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Jonathan Hall

@studymaths.bsky.social
1.3K followers 268 following 969 posts

Maths teacher. Creator of MathsBot.com.

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Reposted by Jonathan Hall
Carl Brandt Long @carlblong.bsky.social · 44m
Are you familiar with @fawnnguyen.substack.com's visual patterns collection? share.google/C9Q1eK412LQ4...
share.google
Visual Patterns
Patterns to grow algebraic thinking and reasoning.
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Jonathan Hall @studymaths.bsky.social · 42m
I am, but like many things I'd forgotten about it! Thanks for the reminder.
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Jonathan Hall @studymaths.bsky.social · 3h
A sequences begins: 4, 6, 10, 16, ... Is it a quadratic or Fibonacci style sequence? Is it possible to be given five (or more) terms of a sequence and still be undecided?
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Jonathan Hall @studymaths.bsky.social · 4h
I didn't get round to it, but I'm hoping to show them this slide soon.
The first 4 terms of 4 different quadratic patterns built from squares.
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Reposted by Jonathan Hall
Nathan Day @nathanday.bsky.social · 19h
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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Jonathan Hall @studymaths.bsky.social · 19h
Two-way completion table? I’ve no idea. I don’t think it’s an SVG though.
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Jonathan Hall @studymaths.bsky.social · 01/10/2026
UPDATE: I've just added randomly generated versions of the 2026, 2025 and 2024 papers to the compact and full versions of the KS2 arithmetic papers. mathsbot.com/primary/ks2M... mathsbot.com/primary/ks2
A screenshot of the Key Stage 2 Arithmetic Test - Compact Version with a drop down menu to the 2024 year.
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Jonathan Hall @studymaths.bsky.social · 30/09/2026
Which led nicely into a discussion with this slide. The algebraic nth term rule at the bottom was initially hidden from view. #MathsToday
The first 5 terms of n^2 + 2n + 3 represented with Dienes blocks.
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Jonathan Hall @studymaths.bsky.social · 30/09/2026
I introduced quadratic sequences with Y11 in #MathsToday with this matching activity.
Four quadratic sequences, each with three different representations - a diagram, the number sequence and the nth term rule.
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Jonathan Hall @studymaths.bsky.social · 29/09/2026
Not seen this, but I know he’s a fan of the primary arithmetic section of the site - which I updated last week.
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Reposted by Jonathan Hall
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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Reposted by Jonathan Hall
Miss Morris @morrismaths359.bsky.social · 28/09/2026
#Mathstoday One of the things I find is in the lesson students can factorise. As soon as you mix up the questions they can't do it. Got my Yr10 to have a go at these and it was unsurprisingly how much slower they were.
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Jonathan Hall @studymaths.bsky.social · 27/09/2026
Update: Added a few more surface area and volume questions. Example here: mathsbot.com/unitTest?id=...
An example mixed exercise on surface area and volume of 3D shapes.
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Reposted by Jonathan Hall
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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Jonathan Hall @studymaths.bsky.social · 25/09/2026
Randomised versions of the 2026 and 2025 papers are now done.
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Jonathan Hall @studymaths.bsky.social · 24/09/2026
Here's another example. What's the same and what's different? It's always nice to link together what pupils may often see as totally different topics. mathsbot.com/unitExample?...
Two objectives side by side. The left is a factorise a difference of two-squares and the other expanding a binomial involving surds and conjugates.
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Jonathan Hall @studymaths.bsky.social · 24/09/2026
The default is to show the same objective side-by-side, but you can click the "Compare" box at the bottom to show a different objective on each side.
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Jonathan Hall @studymaths.bsky.social · 24/09/2026
Update: I tidied up the Example-Problem pair tool a bit today. My favourite feature is the ability to compare any two objectives side by side - making use of variation. Here's a simple example for the volume of a sphere. mathsbot.com/unitExample?...
Two problems side-by-side where you are asked to find the volume of a sphere. One where the radius is given, the other with the diameter given.
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Jonathan Hall @studymaths.bsky.social · 24/09/2026
Yesterday we looked at algebraic function machines. Year 7 enjoyed making the inputs and outputs with the real tiles and asked me if they could use them again in the next lesson. I also enjoyed using my new pen tool of course! #MathsToday
A function machine using algebra tiles shoing why 3(x + 2) = 3x + 6.
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Jonathan Hall @studymaths.bsky.social · 24/09/2026
UPDATE: Demonstrating the new "Custom Years" feature on the MathsBot arithmetic tests. mathsbot.com/primary/ks2 mathsbot.com/primary/ks2M... youtu.be/2XxNDQwzX0E
youtu.be
Custom years added to the Arithmetic Tests. (Finally!)
YouTube video by Jonathan Hall
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Reposted by Jonathan Hall
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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Jonathan Hall @studymaths.bsky.social · 21/09/2026
Looking at the volume and surface area of cones with Y11 in #MathsToday. I scribbled a dodgy version of this task on the board when a few pupils were getting confused with the difference between the height and slope of a cone. I've neatened it up here now.
A picture of two cones, one with the height given and the other the slope length.

