Nathan Day
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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
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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
nathanday.bsky.social
To be fair, I already suggested it to you as a title in a conversation two years ago!
September 18, 2025 at 4:58 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
Or, as David Foster Wallace put it, 'There is no such thing as not worshipping. Everybody worships.'
"Because here’s something else that’s weird but true: in the day-to-day trenches of adult life, there is actually no such thing as atheism. There is no such thing as not worshipping. Everybody worships. The only choice we get is what to worship. And the compelling reason for maybe choosing some sort of god or spiritual-type thing to worship–be it JC or Allah, be it YHWH or the Wiccan Mother Goddess, or the Four Noble Truths, or some inviolable set of ethical principles–is that pretty much anything else you worship will eat you alive. If you worship money and things, if they are where you tap real meaning in life, then you will never have enough, never feel you have enough. It’s the truth. Worship your body and beauty and sexual allure and you will always feel ugly. And when time and age start showing, you will die a million deaths before they finally grieve you. On one level, we all know this stuff already. It’s been codified as myths, proverbs, clichés, epigrams, parables; the skeleton of every great story. The whole trick is keeping the truth up front in daily consciousness. Worship power, you will end up feeling weak and afraid, and you will need ever more power over others to numb you to your own fear. Worship your intellect, being seen as smart, you will end up feeling stupid, a fraud, always on the verge of being found out. But the insidious thing about these forms of worship is not that they’re evil or sinful, it’s that they’re unconscious. They are default settings. They’re the kind of worship you just gradually slip into, day after day, getting more and more selective about what you see and how you measure value without ever being fully aware that that’s what you’re doing." https://fs.blog/david-foster-wallace-this-is-water/
September 13, 2025 at 10:16 AM
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
Other ones we've done include:
1) another nice quadratics task with some lovely generalisinging

2) an odd one out indices task, with opportunities for some creativity when giving the odd ones out friends!
Maths question titled ‘Suggest possible equations for the graphs on the diagram. Generalise your answer.’ The diagram shows two parabolas: one opening upwards and one opening downwards. They touch at a single point above the x-axis, forming a point of tangency. The task is to suggest equations for these parabolas and to generalise the form of such equations. Maths problem saying ‘Identify the odd one out in each row. Fill the gap so that it is no longer odd.’ In each row there are three expressions with powers, with one that is not equal to the other two. There is a space on each row to fill with something equal to the odd one out.
September 8, 2025 at 6:31 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
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
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
[Part 2]

The final slide then just said:
"Ask a mathematical question about islands. Answer it."
Draw an island where the amount of beach is less than the perimeter of the land. Imagine you have an 𝑛 by 𝑛 square island. Write an expression for the: Amount of land Amount of beach Perimeter of land Fraction of the total island that is land Imagine you have an 𝑚 by 𝑛 rectangular island. Write an expression for the: Amount of land Amount of beach Perimeter of land Fraction of the total island that is land Find two different rectangular islands that have the same amount of land as beach. Prove that these are the only two possible islands.
July 20, 2025 at 4:09 PM
nathanday.bsky.social
These are the slides I used in a Year 9 lesson looking at Islands. [Part 1]
Draw: An example of an island. Something that is almost an Island. Something that is definitely not an island. Draw the smallest possible island that has more land than beach. Draw the largest possible island that has more beach than land. Draw an island with the same amount of land as beach.
July 20, 2025 at 4:09 PM
nathanday.bsky.social
These are the first slides I made on Islands.
Islands are made up of pieces of land completely surrounded by beaches. This island has 28 km? of land, and 40 km? of beach. What questions could you ask about islands? Islands are made up of pieces of land completely surrounded by beaches. This island has 28 km? of land, and 40 km of beach. a. What is the smallest possible island that has more land than beach? b. Can you make an island with the same amount of land as beach? c. Is the amount of beach always more than the perimeter of the land?
July 20, 2025 at 4:09 PM
nathanday.bsky.social
It also features in @studymaths.bsky.social's excellent CPD session 'My Top-Five Four-Digit Numbers'.

