Looking ahead to summer examinations, this year there will not be advance infomation as there was last year, but in GCSE Mathenatics students will again have formaule sheets; the exam boards have now published these. This page, Examinations 2023, includes links to infomation and the formulae sheets for each exam board. The page also includes the series of revision pages with many ideas and resources for revision.

Formulae sheets 2023

• AQA
• OCR
• Pearson / Edexcel
• Eduqas Foundation & Higher

OCR additionally have formulae sheets top tips, and GCSE formulae tests.

I often use Jonathan Hall’s wonderful Completion Tables so was delighted to see that these are all in one place on MathsBot, a personal favorite is his Directed Number.

(See Fill in the Blanks for many such exercises, and Negative Numbers for more resources on Negative Numbers.)

Regular readers will be aware a favourite website of mine is Transum, two recent additions are Algebraic HCF with Algebraic HCF and LCM exercises over 5 levels and Gradients now with a new level 2 which features straight lines drawn on axes where the vertical scale is different from the horizontal scale, soe labels are obscured for an additional challenge.

From Chris McGrane on Starting Points Maths, have a look at this lovely task on Integration which provides much needed practice on deciding on the integration required to determine the areas shown. Students are required only to write down the integrals with limits.  

It struck me that the questions could be checked and illustrated on WolframAlpha.

Both MathsBot and Transum featured in my Enduring Websites collection, websites started between 1997 and 2013, and still there! MathsBot and Transum are regularly producing such excellent resources after many years. I believe Starting Points Maths will be included in the next Enduring websites collection!

These slides are from a session I presented at last year’s MA Conference.

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 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.

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.

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

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.