The task asks pupils to decide which cone is easiest to find the volume of and which would be easiest to find the surface area of.
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Reposted by Jonathan Hall
Amanda Austin @draustinmaths.com · 20/09/2026
New A-level Further Maths resources added today: ✨Different Forms of Complex Numbers Fill in the Blanks ✨Multiplying and Dividing Complex Numbers Match-Up Steadily building a (hopefully useful) bank of Further Maths resources at www.draustinmaths.com/a-level-further-maths #MathsToday #ALevelMaths
Multiplying and dividing complex numbers in exponential form match-up activity suitable for A-level Further Maths students.Different forms of complex numbers fill in the blanks activity suitable for A-level Further Maths students.
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Jonathan Hall @studymaths.bsky.social · 20/09/2026
Ha, yes - I just replied to your other post with something similar!
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Jonathan Hall @studymaths.bsky.social · 20/09/2026
I did pretty much the same. I imagine it would be tougher if one row wasn't a nice double of the other.
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Jonathan Hall @studymaths.bsky.social · 20/09/2026
Good idea - done!
The grid method with darker borders added to separate the products from the sums.
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Jonathan Hall @studymaths.bsky.social · 20/09/2026
Update: Just added a "Show Totals" checkbox to my Grid Method resource. It means you can now make some nice working backwards questions. I found this one surprisingly hard - I'd be interested to hear your method for solving it. mathsbot.com/tools/gridMe...
A 2 by 2 digit multiplication problem with only two subtotals given (210 and 300) and the grand total of 315.
All the other information is missing.
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Reposted by Jonathan Hall
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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Jonathan Hall @studymaths.bsky.social · 20/09/2026
The idea of Zero Pairs crops up in a range of topics involving number and algebra. Here are a few examples. Where else do they appear? mathsbot.com/manipulative...
A one-slide poster explaining Zero Pairs and where they might occur across different topics.
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Jonathan Hall @studymaths.bsky.social · 19/09/2026
Oh, and I added the new Pen Tool Thingy as well.
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Jonathan Hall @studymaths.bsky.social · 19/09/2026
Update: I've added a "Toss" button to the Algebra Discs. Mainly (exclusively?) useful for creating quick questions on collecting like terms. mathsbot.com/manipulative...
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Jonathan Hall @studymaths.bsky.social · 19/09/2026
C1 but I'd like to say 0.2C
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Jonathan Hall @studymaths.bsky.social · 19/09/2026
I've rolled this out to some of the other manipulatives now. - Cuisenaire rods - Dienes Blocks - Place Value Counters - Prime Factor Tiles - Fraction Wall mathsbot.com/manipulative... #MathsbotToday
mathsbot.com
Manipulatives - MathsBot.com
A huge collection of virtual manipulatives. Algebra Tiles, Dienes Blocks, Cuisenaire Rods, Geoboards, Counters, and much more.
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Reposted by Jonathan Hall
CantabKitty @cantabkitty.bsky.social · 19/09/2026
I sent this link round to colleagues the day before everyone had to pick their performance management targets (one of which is a "CPD" target) and to my delight/horror, several long-standing admin staffers told me they had decided to learn Excel this year for their CPD target. #ExcelToday
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Jonathan Hall @studymaths.bsky.social · 19/09/2026