Available at mathsbot.com/cpdMenu
(if you're subscribed to the MathsBot Patreon, which you absolutely should be!)
My Top-Five Four-Digit Numbers https://mathsbot.com/cpdMenu
July 8, 2025 at 6:49 PM
nathanday.bsky.social
I got a bit carried away with making Which is Bigger? questions back in 2022!
July 8, 2025 at 6:37 PM
nathanday.bsky.social
Comparing Expressions - ICCAMS (@profsmudge.bsky.social)

www.ncetm.org.uk/media/jaxntu...

Which is larger, 3n or n+3?

The opener to the incredible series of ICCAMS algebra lessons. So many different mathematical ideas can be seen when students approach such a simple-seeming prompt.
Which is larger 3n or n+3? https://www.ncetm.org.uk/media/jaxntuce/iccams-handbook-1.pdf
July 8, 2025 at 6:32 PM
nathanday.bsky.social
Equivalent Fractions - @ncetm.bsky.social Checkpoint

www.ncetm.org.uk/classroom-re...

So many of the NCETM Checkpoints belong in this collection. This one is probably my favourite though.
Equivalent Fractions Checkpoint https://www.ncetm.org.uk/classroom-resources/checkpoints/
July 8, 2025 at 5:57 PM
nathanday.bsky.social
Ooh yes absolutely! I love a trig/pythag pile-up.

This one is a particular favourite:
www.tes.com/teaching-res...
Pythagoras Pile Up https://www.tes.com/teaching-resource/pythagoras-pile-up-11270615
July 8, 2025 at 5:51 PM
nathanday.bsky.social
A related task I love is Paper Clip from Illustrative Mathematics

tasks.illustrativemathematics.org/content-stan...
Paper Clip from Illustrative Mathematics https://tasks.illustrativemathematics.org/content-standards/tasks/415
July 8, 2025 at 5:20 PM
nathanday.bsky.social
Gradient Match (undergroundmathematics.org/introducing-...) is another highlight for me!
Gradient Match from Underground Maths https://undergroundmathematics.org/introducing-calculus/gradient-match
July 8, 2025 at 5:16 PM
nathanday.bsky.social
Ooh yes, I love Picture the Process (undergroundmathematics.org/thinking-abo...)

My favourite has to be Teddy Bear though!
undergroundmathematics.org/circles/tedd...
Teddy Bear from Underground Maths https://undergroundmathematics.org/circles/teddy-bear
July 8, 2025 at 5:15 PM
nathanday.bsky.social
Mental Mathemagician by www.yummymath.com/

Not sure this one is still on their site any more, but I found it on the Internet Archive here:
web.archive.org/web/20160814...

A version sans Comic Sans would be even better!
Mental Mathemagician by YummyMath
July 8, 2025 at 5:14 PM
nathanday.bsky.social
Laws of Exponents from Open Middle (@openmiddle.com) and @shaunteaches.bsky.social

www.openmiddle.com/laws-of-expo...

I love lots of Open Middle tasks. This one is possibly my favourite on the site.
Laws of Exponents on Open Middle https://www.openmiddle.com/laws-of-exponents/
July 8, 2025 at 5:09 PM
nathanday.bsky.social
Absolutely love both of these. NRICH is just full of amazing tasks like these.

nrich.maths.org/problems/sha...

nrich.maths.org/games/factor...
NRICH's Shape Times Shape https://nrich.maths.org/sites/default/files/thumbnails/content-id-5714-ShapeTimesShapeSheet.pdf
July 8, 2025 at 4:56 PM
nathanday.bsky.social
Ooh yes. I love this one!

mei.org.uk/app/uploads/...
MEI Integral's Transforming Graphs https://mei.org.uk/app/uploads/2021/09/07-graphs-and-transformations-res.pdf
July 8, 2025 at 4:55 PM