on MadAsMaths.
Popular Posts 2022

Christmas 2022

If you have finished school today or are already on holiday then have an excellent and well-deserved break. For those still at school, enjoy the last days of the term. If you are still at school for a few days, I have been keeping the Christmas Resources and Advent Calendar pages updated.

Added recently, I do like Dr Tom Bennison’s Christmas Calculated Colouring for A Level students – these make perfect Christmas activities for older students.

Dr Tom Bennison – Christmas Calculated Coloring 2022
Dr Tom Bennison

You can access calculated colouring resources from previous years also and have a look at his other Christmas themed resources.

On the subject of Christmas Cards…

Chalkdust 2021

For the last few years, I have made Christmas Cards for students using Chalkdust resources, Matthew Scroggs has designed the 2022 Chalkdust card. You can use an interactive or pdf version.

See also the cards from 2021202020192018, and 2017.

Recently published is the GCHQ 2022 Christmas Challenge features seven puzzles based on the seven disciplines of languages, engineering, codebreaking, analysis, maths, coding and cyber security 

For more puzzles, a search on the GCHQ site returns many puzzles to keep you busy! We can also search on Christmas, this search returns cards and Christmas puzzles from earlier years.

For arts and craft lovers – construct a Christmas card from Clarissa Grandi on Artful Maths. I see for 2017, Clarissa used Spirograph, a great idea for Christmas cards. As a child, my Spirograph was definitely a favourite toy, if you don’t have a Spirograph set you could use this brilliant digital version, Inspirograph by Nathan Friend. Try altering the gears so that the fixed and rotating gear are the same size, or make one size a factor of the other, make the two sizes have a common factor, or not! Investigate. You can change the colours too and create a work of Art! Now there’s an app too – Spirograph on your phone!

Inspirograph by Nathan Friend

Or we could create cards with Desmos designs!

For many more puzzles and games, something there is more time for in the holidays perhaps then see the Puzzles and Games series of pages.


Erich’s Puzzle Palace – featured on Puzzles Page


Many resources for teaching Mechanics can be found on my A Level teaching resources page, this post highlights just some of the useful Mechanics examples and notes.

Notes and Examples

Mathsbox – Revision Notes

From the excellent MathsBox site, see: A Level Maths Mechanics Revision Notes. The notes have a very comprehensive set of clear and well-explained examples.

Also available are Pure and Statistics notes.

Download Here

Thanks to @TheHBomb @MrsMathematica @JamesMaths1 @DrBennison for the suggestions/checking/corrections.

— SandraD (@mathsbox1) April 23, 2019

Mathsbox has many free samples to try, easily one of the best value subscription sites around in my opinion.

Looking at some A Level texts From Hodder, we see My Revision Notes – Mathematics. The series includes the following books. In each case look for the Quick Links on the left – see Answers and full worked solutions. Questions and fully worked solutions for each section of the book are provided, whilst the documents refer to the books, they are complete in themselves. The Applied books include Mechanics and Statistics.

Hodder – My Revision Notes series

When you select Answers and full worked solutions for any book, see Edexcel Applied for example, as well as the pdf document of questions with full worked solutions for the ‘Target your revision’, ‘Exam-style’ and ‘Review’ questions, you will find test yourself multiple-choice questions for each section.

Lucyjc – Knowledge Organisers

A Level Knowledge Organisers
This page includes a set of knowledge organisers from Lucyjc.  These resources are available free on TES Resources: Mechanics. All include Key Words and Definitions and What Do I Need to Know sections.

Andy Lutwyche – Erica’s Errors series

From an absolute favourite resource Author – Andy Lutwyche, (search his resources by newest on TES). Have a look at his excellent Erica’s Errors series which included Mechanics.

Stoke Maths MEP

These are very attractively presented high-quality resources. Looking at the Spot the Mistake PowerPoints for example, as you can see in the image there is a great collection of questions that include full answers. It’s brilliant to see a Mechanics collection.

The revision question starters provide very useful question sets.

This can be also be found in my Starters collection under Advanced Starters.

Dr Frost Maths – Key Skills
You will find an excellent collection of practice questions – try these key skills for Mechanics under KS5.

DrFrostMaths Key Skills

I was very interested to see this from Susan Whitehouse on car and trailer and objects in a lift problems:

Edexcel’s latest Scheme of Work document now includes many links for the use of technology as well as all the very useful notes for teachers. A link from the Mechanics notes led to these CG50 Mechanics resources.

Casio CG50 Mechanics Resources

Edexcel’s GeoGebra resources include a small number for Mechanics at A level, and more for Further Maths.

Pearson Maths A Level Year 1
Pearson Maths A Level Year 2
Pearson Maths Statistics and Mechanics Year 1
Pearson Maths Statistics and Mechanics Year 2
Further Mathematics
Pearson Maths A level Core Pure 1
Pearson Maths A level Core Pure 2
Pearson Maths A level Further Pure 2
Pearson Maths A Level Further Mechanics 1
Pearson Maths A Level Further Mechanics 2
Pearson Maths A Level Decision 1
Pearson Maths A Level  Decision 2
Pearson Maths A Level Further Statistics 1
Pearson Maths A Level Further Statistics 2

It is good to see all the GeoGebra resources for Further Mathematics, for example, check Explore toppling and sliding using GeoGebra.

Pearson Maths A Level Further Mechanics 2 Toppling and Sliding

Dimensional Analysis
AQA: Optional application 1 – mechanics  Assessed at AS and A Level
AQA Dimensions Specifiication

My post on Dimensional Analysis for Further Maths includes many resources for teaching this topic.

Mathematical Miscellany #78

Since it is Advent, we should start by opening a Christmath door, here’s Door 3 on Transum, the Christmas Toggle Tree; can you light up all 12 lights on the tree using the buttons to toggle the current state of the lights?

Recently added to the Advent Calendar, is Mark Anderson’s Appvent, and I am delighted to see that the first entry is Jonathan Halls’s brilliant Form Time Ideas. and remember you can also use Form Time Numeracy.

NCETM – Checkpoints

NCETM continue to add Checkpoints to their collection, the image here is on Year 8 Estimation and rounding.

On Dr Frost Maths try the new look Skill Explorer which makes it easier to combine skills from multiple topics.

From the younger students to Year 13 – here’s a wonderful resource from Susan Whitehouse, a Year 13 revision lesson, Looking at Quintics. All Susan’s resources can be found here. The revison resource was inspired by Tom Button and Tayyub Majeed. I believe Tom Button started this with his favourite quintic, y = x5 − 5x3 + 5x.

Open Middle

I have mentioned problems from Robert Kaplinsky before, have a look at his Open Middle Math Depth of Knowledge Matrix. Problems are provided for each grade level, the first problem in the column is of a familiar kind, the Open Middle problems classified as DOK 2 and DOK 3 are on the same topic but provide significantly more challenge.

Many problems are available as a GeoGebra resource, from Tim Brzezinski, try this brilliant GeoGebra book of Open Middle themed problems. 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

Robert Kaplinsky also has a collection of over 70 problem-based lessons which you can now browse in a spreadsheet.

Spicy Questions is a new competition for 2023 created by 1st Class Maths. The competition is for students aged 18 or below who are studying in secondary education in the United Kingdom. The questions, stated as harder than standard exam questions and with a problem solving focuswhich are based on GCSE content are suitable for GCSE and A level students. The first question will be posted on Jan 9th, in the meantime you can try the practice question.

Some reading to finish – from Quanta Magazine, The Math Behind Wordle Guesses, you can also browse the Mathematics articles.