Thanks. I should have mentioned I made a template with 8 tabs of fake data so staff can try and replicate what I do in each video. Here it is: 1drv.ms/x/c/b409027c...
1drv.ms
#Templates.xlsx
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Jonathan Hall @studymaths.bsky.social · 19/09/2026
You’ll always be Algebra Tile Man!
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Jonathan Hall @studymaths.bsky.social · 18/09/2026
My youngest just started school so I find myself with DOUBLE my usual MathsBotting time. I do miss Daddy-Daughter day though. 🥲
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Jonathan Hall @studymaths.bsky.social · 18/09/2026
Ha! Apologies for the wait.
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Reposted by Jonathan Hall
Darren Elgar @elgarmaths.bsky.social · 18/09/2026
THIS IS WHAT THE WORLD HAS BEEN WAITING FOR!!!!
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Jonathan Hall @studymaths.bsky.social · 18/09/2026
Only took me 7 years @atulrana.bsky.social.
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Jonathan Hall @studymaths.bsky.social · 18/09/2026
UPDATE: I've just added a pen overlay tool to the Algebra Tiles. It needs a bit of tweaking (rubber tool etc) and once I'm happy I'll roll it out to the rest of the manipulatives. mathsbot.com/manipulative...
A screenshot of the Algebra Tiles tool with the new pen overlay being used. In this case to complete the square.
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Reposted by Jonathan Hall
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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Reposted by Jonathan Hall
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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Jonathan Hall @studymaths.bsky.social · 14/09/2026
Filling the blanks in linear sequences with Y7 in #MathsToday. Can you do it without the number line?
Find the missing terms in these linear sequences.
Four linear sequences each with 7 and 19 given but with an increasing number of gaps to fill between these terms.
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Reposted by Jonathan Hall
Colleen Young @colleenyoung.bsky.social · 14/09/2026
colleenyoung.org/2026/09/12/b...
colleenyoung.org
Mathematics Resources for September 2026.
Explore essential resources for the new term, including GCSE and A Level transition guides, and valuable mathematics materials.
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Jonathan Hall @studymaths.bsky.social · 13/09/2026
And here's me modelling a possible solution. youtu.be/xEptbRgNnmU (Bonus points if you can tell me how many different solutions there are!)
youtu.be
Using Prime Factor Tiles to divide a set of numbers into two groups with equal products.
YouTube video by Jonathan Hall
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Jonathan Hall @studymaths.bsky.social · 13/09/2026
I was reminded of this task by @morrismaths359.bsky.social earlier this week. It's one of my favourites, so I've recorded a quick video to demonstrate how you can model a solution using prime factor tiles. Video in the next post...but first here's the task.
2, 3, 4, 5, 6, 7, 8, 9, 10

Fill the blanks with the numbers above to make the calculation correct. One number is not used.

__ × __ × __ × __ = __ × __ × __ × __
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Reposted by Jonathan Hall
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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Jonathan Hall @studymaths.bsky.social · 13/09/2026
Teaching sharing in a ratio soon? This completion table can generate plenty of practice for each skill - depending on the cells you reveal. mathsbot.com/tables/ratio
A screenshot of the "Sharing in a Ratio" completion table resource from MathsBot.
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Jonathan Hall @studymaths.bsky.social · 12/09/2026
Worth it for the sweet sweet K.
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