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Nathan Day

@nathanday.bsky.social
1.4K followers 266 following 318 posts

Maths (and Computer Science) teacher. Task interweaver. Daydream believer. interwovenmaths.com New! classduels.com/maths #EduSky #UKTeaching

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Reposted by Nathan Day
Francis Su @mathyawp.bsky.social · 03/10/2026
My piece "The Two Timelines" is in the most recent issue of the Notre Dame publication Virtues and Vocations. What does Star Trek have to say about our current moment with Large Language Models? socialconcerns.nd.edu/research/vir... @virtuevocations.bsky.social
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Nathan Day @nathanday.bsky.social · 02/10/2026
The first resource to get me hooked on the Revision Mat was Access Maths's brilliant '100 Questions!' GCSE Crossover page, which I've used with many a Year 10/11 class. Can be found here, near the bottom, below a load of other grade revision resources: www.accessmaths.co.uk/revision-res...
Access Maths 100 Questions GCSE Crossover Revision Maths.

https://www.accessmaths.co.uk/uploads/4/4/2/3/44232537/100_questions_revision_mat.pdf
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Nathan Day @nathanday.bsky.social · 02/10/2026
In #MathsToday, Year 13 Further Maths had a lesson in the morning to revise for an afternoon Core Pure 1 assessment. I printed off a nice double-sided A3 revision mat. There's something about that format that I find feels more approachable than 50 questions in a list! interwovenmaths.com/mats/cp1
Page 1 of a Revision Mat of 50 Core Pure 1 questions in a grid.Page 2 of a Revision Mat of 50 Core Pure 1 questions in a grid.
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Nathan Day @nathanday.bsky.social · 01/10/2026
or is it even a structured variation grid...? @studymaths.bsky.social
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Nathan Day @nathanday.bsky.social · 01/10/2026
It's tricky to do a proper #MathsToday today as I've spent all in Bristol for a meeting. However, I've managed to spend a bit of time on the train back planning some Year 8 Ratio lessons, which reminded me of this rather unusual Combining Ratios Completion Table. interwovenmaths.com/small-tasks
A 5-by-5 table showing ratios between a, b, c, d and e. The diagonal entries a:a, b:b, c:c, d:d and e:e are all 1:1. Given entries are a:b = 5:3, b:c = 6:7, d:a = 9:4 and e:d = 11:12. All other ratios are blank to be completed.
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Nathan Day @nathanday.bsky.social · 01/10/2026
I work at an all-girls school, and wanted my displays to be more relatable to my students than other, otherwise similar, resources. Hence also the focus on applications rather than pure maths.
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Nathan Day @nathanday.bsky.social · 30/09/2026
A nice explanation of the method and why it works (essentially a shortcut of the shortcut that is the substitution method) from the excellent blackpenredpen can be found here: www.youtube.com/watch?v=fgPv...
youtube.com
the cover-up method & why it works! (for partial fractions decomposition)
YouTube video by blackpenredpen
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Nathan Day @nathanday.bsky.social · 30/09/2026
In #MathsToday, I introduced some students (and colleagues) to Oliver Heaviside and his 'cover-up method' for partial fractions. While not ideal for exams, as it isn't much of a written method, I find it a handy check and I'm surprised so many haven't heard of it! en.wikipedia.org/wiki/Heavisi...
en.wikipedia.org
Heaviside cover-up method - Wikipedia
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Nathan Day @nathanday.bsky.social · 29/09/2026
Pretty much!
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Nathan Day @nathanday.bsky.social · 29/09/2026
I'm afraid not - both for copyright reasons and technical limitations (it currently only runs locally as a Mac app). I might, at some point, make a public version that doesn't host any of the questions - just has the categorisation/filters then links to the official papers/mark schemes?
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Nathan Day @nathanday.bsky.social · 29/09/2026
In this case, I narrowed down the topic to similar triangles, sorted by performance, and found a couple of suitably interesting questions.
The GCSE Maths Question Database, narrowed down to Similar Triangles.One particular exam question on similar triangles.
