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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

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

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

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 · 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...

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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

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

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.

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.

$Two algebraic fraction identities labelled a and b, asking which is easier. The coefficients 42 in a and 9 in b are highlighted in purple$ $Two follow-up algebraic fraction identities labelled c and d. Question c asks why the identity with 14 highlighted is impossible; question d asks which other values of the highlighted coefficient d are possible.$

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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

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 · 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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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

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

In #MathsToday, I had my first after-school lesson with Year 10 Level 2 Further Maths. We looked at some different problems that just happened have some Pascal's triangle under the surface. Then explored how you can interpret each problem either recursively or combinatorially.

A selection of problems related to Pascal's triangle.

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Nathan Day @nathanday.bsky.social · 04/09/2026

I'm going to try to do #MathsToday as consistently as possible this year (although I might struggle on days when I only teach Computer Science!). Today, in my first lesson with Y10, we did some of @dandraper.bsky.social's lovely significant figures tasks: mrdrapermaths.wordpress.com/2020/11/14/z...

mrdrapermaths.wordpress.com

Zeros Are Nothing? Zeros Are Everything!

Rounding and Place Value Digit ProblemsDownload Rounding and Place Value Venn DiagramsDownload Open Middle Style Digit Venn Diagram ProblemsDownload Following on from my previous post about using d…

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Nathan Day @nathanday.bsky.social · 31/08/2026

*New* Mathematician of the Week Posters Here's something I've been working on over the summer. A growing set of posters of mathematicians doing cool things with maths. Each comes in black/white or colour, with a quote and a link to read more. Check them out at: interwovenmaths.com/mathematicians

Collage of 25 posters of mathematicians.

Screenshot of week 1, showing a poster, a quote and a link.

Screenshot of week 14, showing a poster, a quote and a link.

Screenshot of week 12, showing a poster, a quote and a link.

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Nathan Day @nathanday.bsky.social · 13/08/2026

In retrospect, redesigning the mobile view of my Edexcel Grade Boundaries page wasn't a task best left for the morning of Results Day. Oh well, here it is. interwovenmaths.com/grade-bounda...

Edexcel A Level Maths Grade Boundaries by Paper.

Edexcel Further Maths Individual Paper boundaries

Edexcel Further Maths Grade Boundaries by Option Choice

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Nathan Day @nathanday.bsky.social · 06/07/2026

I'm on my way to Lincoln Bishop University to talk about all things Interweaving at the East Midlands East Maths Hub Annual Conference. If you'd be interested in me doing a workshop or similar at your school, conference, university, work group, etc., just reach out! interwovenmaths.com/cpd

Title slide for Don’t Stop Interweavin’, a CPD presentation about Interweaving.

Slide comparing six proportional reasoning problems and asking which one is the odd one out.

Slide showing several right-angled triangle questions with equivalent side-length structures in different forms.

Slide showing six multiplication-related questions built around the fact that 32 × 45 = 1440.

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Nathan Day @nathanday.bsky.social · 01/07/2026

I'm on my way to my first MEI Conference #MEIConf2026, and have packed with just enough space to hopefully take home one of @danihosford.bsky.social / @tlmaths.bsky.social 's books! Excitement abounds.

A photo of me on a train at Nottingham station.

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Jo Morgan @mathsjem.bsky.social · 07/06/2026

New! My 199th gems post. Ideas, updates and resources for maths teachers. 💎 www.resourceaholic.com/2026/06/5-ma... Hat tips to follow. #ukmathschat #mathstoday

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Nathan Day @nathanday.bsky.social · 01/06/2026

Interwoven Maths has had an exciting Half Term, including the following: 1) interwovenmaths.com/resources A whole new homepage, allowing you to sort by popularity and search for any topic.

interwovenmaths.com

Interwoven Maths | Maths Teaching Resources by Nathan Day

Maths teaching resources, interwoven tasks, booklets and classroom tools by Nathan Day.

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Nathan Day @nathanday.bsky.social · 17/05/2026

Here's something I've been working quite hard on recently: classduels.com/maths/ A Maths game featuring: - two-player (split screen, can be done on a interactive whiteboard) and single-player modes - 50+ topics across KS3-KS5 - a version for the Australian curriculum: classduels.com/maths/au/ 😉

classduels.com

Maths Revision Quizzes | Class Duels

Practise maths with free Class Duels revision quizzes for KS3, GCSE and A Level, covering Negatives, Rounding, Fractions, Percentages and more.

