Advent – Open the Christmath Doors!

It’s December! So many mathsy doors to open!
See my updated Advent Calendar collection.

Now it’s December – you can open Transum door 1 to reveal this gem!

Transum Dec 1st
Transum Maths Advent Calendar

I do like this Dec 1st Transum activity. Use the given palette to make sure that all the trees are decorated differently – brilliant for thinking about systematic listing strategies. Note the different levels available.

Look at all the wonderful collections on Nrich on Working Systematically.

Staying with Nrich…

Nrich Advent 2022

Nrich publishes annual Advent Calendars – one for Primary (2022)  and one for Secondary (2022). Both feature twenty-four activities, one for each day in the run-up to Christmas; for 2022 the calendars have twenty-four poster problems. Both Nrich and Plus Magazine have published such good collections of Advent resources, clearly, for an Advent Calendar, the year does not matter so we have lots of choices! See for example this whole collection of advent calendars on Nrich, note the different themes available – a Sudoku for each day perhaps? The 2016 Primary Calendar featured tasks to encourage mathematical habits of mind something we need to encourage in students of all ages.

Matthew Scroggs – Advent 2022

From Matthew Scroggs – try his Advent Calendar for 2022; behind each day (except Christmas Day), there is a puzzle with a three-digit answer, solve the puzzles to help Santa by destroying the drones so that he can deliver presents before Christmas is ruined for everyone; you can read all the details in his post.

From the brilliant Mathigon site, see Puzzles 2022, puzzles are revealed at 9am GMY every day in December and solutions are availble on the following day. And perhaps have a look back at their puzzles from earlier years…

Mathigon 2021

Looking again at some of these Advent calendar resources, I think many are useful for end of term Christmas activities for examination classes. In this category we have for example:

JCalderwood revision

J Calderwood has provided three Advent Calendars – Advanced Higher, HIgher and N5 Maths for Scottish Students. A great revision resource that could be adapted for different courses.

Access Maths Christmas Revision

Alternatively how about a Christmas Revision Calendar from Access Maths? Three Christmas Calendars are available, one for KS3, and two for GCSE – Foundation and one for Higher.


…at the time of writing, it’s nearly December so we can start opening the Christmathy doors on Mathematical Advent Calendars.

Andy Lutwyche Advent Calendar
Andy Lutwyche

Also checked and updated is the Christmas Mathematics Resources page.

Transum Christmas Tree Trim – Level 3
Wayne Chadburn

A new month is always a good time to remind readers of 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.

Staying with calendars we could return to MacTutor for A Brief History of Time and Calendars. Thinking about the history of the calendar, here’s a good calendar for some probability questions, is anything ever certain?!

We could work out the day on which any date falls, this reminds me of a legacy MEI Decision Maths paper where students were provided with an algorithm to compute the date of Easter Sunday in the Gregorian calendar system; my students of the time came to find me after the exam to tell me about the algorithm question!

OCR MEI D1 Jan 2008 question 3

and here is the mark scheme in case anyone wishes to work through this.

Many investigations can use calendars, here’s an example from Nrich – Calendar Capers.


Perhaps a little puzzle from Mathisfun!


Mathematical Miscellany #77

A compilation post this week…

One of my go-to websites is Corbett Maths, I was interested to see that John Corbett has been adding some updates. He has added 6 new Estimated Mean and 10 new Order of Operations questions the Practice Questions, along with video solutions.

Corbett Maths – Order of Operations
Corbett Maths – Estimated Mean

See the slides from my session Enduring Mathematics Websites presented at last year’s MA Conference – some sites (including Corbett Maths) that have been with us for many years and all still there!

Each of these pages include sites easily searched by topic for quality resources.

From Complete Maths check their Free Resources section, the wonderful Task Booklet keeps on growing!

The tasks aim to promote mathematical thinking and behaviour in the classroom and have been designed to be used with an appropriate model or manipulative. (See also NCETM’s Using Mathematical Representations at KS3.)

Note the playlist, Tasks on the Complete Maths YouTube CPD channel where Jonathan Hall is sharing his thoughts on some of these tasks. He recently shared this on Volume of Cuboids – a lovely link to prime factorisation here,

Complete Mathematics

A recent post from the SERP institute on Math by Example describes the excellent (free) resources, MathByExample and AlgebraByExample. I featured these resources on my Misconceptions page.

Dr Austin Maths

Checking the New section on Dr Austin Maths, note the 6th November entry, a couple of resources for Year 12, (expect more from Dr Austin for A Level in the coming months). These resources can currently be found in Advanced Maths where we see Trigonometric Ratios Decode the Joke and Trigonometric Identities Match-Up.