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Nathan Day @nathanday.bsky.social · 29/09/2026
In #MathsToday, Year 10 did some exam question practice based on recent work on Similar Shapes. This term, I have been very much enjoying the benefits of having spent part of my summer holiday building a 8000+ question database of all GCSE Maths past paper questions.
Screenshot of a GCSE Maths Question database.
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Nathan Day @nathanday.bsky.social · 28/09/2026
This, and all my previous MathsToday posts, can be found at: interwovenmaths.com/mathstoday
interwovenmaths.com
#MathsToday | Interwoven Maths
An archive of Nathan Day's #MathsToday posts: an example of something taught or a resource used in maths lessons each school day.
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Nathan Day @nathanday.bsky.social · 28/09/2026
There are 10 ways for two people to get one vote each (indistinguishable votes due to secrecy!), i.e. the answer to (b). Then 5 extra ways for one person to end up with both votes.
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Nathan Day @nathanday.bsky.social · 28/09/2026
We also, naturally, also looked at the opposite - scenarios which look very different on the surface, but have the same underlying mathematical structure.
Bonnyrigg Rose beat East Fife 4–2. A 3 × 5 grid is provided to explore the question: “How many different scores could there have been at half time?” The score 3–1 is shown as an example.Two-digit numbers are formed where the first digit is a square number and the second digit is odd. A 3 × 5 grid is provided to explore how many numbers are possible, with 47 shown as an example.The number 400 with the question: “How many different factors does this number have?” A 3 × 5 grid, labelled “Power of 2” and “Power of 5”, represents possible factors. 2^3*5^1=40 is shown as an example.Four counting problems linked by the question “Why do these questions all have the same answer?” The problems concern possible half-time scores in a 4–2 football match, factors of 400, two-digit numbers with a square first digit and odd second digit, and the number of lines connecting five points to three points.
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Nathan Day @nathanday.bsky.social · 28/09/2026
In #MathsToday, Year 10 were looking at the Product Rule for Counting. We looked at how subtly different scenarios lead to different calculations, each with different geometric/algebraic generalisations. I spent quite a while coming up with a context where all four variations felt meaningful.
Four-part task asking how many outcomes are possible when five students enter a music competition: awarding first and second place; choosing two winners; two judges each secretly voting for a favourite; and awarding Best Performance and Best Composition.The same four-part music competition task, illustrated using 5 × 5 grids to represent possible pairs of students. Coloured squares show which combinations are possible or distinct in each scenario.Generalisation of the music competition task to n students. The numbers of outcomes are shown as n(n-1) for first and second place, {n(n-1)/2 for two winners, n(n+1)/2 for two secret votes, and n^2 for Best Performance and Best Composition.
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Nathan Day @nathanday.bsky.social · 25/09/2026
In #MathsToday, Year 13 did some Integrating Factor, Year 10 worked on similar shapes, and Year 8 found some surface areas and volumes of cuboids. interwovenmaths.com/faces-of-cub...
interwovenmaths.com
Faces of Cuboids | Interwoven Maths
Cuboid practice for finding volume and surface area from dimensions or face areas, including missing lengths.
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Nathan Day @nathanday.bsky.social · 24/09/2026
In #MathsToday, I had no Maths lessons. But in Computer Science, Year 7 have been continuing to build flowcharts with Flowol, Year 8 have been comparing cloud and local storage options, and Year 9 have been consolidating their Python lists skills with: interwovenmaths.com/lists
interwovenmaths.com
Python Lists
Multiple-choice practice reading Python programs that use lists: indexing, len, append, insert, sort, remove and changing items.
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Nathan Day @nathanday.bsky.social · 23/09/2026
Linked here! interwovenmaths.com/mathematical...
interwovenmaths.com
Mathematical Gettier Questions | Interwoven Maths
Explore incorrect methods that can sometimes give correct answers, through simplifying fractions, rounding, double angle formulae and second derivatives.
