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nathanday.bsky.social
Nathan Day
@nathanday.bsky.social
1.3K followers 250 following 220 posts
Maths (and Computer Science) teacher.
Task interweaver.
Daydream believer.

https://interwovenmaths.com
aka @nathanday314, @[email protected]

#EduSky #UKTeaching
Posts Replies Media Videos
nathanday.bsky.social
Look who I happened to bump into...
A photo of me and Karen in a grotto/fernery.
October 23, 2025 at 5:00 PM
Reposted by Nathan Day
pippinsboss.bsky.social
If you don't know the history of zero, here's an explainer to get you up to speed with a fascinating story. Really there are two zeros: zero the digit and zero the number. So I start by exploring ancient number systems that had one or the other or both or neither.

youtu.be/7jQNTfe-5FM
Zero - The Story of a Number
YouTube video by Jim Simons
youtu.be
October 16, 2025 at 6:44 PM
Reposted by Nathan Day
atulrana.bsky.social
The greatest hits of tasks by @nathanday.bsky.social 🎉
October 11, 2025 at 11:33 AM
nathanday.bsky.social
In #MathsToday*, I introduced Year 12 to the brilliant game Digit Disguises by @davidkbutler.bsky.social.

See here:
www.adelaide.edu.au/mathslearnin...

They really enjoyed it and immediately started coming up with lots of clever strategies.

*(Actually #Maths~16DaysAgo, but I've been a bit busy!)
October 6, 2025 at 6:50 PM
Reposted by Nathan Day
arithmaticks.bsky.social
Used @nathanday.bsky.social ’s sum-product(-difference-quotient) tables in an intervention session with Y10 in #MathsToday to support their factorisation of quadratics with negatives. Was really helpful to isolate the step of considering all the sign combos! 🤩
interwovenmaths.com/four-ops-tab...
Four Operations Completion Tables - Interwoven Maths
by Nathan Day (@nathanday314) https://twitter.com/hashtag/FourOpsTables PPT Download PDF Download
interwovenmaths.com
September 23, 2025 at 5:53 PM
nathanday.bsky.social
I'm not sure 'taught and shared' sounds quite enough like 'thought and said' for this title to work, but oh well.
lasalleed.bsky.social Complete Mathematics @lasalleed.bsky.social · Sep 18
📣 #MathsConf39: The Best That Has Been Taught and Shared with Nathan Day (@nathanday314)

Explore all-time great maths tasks, why they work, and how to adapt or design your own to enrich lessons & inspire learners.

completemaths.com/community/ma...

#UKMathsChat
September 18, 2025 at 4:38 PM
Reposted by Nathan Day
lasalleed.bsky.social
📣 #MathsConf39: The Best That Has Been Taught and Shared with Nathan Day (@nathanday314)

Explore all-time great maths tasks, why they work, and how to adapt or design your own to enrich lessons & inspire learners.

completemaths.com/community/ma...

#UKMathsChat
September 18, 2025 at 4:02 PM
nathanday.bsky.social
In #MathsToday, Year 12 tackled some Underground Maths tasks on inequalities.

Inequality sets: undergroundmathematics.org/polynomials/...

Inequalities for some occasions:
undergroundmathematics.org/quadratics/i...

I always find with their tasks there's more to them than initially meets the eye.
A three-circle Venn diagram labelled A, B, and C inside a rectangle. Each region represents inequalities with certain properties: • A: the solution set is a subset of x \leq 1. • B: the solution set is of the form a \leq x \leq b. • C: the inequality is satisfied by x = 4. Below the diagram is a set of numbered inequalities in boxes. The task is to place each inequality into the correct region of the Venn diagram according to the properties of its solution set. https://undergroundmathematics.org/quadratics/inequalities-for-some-occasions A table with three columns: “Solution set”, “Graph”, and “Inequality”. Each row must be completed so that it contains: • a solution set written in set notation, • a graph showing a function or curve to help solve the inequality, • the inequality itself. Some rows are partially filled with either a solution set, a graph, or an inequality, and the student must fill in the missing parts to match them consistently. https://undergroundmathematics.org/polynomials/inequalities
September 15, 2025 at 5:10 PM
nathanday.bsky.social
In #MathsToday, Year 12 looked at some graph intersections and solving some simultaneous equations, and then sketching the graphs!
A maths worksheet titled “Simultaneous Equations & Points of Intersection.” It shows a grid where different pairs of equations intersect, and the task is to fill in the correct intersection points from a list of given coordinates. Some boxes are shaded and students must explain how many intersection points there are, without calculating the coordinates. The previous task, but with answers. An image of the graphs from the task.
September 12, 2025 at 7:06 PM
nathanday.bsky.social
In #MathsToday, Year 12 and I enjoyed doing some Susan Wall tasks.

