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Jonathan Hall @studymaths.bsky.social · 12h

In #MathsToday we were rearranging where factorising is required. I like how the first three are relatively easy, but our answer to "make c the subject" gives us an insight into how we might rearrange for x.

A slide with the formula ax = bx + c and four prompts to rearrange in terms of a, b, c and finally x.

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Jonathan Hall @studymaths.bsky.social · 02/10/2026

Need 100 higher tier GCSE questions for some reason? MathsBot can do that for you with one-click. mathsbot.com/revise?min=1...

A screenshot of 100 GCSE questions randomly generated with MathsBot.

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Jonathan Hall @studymaths.bsky.social · 02/10/2026

UPDATE: I finally spent a few minutes adding a much requested timer to the KS2 arithmetic tests. If you don't like it, you can click on it and it disappears. I've also created random versions of the 2024, 2025 and 2026 papers - which was A LOT more work. mathsbot.com/primary

A screenshot of a randomly generated KS2 arithmetic test with the new timer on display.

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Jonathan Hall @studymaths.bsky.social · 02/10/2026

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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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 · 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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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

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 · 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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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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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

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 · 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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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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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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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

Teaching direct or inverse proportion next week? This completion table might be useful. Try hiding different cells in each row to add to the level of challenge. mathsbot.com/tables/propo...

A screenshot of a completion table on proportion.

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Jonathan Hall @studymaths.bsky.social · 11/09/2026

UPDATE: I've just added the custom test feature to the full-sized versions of the Year 3, 4 and 5 tests. mathsbot.com/primary/year3 mathsbot.com/primary/year4 mathsbot.com/primary/year5

A screenshot of the custom test feature.

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Jonathan Hall @studymaths.bsky.social · 10/09/2026

You could show this quite nicely with Prime Factor Tiles. 😜

Using Prime Factor Tiles to demonstrate why this nice little "trick" works.

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Jonathan Hall @studymaths.bsky.social · 10/09/2026

Update: I've spent the morning adding a bunch of questions to the "Direct and inverse proportion" topic. Here's an example of a mixed exercise (and solutions) you can generate with a few clicks.

16 questions on Direct and inverse proportion.

The solutions to the questions on Direct and inverse proportion.

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Jonathan Hall @studymaths.bsky.social · 09/09/2026

First #MathsToday of the new term! Y10 were decomposing algebraic expressions into their individual factors using Prime Factor Tiles. This then led into multiplying and dividing expressions.

Prime Factor Tiles showing the algebraic decomposition of 30x²y³.

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Jonathan Hall @studymaths.bsky.social · 05/09/2026

I’m pretty sure my kid’s school got @draustinmaths.com to design their packed lunch ideas.

Idea for lunchboxes poster in the style of Dr Austin’s practice strips.

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Jonathan Hall @studymaths.bsky.social · 26/08/2026

Better late than never. mathsbot.com/gcse/boundar...

A screenshot of the latest GCSE maths grade boundaries.

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Jonathan Hall @studymaths.bsky.social · 02/08/2026

Very hot run done, now playing the SNES and listening to CD’s in the garden. I’m convinced we peaked in the 90’s.

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Jonathan Hall @studymaths.bsky.social · 13/06/2026

Update: I added a whole bunch of average and range questions to the MathsBot curriculum yesterday. Example here: mathsbot.com/unitTest?id=...

An example of a "one-click" mixed exercise on average and range. 20 different randomly generated questions.

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Jonathan Hall @studymaths.bsky.social · 11/06/2026

This was my starter yesterday to get pupils to appreciate the importance of the centre of rotation. And for the impossible one, why we also need translations. #MathsToday

Four congruent triangles drawn on a square grind in various orientations.
Above is the prompt "Can you always rotate from one triangle to another?"

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Jonathan Hall @studymaths.bsky.social · 19/05/2026

Gave this to Y8 as a starter yesterday. "If only there was a way to work it out exactly..." #MathsToday

A circle drawn on a square grid with the prompt "Estimate the area of this circle."

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Jonathan Hall @studymaths.bsky.social · 19/05/2026

We explored the link between Pythagoras and the Cosine rule in #MathsToday

A right angled triangle and a triangle with an angle of 89 degree.

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Jonathan Hall @studymaths.bsky.social · 16/05/2026

Update: You can now share example-problem pairs with an URL. Here are 24 increasingly difficult questions on Factors, Multiples and Primes. mathsbot.com/unitExample?...

An example-problem pair taken from the MathsBot curriculum.

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Jonathan Hall @studymaths.bsky.social · 09/05/2026

The weather is terrible so I've gone back into winter mode and messed around with MathsBot for a while. I've added a few new question to the averages and range topic. Example here: mathsbot.com/unitTest?id=...