Image by Simon Gregg – from his Which one doesn’t belong? collection

Which one doesn’t belong? Have a look at this post from Terri Eichholz which includes an album from Simon Gregg of over 200 WODB images for educators to use for math discussions.

Mathsvent Calendar – Phil Bruce

It’s not quite December yet, but I can see from my WordPress statistics that people are searching for Advent resources, so I have added my Mathematical Advent Calendars page to the menu of featured posts.

Brooke Hunter has shared these excellent sessions used by her Maths department. As she states, the critical element is the discussion generated in the session.

Advanced Problems in Mathematics – Stephen Siklos

Note the announcement below from Cambridge Admissions Testing; I have added the information to my page on University Admissions Tests, these resources provide challnging questions for Mathematics students whether or not they are taking any tests.

Update November 2022: “Cambridge Assessment Admissions Testing is to withdraw from running a series of university admissions exams with effect from 2024-5. This includes BMAT (medicine), ENGAA (engineering), NSAA (natural sciences) and TMUA (mathematical skills) tests.”

Some reading, from Hannah Fry, a piece she wrote for the i newspaper on November 11, 2022 about why she thinks you don’t see more girls doing maths.

On the subject of encouraging girls to study Mathematics, remember the information and ideas from amsp.

For your amusement, in case you missed it, be inspired by Jonathan Hall’s Thing on Mathsbot.

Geometric Sparks

I really enjoyed attending a London Maths session yesterday morning – led by Dietmar Kücheman, we had several very enthusiastic Maths teachers working on his lovely Geometric Sparks tasks.

Dietmar Küchemann – Geometric Sparks, created on Autograph web

I created the illustration here with Autograph (web version) and was reminded how much I like the features of Autograph web including that lovely colour palette for styling objects! I created a very simple Autograph web file which allows you to move point C along the line (y = -2x + 16), you can also move points B and D to create a rectangle, the Area will be shown for any rectangle. For a more sophisticated version, try this, created by Robert Smith (@RJS2212) (on his phone!)

Dietmar Küchemann – Geometric Sparks, created on Autograph web by Robert Smith

You can see these tasks on Dietmar Küchemann’s blog Geometric Sparks, but note that Dietmar has now updated these tasks and they have been published by ATM, see Geometric Sparks – Generating links with shapes in space, book and slides, by Dietmar Küchemann.

As you can see from the Introduction to the tasks on his blog, Dietmar Küchemann has based the tasks on NCETM’s Secondary Mastery Professional Development Materials, Theme 6 is on Geometry.

See also, published by the DfE, new guidance -written by the NCETM’s Secondary Team to support the teaching of maths at Key Stage 3. This guidance offers a detailed ordering of the maths that students need to learn from the beginning of Year 7 until the end of Year 9. (See more on KS3 on my KS3 page).

You can look inside the Geometric Sparks publication to see the format for each task. Each task is clearly presented with a commentary and possible methods of solution, including the answer/s.

Perhaps an approach many students might use…

We looked at several tasks in the session, Week 3 Monday provides a lovely illustration of how useful it can be to add lines to a diagram. From Robert Smith, on Autograph again, see his Autograph file for this task.

I took Rob’s file and added some lines and displayed the angles….

It’s a small world sometimes – in October I included Enigma Maths hub in my post on solving linear equations, so I was delighted to meet Jayne Webster at the Geometry Sparks event. Do keep an eye on that site for future developments too.

We can check the Geometry resources on Enigma Maths hub.

Enigma Maths hub – 6.2 Perimeter, Area and Volume

Mathematical Miscellany #76

MathsBot GCSE Countdown Timer

With two GCSE papers done and just one to go, see November Examinations for resources including papers from 1st Class Maths.

From Mrs Jagger, @Jaggersmaths

Trigonometry (Area) – Fill In The Blanks, Andy Lutwyche

Fill in the blanks worksheets can be so good – for many more examples, see my post, Fill in the blanks…

From Brooke Hunter, why not practice rearringing formulae to support your Science colleagues?

Thinking about misconceptions in Algebra recently I came across “2b or not 2b: Misconceptions in algebraic reasoning” from Barbara J. Dougherty. This has been added to my page on Misconceptions.

Something Dan Meyer said at the MEI Conference 2021 really struck a chord with me, he said “There are no mistakes or misconceptions, just takes and conceptions.” Dan Meyer mentioned WW Sayer who said:

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong’. Rather he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole art of teaching.

WW Sayer

In case you missed it, Mathematical Miscellany #75 on some brilliant resources has proved very popular.

Jake Gordon – Worked Examples