How best to explain rounding 21.983 to 1 decimal place? I tend to say: - Imagine a ‘cut-off line’: 21.9 | 83. - We’re rounding up because 8≥5. - Imagine 21.9 without its point, as 219. - Add 1 to get 220 - Put the point back again. It’s 22.0. Can you improve this?

Website update: Expanded and restructured the “Notes and videos” sections on the Higher Maths and Advanced Higher Maths topic pages. For example: www.maths.scot/higher/strai...

Website update: While tutoring yesterday evening, I saw one of my Higher Maths students scroll up and down the main Higher Maths page looking for the link to past papers. So I’ve redesigned the “menu pages” for N5 Maths, H Maths and AH Maths to make such links more obvious.

Website update: Added all SQA Intermediate 2 past papers 2000-2015 and all Standard Grade Credit past papers 1996-2013 - for the keenest N5 Maths students! Most with SQA marking instructions. That failing, worked solutions. That failing, brief answers. www.maths.scot/national-5-m...

Website updates: 1. Added Clelland Maths video links to worked examples in the N5 Maths numeracy topics. 2. Updated the N5 Maths “past papers by topic” PDF files to bring them bang up-to-date (all 2014-2025 PPQs). www.maths.scot/national-5-m...

Website update: Added another 206 relevant Standard Grade Credit past paper questions and solutions to the N5 Maths topic pages. This concludes the process of adding all applicable Credit and Intermediate 2 questions to the Nat 5 pages. www.maths.scot/national-5-m...

Website updates: 1. Added 500 pre-2015 specification Higher Maths past paper questions and answers to the Higher Maths topic pages. 2. Added 453 carefully-selected Standard Grade Credit and Intermediate 2 past paper questions and answers to the N5 Maths topic pages.

Website updates: Added 12 new worksheets and 238 old specification past paper questions (2001-2015) for Advanced Higher Maths. www.maths.scot/advanced-hig...

Website update: Brought the N4 Maths page up to the same standard as the pages for N4 and N5 Applications. The N4 Maths page now contains resources organised neatly by unit (E&F, REL, NUM) and topic, including 112 worksheets and test practice materials. www.maths.scot/national-4-m...

Website update: Added six new worked solutions for Advanced Higher Maths PPQs: Binomial Theorem: 2025 P1 Q1 Complex Numbers: 2025 P1 Q3 Functions and Graphs: 2024 P1 Q5 Maclaurin Series: 2024 P2 Q7 Matrices: 2025 P1 Q4 Sequences and Series: 2024 P1 Q3 www.maths.scot/advanced-hig...

Website updates: 1. All AH Maths PPQs 2016-2025 now open in their own separate PDF files, rather than from the complete past paper files. 2. Improved the “sub-topic” categorisation of AH Maths PPQs on the topic pages, for more focused study. www.maths.scot/advanced-hig...

Happy New Year! Today I have mostly been eating steak pie, exploring the post-Japan works of Mick Karn, nursing the tail-end of a nasty cold and creating 2024 and 2025 past paper question files to update the topic pages at www.maths.scot/advanced-hig... - enjoy!

Website update: Added 47 new worksheets for N5 Maths, bringing the total for that course to 342 and the total for all courses to 1009. This concludes the recent flurry of website development work. Wishing you a Merry Christmas and a Happy New Year, when it comes!

Website update: 1. Added 51 new N5 Maths worksheets, taking the current total to 295. All high quality - no filler! 2. Made the “page sections” links on each topic page more prominent, to further simplify navigation.

Website update: Sourced, selected and added yet more worksheets or online worksheets: • 50 for N5 Maths • 29 for Higher Maths • 5 for Advanced Higher Maths. I am now close to being happy with the range and quality on offer.

Website update: 1. Added 32 new N5 Maths worksheets. 2. Removed some lower quality N5 worksheets - quality over quantity! 3. Improved the format of the N5 worksheet sections for quicker, simpler access. 4. Added a note to say whether or not each N5 worksheet has answers.

Imitation is the sincerest form of flattery. 🤣 www.maths.scot/nat5/trig-eq... www.national5maths.co.uk/cast-diagram/

Website update: Finished improving the in-page navigation for the N5 Maths topic pages. Each page now includes the following subsections: • Topic content • Key ideas • Worked examples • Past paper questions • Worksheets • Notes and videos www.maths.scot/national-5-m...

Website update: Added 20 new theory guides and 33 new worksheets for Advanced Higher Maths. www.maths.scot/advanced-hig... Pending jobs: 1. Get the in-page navigation for the N5 Maths topic pages up to the same standard as H and AH. 2. AH PPQs for 2024 and 2025 by topic.

Website update: Massively increased the number of Higher Maths worksheets: from 55 to 153. www.maths.scot/higher-maths

Website updates: 1. Refined the operation of the page section links within the Higher Maths topic pages. www.maths.scot/higher-maths 2. Replicated this navigation system across the Advanced Higher topic pages. www.maths.scot/advanced-hig... 3. Added 19 new Higher Maths worksheets.

Website update: Added “Quick links on this page” to substantially improve navigation within each Higher Maths topic page. These in-page section links have been placed at the very top of each topic page, above even the topic specification. Example: www.maths.scot/higher/integ...