I particularly enjoyed this one. We matched the graphs up, and then found the coordinates of all the interesting points.
“Maths question titled ‘Which equation matches which graph?’ On the left, five quadratic equations are listed: (1) y = 6x – 3x² – 3, (2) y = x² – 2x + 5, (3) y = x² – 2x – 3, (4) y = 2x – x² + 3, (5) y = 3x² – 6x + 3. On the right, five parabolas are drawn on a coordinate grid, some opening upwards and some downwards, intersecting around the origin. The task is to match each equation to its corresponding parabola and explain the reasoning.”
September 8, 2025 at 6:14 PM
Reposted by Nathan Day
nathanday.bsky.social
For those unfortunate enough to be starting back tomorrow...

Over the summer Duelling Mathematicians has had a bit of an upgrade.

Loads of new question types, game statistics, and design tweaks, but the same frenetic music and sound effects.

More to come!

interwovenmaths.com/_Duels.html
A screenshot of the end screen to a game of Duelling Mathematicians, showing the new Duel Statistics pop-up.
August 25, 2025 at 7:09 PM
nathanday.bsky.social
I hope my Year 10s have enjoyed their summer holiday work, which included various options from the likes of @ayliean.bsky.social, @tibees.bsky.social, @elliesleightholm.bsky.social, @meimaths.bsky.social, @nrichmaths.bsky.social, @simonsinghnerd.bsky.social, and @desmos.com.

(All links in alt text)
A screenshot of the following text: In case you want to do something a bit different, here's some other Mathematical things you can do over the Summer: 1) Watch some Mathematical YouTube videos. I'd suggest: Ayliean - https://www.youtube.com/@Ayliean/videos Tibees - https://www.youtube.com/@tibees/videos Ellie Sleightholm - https://www.youtube.com/@EllieSleightholm/videos 2) Do some Mathematical art. Lots of ideas here: https://www.artfulmaths.com/blog 3) Play a Mathematical game. I strongly recommend the Sumaze games (https://www.mei.org.uk/sumaze/) and Euclidea (https://www.euclidea.xyz/) 4) Read a Mathematical book. Some good suggestions here: https://nrich.maths.org/recommended-books 5) Watch a Mathematical film/documentary. I'd suggest: Hidden Figures, The Man Who Knew Infinity, or Fermat's Last Theorem (https://www.bbc.co.uk/iplayer/episode/b0074rxx/horizon-19951996-fermats-last-theorem), 6) Have a go at some Mathematical puzzles. https://nrich.maths.org/students/secondary 7) Explore Mathigon. There's lots of really cool stuff on there. https://mathigon.org/activities 8) Sign up to Parallel and have a go at some of the Parallelograms puzzles: https://parallel.org.uk/parallelograms?latest=1 9) Create some Desmos art: https://www.desmos.com/art
August 27, 2025 at 12:45 PM
Reposted by Nathan Day
karenshancock.bsky.social
I've done some work on collated my worked examples over the holidays.
Here's the database of those I've created over the past few years. Perhaps you can make use of them in your teaching too?

kshancock.co.uk/workedexampl...

#UKMathsChat
Worked Example Database | kshancock.co.uk
kshancock.co.uk
August 27, 2025 at 8:05 AM
nathanday.bsky.social
For those unfortunate enough to be starting back tomorrow...

Over the summer Duelling Mathematicians has had a bit of an upgrade.

Loads of new question types, game statistics, and design tweaks, but the same frenetic music and sound effects.

More to come!

interwovenmaths.com/_Duels.html
A screenshot of the end screen to a game of Duelling Mathematicians, showing the new Duel Statistics pop-up.
August 25, 2025 at 7:09 PM
nathanday.bsky.social
Just gave this a rather significant visual upgrade.

It's now quite colourful, matching the textbooks!

I've also added in totals, but they tend to be off by a couple of marks from the official ones as they are just the sums of the notional component boundaries.

interwovenmaths.com/_GradeBounda...
A screenshot of a website showing grade boundaries for different Maths and Further Maths papers.
August 17, 2025 at 4:43 PM
nathanday.bsky.social
FYI, I have updated my Edexcel Grade Boundaries page:
interwovenmaths.com/_GradeBounda...

Some interesting Further Maths component-level boundaries!
A Level Grade Boundaries
interwovenmaths.com
August 14, 2025 at 8:49 AM
nathanday.bsky.social
Well that's one job from my summer to-do list done! - an updated Islands generator via @desmos.com

www.desmos.com/calculator/e...