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Nathan Day @nathanday.bsky.social · 23/09/2026
In #MathsToday, Year 13 did a new Mathematical Gettier Question linking to Differential Equations (and then we started looking at Integrating Factors).
Mathematical Gettier Question titled “Second Derivative”. Oona incorrectly finds the second derivative of y=e^{-x^2} by squaring the first derivative. Questions ask students to find the correct second derivative, then solve a differential equation to determine all functions for which Oona’s method would give the correct answer.
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Nathan Day @nathanday.bsky.social · 22/09/2026
In #MathsToday, Year 8 were doing Plans and Elevations. Inspired by this NCETM Checkpoint, we may have gone on a slight tangent into the history of the Egyptian pyramids. www.ncetm.org.uk/classroom-re...
Checkpoint asking which of four buildings—the Eiffel Tower, Elizabeth Tower, One Canada Square or the Great Pyramid—could have the shown bird’s-eye views. Diagrams show a square with diagonals and a tapered square structure viewed from above.Solution slide showing possible bird’s-eye-view sketches of One Canada Square and Elizabeth Tower. One Canada Square is represented by overlapping squares with diagonals; Elizabeth Tower by nested squares with diagonal lines and an ornate outer edge.Aerial view looking directly down on the Great Pyramid of Giza, showing its square base and four triangular faces meeting at the centre.
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Nathan Day @nathanday.bsky.social · 21/09/2026
In #MathsToday, Year 10 Level 2 Further Maths wrapped up Binomial Expansion with some lovely questions from @draustinmaths.com, who has an excellent selection of L2FM worksheets at: www.draustinmaths.com/level2fm
draustinmaths.com
LEVEL 2 FM | Dr Austin Maths
NUMBER
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Nathan Day @nathanday.bsky.social · 20/09/2026
I've now marked them. Median 10/11. For many, marks were lost on a couple of subtle points in 'show that' questions, which will be good to talk about in lesson. Quite a few full markers to publicly celebrate, and a couple of lower scores to have individual conversations with.
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Nathan Day @nathanday.bsky.social · 18/09/2026
[More serious answer: depends on the student, the number of marks lost, the cause of the marks lost, how far through the year, etc. But they won't get a stamp of a hippo saying 'well done!' or a ladybird saying 'good job!'. And in many ways, that's the harshest punishment of all.]
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Nathan Day @nathanday.bsky.social · 18/09/2026
static.klipy.com
Right to Jail, Right Away
ALT: Right to Jail, Right Away
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Nathan Day @nathanday.bsky.social · 18/09/2026
I've not marked them yet - but with previous classes, it has usually taken a few weeks for some to get used to the format and the expectations.
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Nathan Day @nathanday.bsky.social · 18/09/2026
...they had to be able to complete a sample of the questions (including with slight changes to numbers) in a mini-quiz in the lesson, with an expectation of getting 100%. This keeps the focus on learning from the homework, not just doing the homework (to paraphrase @adamboxereducation.bsky.social).
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Nathan Day @nathanday.bsky.social · 18/09/2026
In #MathsToday, Year 10 had their first 'Homework Quiz' of the year. Inspired by @karenshancock.bsky.social, they had a week to complete a set of questions. They could work together if desired, get help from others, or even use the solutions that were provided towards the end of the week. But...
Homework Page 1Homework Page 2Homework Page 3Homework Page 4
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Nathan Day @nathanday.bsky.social · 17/09/2026
Not much Maths to report on in #MathsToday, but in Computer Science Year 8 had fun making programs with the Little Man Computer: www.peterhigginson.co.uk/lmc/ #ComputerScienceToday
peterhigginson.co.uk
Little Man Computer - CPU Simulator
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Nathan Day @nathanday.bsky.social · 16/09/2026
(I must say, 2026-me is really appreciating the effort 2024-me went to in making a function to control the speed at which the purple line sweeps - giving it that little bounce between powers.)
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Nathan Day @nathanday.bsky.social · 16/09/2026
Yes! And there's something I just love about seeing the power build up and do all the loops needed to reach the original number.
