@nathanday.bsky.social
Maths (and Computer Science) teacher. Task interweaver. Daydream believer. https://interwovenmaths.com aka @nathanday314, @nathanday@mathstodon.xyz #EduSky #UKTeaching
A selection of 4 questions involving the Harmonic Mean in different contexts.
A selection of 4 questions involving Product Rule for Counting in different contexts.
And a couple more...
28.01.2026 22:37 — 👍 0 🔁 0 💬 0 📌 0
A selection of 6 questions using proportional reasoning in different contexts with the same numbers. A prompt saying 'Which is the odd one out?'
A selection of 6 questions using linear relationships in different contexts with the same numbers. A prompt saying 'Change each question to make the answer 43.'
A selection of 6 questions involving reciprocals in different contexts with the same numbers.
A selection of 6 questions involving manipulating a given multiplication in different contexts.
I'd consider these to all be in the realm of Different Surface Same Deep, I reckon.
Some more available here:
interwovenmaths.com/daydream-int...
and here: interwovenmaths.com/making-conne...
Only the two I saw on the Chalkdust website! 🙂
16.12.2025 19:58 — 👍 0 🔁 0 💬 0 📌 0'Christmaths Carols' has had a big upgrade for this year.
Now featuring 12 different songs, and recordings with my slightly dodgy piano and vocals!
interwovenmaths.com/christmaths
I'm looking forward to having a big sing-along with them in school later this week.
'Which of these numbers changes most when rounded to 4 decimal places?'
24.10.2025 13:02 — 👍 2 🔁 0 💬 0 📌 0Thankfully not! We were in the grotto/fernery in the Swiss Garden at Shuttleworth.
23.10.2025 18:31 — 👍 1 🔁 0 💬 0 📌 0
A photo of me and Karen in a grotto/fernery.
Look who I happened to bump into...
23.10.2025 16:59 — 👍 4 🔁 0 💬 1 📌 0
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
The greatest hits of tasks by @nathanday.bsky.social 🎉
11.10.2025 11:33 — 👍 2 🔁 1 💬 0 📌 0Unfortunately, for me, there was an even number in the class, so I had no-one to play against.
Fortunately, however, I had an online version of the game I made, which allowed me to play against the computer instead!
interwovenmaths.com/_DigitDisgui...
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!)
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...
To be fair, I already suggested it to you as a title in a conversation two years ago!
18.09.2025 16:58 — 👍 1 🔁 0 💬 0 📌 0I'm not sure 'taught and shared' sounds quite enough like 'thought and said' for this title to work, but oh well.
18.09.2025 16:38 — 👍 2 🔁 0 💬 2 📌 0
📣 #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
In particular, the second row of the table (Finding an inequality with solution set 0 < x ≤ 1) prompted great discussions about whether it could be done with a quadratic, properties of asymptotes, etc.
15.09.2025 17:12 — 👍 2 🔁 0 💬 0 📌 0
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
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.
"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/
Or, as David Foster Wallace put it, 'There is no such thing as not worshipping. Everybody worships.'
13.09.2025 10:16 — 👍 1 🔁 0 💬 1 📌 0
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.
In #MathsToday, Year 12 looked at some graph intersections and solving some simultaneous equations, and then sketching the graphs!
12.09.2025 19:06 — 👍 18 🔁 6 💬 1 📌 2Lots more of Susan Wall's excellent tasks can be found at:
www.stem.org.uk/resources/re...
I'm finding a lot of them are great for generating interesting discussions and helping me work out which bits of the early chapters of AS Pure can be skipped.
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.
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 ‘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.”
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.
A screenshot of the end screen to a game of Duelling Mathematicians, showing the new Duel Statistics pop-up.
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
It's a ship joke.
29.08.2025 13:04 — 👍 1 🔁 0 💬 1 📌 0
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
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)
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
I love these reflections, especially 4.
I often tell students how I used to teach DofE expeditioners to keep checking that things they could see on the map matched reality and that things they saw in reality could also be found on the map.
Always looking out for mathematical points of interest!
A screenshot of the end screen to a game of Duelling Mathematicians, showing the new Duel Statistics pop-up.
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
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...
FYI, I have updated my Edexcel Grade Boundaries page:
interwovenmaths.com/_GradeBounda...
Some interesting Further Maths component-level boundaries!