See below for some questions I've used with it!
Islands
www.desmos.com
July 20, 2025 at 4:09 PM
nathanday.bsky.social
Calling all Maths teachers!

What are some of your all-time great tasks for secondary Maths?

Ones that could have their place in any curriculum, one that should be studied in PGCE courses, ones that started whole new genres of tasks...
... or just ones you really like.

(see some of mine below)
July 8, 2025 at 4:26 PM
nathanday.bsky.social
In Year 10 #MathsToday, we did this series of algebray volume and surface area questions that originated in a lovely Don Steward task.

The third row gave nice practice of expanding triple brackets and factorising non-monic quadratics.

donsteward.blogspot.com/2014/03/cubo...
A series of maths questions featuring cuboids with the same volumes/surface areas, allowing you to form and solve equations to find missing lengths. The original task, featuring 7 cuboids with the same volume and missing lengths, from Don Steward.
July 4, 2025 at 5:59 PM
nathanday.bsky.social
In #MathsToday, Year 10 enjoying having a go at this Quadratics Always/Sometimes/Never task (which I did as a card sort in pairs).

It was really interesting to tease out the subtleties, look at different edge cases, and keep bringing things back to the graphs.
Always? Sometimes? Never? x^2 + Ax + B = (x+c)^2+8 1. C is less than A. 2. The vertex has an x-coordinate of 8. 3. B is less than A. 4. If C is an integer, so is A. 5. If A is an integer, so is B. 6. B is greater than 8. 7. If you know B, you can work out A and C. 8. The quadratic has two roots. 9. The minimum value of the quadratic is 8. 10. If you know A, you can work out B and C. Printable version of the activities, to be cut up and used as a card sort.
June 25, 2025 at 4:36 PM
nathanday.bsky.social
I think these questions need a tag! Maybe #x^2-7x+10?
@ljohns6.bsky.social
The masses of 28 parcels are represented in the histogram. Find x. An image of a histogram with: • the first bar covering 0 < m < 3 kg and with frequency density 2; • the second bar covering 3 < m < 7 kg with frequency density 1; • the third bar covers 7 < m < x kg with frequency density x Find an expression for the value of the 𝑛th square to be shaded in. A bag contains 𝑥 counters. Three of the counters are green. Two of the counters are red. The rest of the counters are blue. Pete takes a counter from the bag and replaces it. Liza then also takes a counter from the bag. Find an expression for the probability that Pete’s counter was blue and Liza’s counter wasn’t red. A right-angled triangle with a horizontal hypotenuse of length 7 and a height of sqrt(10). x is labelled as the distance from where the height meets the hypotenuse to the corner of the triange. The question says to find x.
June 21, 2025 at 7:54 PM
Reposted by Nathan Day
ljohns6.bsky.social
Just delivered my first maths workshop at #MathsConf38 and I’m buzzing! Being 10% braver is HARD but so worth it.💪
Thank you to everyone who came along. Keep an eye out for resources and join the challenge! @nathanday.bsky.social has set the bar high! 🔥 #InterweavingMaths
#MathsForFun
#LoveMaths
June 21, 2025 at 6:34 PM
nathanday.bsky.social
I had a great time today at #MathsConf38.
I particularly enjoyed @ljohns6.bsky.social's workshop about connecting concepts.

At the end we were challenged us to come up with a question featuring the expression 𝑥² − 7𝑥 + 10.

Here's what I came up with.
The masses of 28 parcels are represented in the histogram. Find x. An image of a histogram with: • the first bar covering 0 < m < 3 kg and with frequency density 2; • the second bar covering 3 < m < 7 kg with frequency density 1; • the third bar covers 7 < m < x kg with frequency density x
June 21, 2025 at 5:56 PM
nathanday.bsky.social
I just made a last minute sign up to attend #MathsConf38!
Looking forward to seeing
1 - @stephenfroggatt.bsky.social,
2 - @arithmaticks.bsky.social,
3 - Paul Rodrigo,
4 - @mathsjem.bsky.social,
5 - @ljohns6.bsky.social!
June 18, 2025 at 7:28 PM
nathanday.bsky.social
It's Pride Month.
I feel like it is important to recognise this in school, especially given recent developments at home and abroad.

Here's two ways I'm doing that.

LGBTQIA+ Mathematicians (new!): interwovenmaths.com/famous-mathe...

Pride Flag Maths activities:
interwovenmaths.com/pride-flag-m...
A title page for a set of posters of 'LGBTQIA+ Mathematicians from around the world' Thumbnails of posters of 12 different 'LGBTQIA+ Mathematicians from around the world' A set of Maths questions based on the Progress Pride flag. Another set of Maths questions based on the Progress Pride flag.
June 2, 2025 at 8:18 PM