Website update: Added “page section links” to the N5 Maths topic pages to make it easier to navigate between topic notes, worked examples, worksheets, PPQs etc. For example: www.maths.scot/nat5/trig-eq... This feature will be added to the Higher and AH topic pages later this week.

Website update: Added 2025 past paper question files to the Higher Maths topic pages: www.maths.scot/higher-maths The N5 Maths and Higher Maths pages are now completely up-to-date. Advanced Higher next.

Website update: Added Clelland Maths video solutions for these N5 Maths topics: Expanding Factorising Quadratics Arcs and Sectors Volume Pythagoras Angles in Shapes Similarity Vectors 3D Coordinates Triangle Area Sine/Cosine Rule Trig Graphs/Equations/Identities Data Sets

Website update: Added two new worked examples for N5 trig graphs. www.maths.scot/nat5/trig-gr...

Website update: added six more worked examples for N5 Maths, drawn from the SQA 2025 exam papers. www.maths.scot/national-5-m...

Website update: added individual files for 2024 Higher Maths questions to the topic pages at maths.scot/higher-maths The 2025 Higher Maths questions will be added before the end of this year and I’ll clear the Advanced Higher backlog ASAP.

Website updates: - Worked solutions to 2025 N5 Maths and 2025 Higher Maths added - 2025 N5 Maths P1 and P2 questions attached to individual topic pages.

Website update: 2025 SQA exam papers and marking instructions added. Six new N5 Maths worked examples added (more to follow).

My most interesting pupil question this week: "Will 3D Pythagoras always be on the calculator paper?" This led us into a fun sideline discussion about square numbers that equal the sum of three squares: 9, 49, 169, 441, 961, etc (i.e. Pythagorean quadruples). The smallest two would be fair game.

#WorldPoetryDay2025 Mathematical Limerick by Leigh Mercer A dozen, a gross and a score Plus three times the square root of four Divided by seven Plus five times eleven Is nine squared and not a bit more.

What did this pupil do wrong? How to fix their misunderstanding? The question was a worded problem (non-calculator) which they correctly understood required them to calculate 43×6+4. The student’s answer was 702. Hint: They did the multiplication correctly. #mathstoday

Website update: Clelland Maths video solutions to the 16 worked examples for the National 5 Maths 'Change of Subject' have now been added to the written solutions on www.maths.scot/nat5/change-...

Website update: Clelland Maths video solutions to the worked examples for the Advanced Higher Maths 'Number Theory' topic have now been added to the written solutions on www.maths.scot/advanced-hig...

Website update: Clelland Maths video solutions to the 18 worked examples for the Higher Maths Differentiation topic have now been added to the written solutions on www.maths.scot/higher/diffe...

Website update: Clelland Maths video solutions to the 11 worked examples for the National 5 Maths 'Simultaneous Equations' topic have now been added to the written solutions on www.maths.scot/nat5/simulta...

Website update: Clelland Maths video solutions to the 14 worked examples for the Advanced Higher Maths 'Methods of Proof' topic have now been added to the written solutions on www.maths.scot/advanced-hig...

What is *Mathematics* about? I'm looking for pithy, engaging, relatable, positive, short (1 or 2 words) about what makes mathematics mathematics? How can you spot it in the wild? I'm thinking "patterns", "relationships", "shapes", "changes",... What else?

How to cheer students up on their first day back of the new year: “None of us had been born in 1936 and we’ll all be dead by 2116.”

New report from the Commission on School Reform highlights worrying FOI data based on the number of pupils in the S4 cohort, rather than the number which sit the exams. While 75% of S4 pupils passed Nat 5 English in 2024, only 40% passed Nat 5 Maths www.reformscotland.com/publication/...

What’s going on here? Student could convert 2¾ into an improper fraction, but then had no idea how many quarters are in 2¾.

Revealed: How not a single maths department in Moray’s schools is fully staffed

N5 Maths: factorising a difference of two squares. In the SQA specification, the given format is p²𝑥² − a². 2016 P2 Q4: 3𝑥² − 48 2017 P2 Q9: 4𝑥² − 25 2019 P2 Q13: 4p² − 9 2021 P2 Q3: 3a² − 75 2022 P2 Q12: b² − 9 2023 P2 Q12: 𝑥² − 16 So would 9 − x² or 𝑥² − y² be unfair? Thoughts? #ScottishMaths

More #ScottishMaths teachers to follow: @juliemorgan.bsky.social @audproctor77.bsky.social @kevinghall.bsky.social

Today’s poem celebrates Fibonacci Day. It’s called ‘Word Crunching’.

#ScottishMaths The @bsky.app community is growing! Who to follow: @mistercorzi.bsky.social @mrwilsoncompsci.bsky.social @segarrogers.bsky.social @brynspiration.bsky.social @garyl.bsky.social @mrallanmaths.bsky.social @khuntermaths.bsky.social @missdicksonmaths.bsky.social @maths-geek.bsky.social

I have created a #ScottishMaths feed to help us follow relevant posts. The tag is intended for use by primary and secondary teachers of mathematics in Scotland.

With many schools now reassessing their use of social media, @nuthmani.bsky.social weighs up the advantages and potential challenges of having an online presence

Hello Bluesky! #maths #math #mathschat #scotland #education #ukmathschat #teachers #mathsresources