December

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

Also checked and updated is the Christmas Mathematics Resources page.

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!

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.

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,

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.

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.

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.

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.

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.

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!)

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.

Mathematical Miscellany #76

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

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.

November – Barvember

It’s Barvember from White Rose Maths. Barvember, from White Rose Maths, was created to encourage the use of the bar model. Bar models can really help children visualise and then solve maths problems. You could solve the problems using this great digital tool from White Rose Maths, Bar Model