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Nathan Day @nathanday.bsky.social · 16/09/2026
In #MathsToday, Year 13 Further Maths were continuing with Complex Numbers. I used some of the @desmos.com graphs I made a couple of years ago.
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Nathan Day @nathanday.bsky.social · 15/09/2026
In #MathsToday, Year 8 did my Sequences Completion table. interwovenmaths.com/sequences-co... Inspired, of course, by @studymaths.bsky.social's dynamic version available at: mathsbot.com/tables/nthTerm
interwovenmaths.com
Sequences Completion Table | Interwoven Maths
Sequences completion table linking term-to-term rules, nth terms, zeroth and tenth terms, first five terms and sums.
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Nathan Day @nathanday.bsky.social · 14/09/2026
Yes - I was thinking about that one also. Of course, Don has already done the groundwork for that one too! donsteward.blogspot.com/2017/11/equa...
donsteward.blogspot.com
equable shapes
ideas and resources for mathematics teachers of 10 to 16 year olds
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Nathan Day @nathanday.bsky.social · 14/09/2026
In #MathsToday, I did some Mathematical Gettier Questions with Y8 and Y13. Mathematical Gettier Questions are tasks that explore how incorrect methods sometimes give correct answers. Explained in more detail here: interwovenmaths.com/mathematical... What ideas can you think of for similar tasks?
Simplifying Fractions: Mathematical Gettier Question showing Ellie incorrectly simplifying 12/24 to 1/4 by cancelling the digit 2. Students explain the error, find a fraction where the method works, and test the claim that it works for 49/98.Simplifying Fractions – Sorting: Students sort 12 fractions according to whether Ellie’s digit-cancelling method does not work, partially works, or fully works.Double Angle Formula: Mathematical Gettier Question showing Ramona incorrectly assuming cos 2θ = 2 cos θ, giving 6/5 when cos θ = 3/5. Students find the correct answer, explain why 6/5 is impossible, and determine when her method would work.
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Nathan Day @nathanday.bsky.social · 13/09/2026
I've just added the Algebraic Identities / Comparing Coefficients / Algebraic Fractions tasks I made back in 2022 to interwovenmaths.com/algebraic-id... My favourite part is these discussions, where [spoilers] you can show that 42 and 9 are in fact the only options, each with a nice interpretation.
Two algebraic fraction identities labelled a and b, asking which is easier. The coefficients 42 in a and 9 in b are highlighted in purpleTwo follow-up algebraic fraction identities labelled c and d. Question c asks why the identity with 14 highlighted is impossible; question d asks which other values of the highlighted coefficient d are possible.
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Reposted by Nathan Day
Paul Rowlandson @drrowlandson.bsky.social · 12/09/2026
New blog post - Explores one of my favourite questions to ask after finishing a worked example: What would happen if I changed the question? wp.me/p9t8DE-s8 #mathschat #MTBoS #ukmathschat #iTeachMaths
wp.me
What Would Happen if I Changed the Question?
After completing a worked example on the board, one of my favourite questions to ask is, “What would happen if I changed the question?” More specifically, point to a number or term within the quest…
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Nathan Day @nathanday.bsky.social · 11/09/2026
In #MathsToday, Year 10 had a brief diversion to learn about the mathematics of Gerrymandering - the focus of this topic's mathematician, Moon Duchin. We watched a nice video: www.youtube.com/watch?v=tqCa... and discussed some questions from: mathematics-democracy-institute.org/gerrymanderi...
A cover page of a booklet on Chapter 2 - Expressions, featuring a bio of Moon Duchin.A slide from https://mathematics-democracy-institute.org/gerrymandering/ on the Polsby-Popper Compactness Score.
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Nathan Day @nathanday.bsky.social · 10/09/2026
Not that I know of! I'm sure there's others like it out there though.
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Nathan Day @nathanday.bsky.social · 10/09/2026
I recall weeping as it ended, for there were no worlds left to conquer.