A screenshot of a 10 question mixed exercise on averages and range from the MathsBot curriculum.

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Jonathan Hall @studymaths.bsky.social · 08/05/2026

Update: Just added all 9 variations of the "bread and butter" trig questions. Example here: mathsbot.com/unitTest?id=...

A mixed exercise covering all 9 variation of basic trigonometry questions.

A list of trigonometry objectives in a Strength/Target format.
1 Use the sine function to calculate the opposite side length in a right-angled triangle.
2 Use the sine function to calculate the length of the hypotenuse in a right-angled triangle.
3 Use the cosine function to calculate the adjacent side length in a right-angled triangle.
4 Use the cosine function to calculate the length of the hypotenuse in a right-angled triangle.
5 Use the tangent function to calculate the opposite side length in a right-angled triangle.
6 Use the tangent function to calculate the adjacent side length in a right-angled triangle.
7 Use the sine ratio to find missing angles in right-angled triangles.
8 Use the cosine ratio to find missing angles in right-angled triangles.
9 Use the tangent ratio to find missing angles in right-angled triangles.

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Jonathan Hall @studymaths.bsky.social · 07/05/2026

In "broken calculator" style, find angle x, but your sin button is bust. Tried a few of these types of questions with Y10 earlier this week. #MathsToday

A right angled triangle with hypotenuse 14 m and short leg 6 m. The angle between the hypotenuse and other (unlabeled) short leg is x.

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Jonathan Hall @studymaths.bsky.social · 25/04/2026

Looking to develop confidence with those "easy" one-markers? Click the question number to replace a question. The lock button keeps the topics the same if you hit "New Questions" mathsbot.com/gcse/oneMark...

A screenshot of the one-mark wonder resource.

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Jonathan Hall @studymaths.bsky.social · 25/04/2026

Update: I've created a bunch of tutorial videos for the KS2 arithmetic tests and added a link from the Primary Menu. For some reason it's getting loads of hits at the moment... mathsbot.com/primaryMenu

A screenshot of the MathsBot Primary menu.

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Jonathan Hall @studymaths.bsky.social · 17/04/2026

And today we made a maze for our Lego characters. One day I’m hopeful we might actually play Bananagram.

A maze made from banagram tiles with a Lego figure in the middle.

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Jonathan Hall @studymaths.bsky.social · 15/04/2026

We’ve arranged all the Bananagram tiles into a bar chart. #MathsToday

All the tiles in a bananagram set arranged as a bar chart.

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Jonathan Hall @studymaths.bsky.social · 05/04/2026

Update: Just added a bunch more questions to the generators. This one is one of my favourites to ask.

An example-problem pair asking if 3 lengths form a triangle.
Q1: Can you form a triangle with 2, 8 and 10 cm?
Q2: Can you form a triangle with 5, 10 and 7 cm?

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Jonathan Hall @studymaths.bsky.social · 04/04/2026

A rough draft of an idea for a goal-free style task. I want it to be as clean as possible but need to add a few more details to make it mathematically correct in terms of all the right-angles in the diagram. Any thoughts welcome.

A diagram of a circle with a radius of 1. A right-angled triangle is drawn from the centre with the hypotenuse tangent to the circle.

Above, a prompt says "What angles and lengths can you find?".

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Jonathan Hall @studymaths.bsky.social · 04/04/2026

A simple task, but one of my favourites. How do you see it?

A 4 by 4 square drawn on a grid with the instructions "Draw another square with an area twice as large."

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Jonathan Hall @studymaths.bsky.social · 02/04/2026

Watching my neighbours skip being replaced with a new empty one - I can’t help but think of Tower of Hanoi.

A full skip being replaced with an empty one.

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Jonathan Hall @studymaths.bsky.social · 29/03/2026

Finding missing side lengths is the biggest prerequisite to being able to work out the area of these shapes. Here's a simple Blank is Best to practise this skill. Before you use the slide, consider: What's the minimum number of lengths you must provide? Does it matter which ones you give?

A rectilinear hexagon with all the side labels blank - to be filled in by the teacher.

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Jonathan Hall @studymaths.bsky.social · 29/03/2026

Which calculation do you prefer? Can you explain why they all work?

An L-shaped hexagon with 4 sides labelled. Next to it are 3 calculations which all give the correct area of the shape.

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Jonathan Hall @studymaths.bsky.social · 28/03/2026

Update: I spent a fair bit of time updating my Examples tool yesterday. I added the ability to replace/hide questions on each side and improved the pen functionality. Here's a visual method for completing the square - a halfway step between algebra tiles and an algebraic method.

A screenshot of my example-problem pair tool, with a question on completing the square.

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