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Karen @karenshancock.bsky.social · 22/04/2026

Some "Power Equations" , equations with indices, or whatever you like to call them. (And so detached from posting here I realise I don't have a clue what hashtag to use... 😐) Downloadable version with worked solutions here: kshancock.co.uk/lessonresour...

A white page showing four handwritten algebra questions, each inside a red rectangular box, about solving equations using indices.
The first box reads: “Solve: 3 to the power 2x squared times 27 to the power 2x squared times 21 to the power x minus 1 equals 7 to the power x times 3 to the power 6, all over 63.”
The second box reads: “Solve: open bracket 4x times 2 to the power x close bracket squared, times 100 to the power x, times 2 to the power 14 equals 5 to the power 2x over 2 times 4 to the power 2x.”
The third box reads: “Solve: 9 to the power three quarters times 5 to the power x times seven fifths equals 3 times the square root of 21 times 35 times 5 to the power x plus 1.”
The fourth box reads: “Solve: 5 to the power minus x squared times 6 to the power x times 10 equals 2 to the power x plus 1 times 3 squared times 25 to the power minus x plus three halves.

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Nathan Day @nathanday.bsky.social · 10/04/2026

Anybody else coming along to this tomorrow? It would be nice to see some familiar faces 😀

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Nathan Day @nathanday.bsky.social · 20/03/2026

A few weeks ago, I asked for different ways a student might notice they've made a mistake. I'd now love your ideas for techniques that can students use to check their answers. e.g. - substitute a solution back in to check it works - redo a question with a different method bsky.app/profile/nath...

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Nathan Day @nathanday.bsky.social · 01/03/2026

What warning signs could students pick up on that they might have gone wrong in an answer? e.g. - an unexpected negative/decimal answer, - an answer requiring many more/fewer steps than the number of marks would suggest, - an answer that would be weird in context (e.g. a taxi costing £3000) ...

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Nathan Day @nathanday.bsky.social · 15/12/2025

'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.

interwovenmaths.com

Christmaths Carols - Interwoven Maths

Full Lyrics Fairytale of Arboretum Street (by Mr Day) O Sum All Your Data (by Madeline Barnicle, adapted by Mr Day) Hark! The Herald Angles

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Nathan Day @nathanday.bsky.social · 23/10/2025

Look who I happened to bump into...

A photo of me and Karen in a grotto/fernery.

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Jim Simons @pippinsboss.bsky.social · 16/10/2025

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

youtu.be

Zero - The Story of a Number

YouTube video by Jim Simons

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Atul Rana @atulrana.bsky.social · 11/10/2025

The greatest hits of tasks by @nathanday.bsky.social 🎉

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Nathan Day @nathanday.bsky.social · 06/10/2025

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!)

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Kathryn Clark @arithmaticks.bsky.social · 23/09/2025

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...

interwovenmaths.com

Four Operations Completion Tables - Interwoven Maths

by Nathan Day (@nathanday314) https://twitter.com/hashtag/FourOpsTables PPT Download PDF Download

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Nathan Day @nathanday.bsky.social · 18/09/2025

I'm not sure 'taught and shared' sounds quite enough like 'thought and said' for this title to work, but oh well.

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Complete Mathematics @lasalleed.bsky.social · 18/09/2025

📣 #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

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Nathan Day @nathanday.bsky.social · 15/09/2025

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

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Nathan Day @nathanday.bsky.social · 12/09/2025

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.

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Nathan Day @nathanday.bsky.social · 08/09/2025

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.”

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Nathan Day @nathanday.bsky.social · 25/08/2025

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.

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Nathan Day @nathanday.bsky.social · 27/08/2025

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)

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Karen @karenshancock.bsky.social · 27/08/2025

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

kshancock.co.uk

Worked Example Database | kshancock.co.uk

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Nathan Day @nathanday.bsky.social · 25/08/2025

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Nathan Day @nathanday.bsky.social · 17/08/2025

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.

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