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Nathan Day @nathanday.bsky.social · 10/09/2026
I had no Maths lessons in #MathsToday. But in #ComputerScienceToday a Year 8 class spent some time on my favourite Computer Science resource: compute-it.toxicode.fr?progression=... which has such incredible attention to detail for its level progression and visual design.
compute-it.toxicode.fr
Compute It
Let's switch roles: this time YOU are the computer !
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Nathan Day @nathanday.bsky.social · 10/09/2026
It's so good. This remains (along with the 7.1 s Nasty Negatives run) one of the achievements I'm proudest of in my life. bsky.app/profile/nath...
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Nathan Day @nathanday.bsky.social · 09/09/2026
Questions which look really messy and complicated, requiring lots of workings out that all eventually cancel out and resolve to 1 (or similar). Not unlike how the orchestra in the Beatles' A Day in the Life starts the finale jumbled, disorganised and chaotic before all resolving into a single note.
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Nathan Day @nathanday.bsky.social · 09/09/2026
In #MathsToday, Year 10 did some some variation-inspired expanding and factorising of single brackets (Task 1 in interwovenmaths.com/quadratics) before moving on to some algebraic fractions, ending with a classic 'A Day in the Life' resolution question.
Worksheet titled “Task 1: Expanding and Factorising Single Brackets”, containing questions a–z in two tables. Each row gives either a factorised or expanded algebraic expression, with a blank space for students to complete the equivalent form; expressions increase in complexity from simple linear terms to multivariable polynomials.An algebraic fractions question that cancels out to 1.
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Nathan Day @nathanday.bsky.social · 08/09/2026
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Reposted by Nathan Day
Alison Kiddle @alisonkiddle.bsky.social · 08/09/2026
These problems formed the basis of a really nice conversation between me and @samholloway.bsky.social as we were on our habitual post prandial walk yesterday evening. Trying to identify the same structure led us to talk about other related problems with this structure.
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Nathan Day @nathanday.bsky.social · 08/09/2026
Meanwhile, Year 8 in #MathsToday were continuing with their progress through their Maths Pad @mathspadnicola.bsky.social sequences booklet (which are always astonishingly good), and getting used to the format of their starters, which are currently focussing on some key number work.
Page 1 of a set of starters. Each starter is divided into four sections: Numeracy, Sequences, Solving Equations and Decimals.Page 2 of a set of starters. Each starter is divided into four sections: Numeracy, Sequences, Solving Equations and Decimals.
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Nathan Day @nathanday.bsky.social · 08/09/2026
In #MathsToday, Year 10 did some some Interwoven Related Calculations and then started on my all-new Algebra Fluency page - answering 1000+ questions between them! interwovenmaths.com/algebra It also gave me lots of data to know where to focus lessons in the Algebra topic we're about to start.
A maths worksheet titled “Task 1.3.3 Adjusted Multiplications”. It begins with “Given that 32 × 45 = 1440” and presents six questions using this fact: calculate 1/32 + 1/45; solve 32x = 1440; find the area of a 32 m by 45 m rectangle; find 32% of £45; share £1440 in the ratio 44:1; and expand 32(45x − 1).

A second section headed “Hence…” gives six related questions with adjusted values: calculate 1/16 + 1/45; solve 32x = 1472; find the area of a 32 m by 4.5 m rectangle; find 33% of £45; share £1395 in the ratio 44:1; and expand 31(45x − 1).A screenshot of https://interwovenmaths.com/algebra question
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Nathan Day @nathanday.bsky.social · 07/09/2026
There are some pages in the preview on the site. What I most appreciated was the number of questions, usually 25-40+ per section, allowing for quite a bit of granularity and variety on topics like geometry problems with complex roots that only have a couple of questions in the main textbook I use.
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Nathan Day @nathanday.bsky.social · 07/09/2026
In retrospect, I would probably have different individuals/groups work on different problems, and then come together to share their problem's solution [and find them to be the same]. Something similar to this: mathcoachblog.com/2013/05/28/t... from @boblochel.bsky.social
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