ProfSmudge
@profsmudge.bsky.social
School maths should be more than tables and algorithms. I try to write materials that show that. Dietmar Küchemann
Two subtly different methods for solving an equation with the unknown on both sides
February 13, 2026 at 11:43 AM
Two subtly different methods for solving an equation with the unknown on both sides
Lawrence Atkinson, a 'minor' British artist (!873 - 1931).
Fab
Fab
February 8, 2026 at 7:30 PM
Lawrence Atkinson, a 'minor' British artist (!873 - 1931).
Fab
Fab
In #MathsToday we worked on 16÷6.
A good follow up might be to explore '4 chocolate bars shared by 6 people'.
A good follow up might be to explore '4 chocolate bars shared by 6 people'.
February 4, 2026 at 3:31 PM
In #MathsToday we worked on 16÷6.
A good follow up might be to explore '4 chocolate bars shared by 6 people'.
A good follow up might be to explore '4 chocolate bars shared by 6 people'.
In the January 2026 edition of Maths in School, the LUMENaries Shore, Foster and Francome present an intriguing method for solving simultaneous equations. Here it is applied to a simple linear equation in one unknown:
February 4, 2026 at 3:09 PM
In the January 2026 edition of Maths in School, the LUMENaries Shore, Foster and Francome present an intriguing method for solving simultaneous equations. Here it is applied to a simple linear equation in one unknown:
I was looking for an image of that doomed advertising campaign from long ago for Strand cigarettes. This is what Google's AI toddler gave me when I typed the advertising slogan, You're never alone with a Strand:
February 3, 2026 at 11:13 AM
I was looking for an image of that doomed advertising campaign from long ago for Strand cigarettes. This is what Google's AI toddler gave me when I typed the advertising slogan, You're never alone with a Strand:
Stolen Moments. This is what they look like.
[According Shazam/Apple]
[According Shazam/Apple]
February 1, 2026 at 8:08 PM
Stolen Moments. This is what they look like.
[According Shazam/Apple]
[According Shazam/Apple]
SHAZAM is an amazing demonstration of the power of AI to search through masses of data in seconds. And then it gives minimal information beyond providing a link to buy the identified track from APPLE, the owners of the app.
February 1, 2026 at 8:04 PM
SHAZAM is an amazing demonstration of the power of AI to search through masses of data in seconds. And then it gives minimal information beyond providing a link to buy the identified track from APPLE, the owners of the app.
Music in pictures ?!
February 1, 2026 at 7:05 PM
Music in pictures ?!
#MathsToday A young student putting numbers on a number line segment (starting at the bottom of the page).
His approach was to count in ones, starting from the left (0), with little or no attention paid to the number on the right end of the segment.
Seems like an information-processing issue.
His approach was to count in ones, starting from the left (0), with little or no attention paid to the number on the right end of the segment.
Seems like an information-processing issue.
January 28, 2026 at 8:08 PM
#MathsToday A young student putting numbers on a number line segment (starting at the bottom of the page).
His approach was to count in ones, starting from the left (0), with little or no attention paid to the number on the right end of the segment.
Seems like an information-processing issue.
His approach was to count in ones, starting from the left (0), with little or no attention paid to the number on the right end of the segment.
Seems like an information-processing issue.
This seems kinda strange.
The graph is a powerful model for showing that with simultaneous equations we are looking to see where values coincide. But while we can immediately see from these equations that they coincide when x=4, this would be far less obvious from just trying to visualise the graph.
The graph is a powerful model for showing that with simultaneous equations we are looking to see where values coincide. But while we can immediately see from these equations that they coincide when x=4, this would be far less obvious from just trying to visualise the graph.
January 26, 2026 at 10:53 AM
This seems kinda strange.
The graph is a powerful model for showing that with simultaneous equations we are looking to see where values coincide. But while we can immediately see from these equations that they coincide when x=4, this would be far less obvious from just trying to visualise the graph.
The graph is a powerful model for showing that with simultaneous equations we are looking to see where values coincide. But while we can immediately see from these equations that they coincide when x=4, this would be far less obvious from just trying to visualise the graph.
#MathsToday
Counting matchsticks by matching in pairs
Counting matchsticks by matching in pairs
January 14, 2026 at 1:11 PM
#MathsToday
Counting matchsticks by matching in pairs
Counting matchsticks by matching in pairs
London today.
If you think the sun rises in the East and sinks in the West, think again!
If you think the sun rises in the East and sinks in the West, think again!
January 11, 2026 at 10:52 AM
London today.
If you think the sun rises in the East and sinks in the West, think again!
If you think the sun rises in the East and sinks in the West, think again!
Man City owned by the Abu Dhabi royal family, Exeter City owned by its supporters. Sad.
January 11, 2026 at 10:32 AM
Man City owned by the Abu Dhabi royal family, Exeter City owned by its supporters. Sad.
This was taken on Wednesday, 15 minutes before sunrise. How is it that the moon is already 'pointing upwards'?
January 10, 2026 at 8:45 AM
This was taken on Wednesday, 15 minutes before sunrise. How is it that the moon is already 'pointing upwards'?
In #MathsToday we tried to solve this pair of mis-transcribed 'simultaneous equations':
4x + 4 = 14
3x – 4 = 14.
So 7x = 28, so x = 4.
[It seems to me we need to radically rethink the content of GCSE maths and how we teach it!]
4x + 4 = 14
3x – 4 = 14.
So 7x = 28, so x = 4.
[It seems to me we need to radically rethink the content of GCSE maths and how we teach it!]
January 8, 2026 at 12:13 PM
In #MathsToday we tried to solve this pair of mis-transcribed 'simultaneous equations':
4x + 4 = 14
3x – 4 = 14.
So 7x = 28, so x = 4.
[It seems to me we need to radically rethink the content of GCSE maths and how we teach it!]
4x + 4 = 14
3x – 4 = 14.
So 7x = 28, so x = 4.
[It seems to me we need to radically rethink the content of GCSE maths and how we teach it!]
December 29, 2025 at 5:30 PM
That took me a while to understand...
December 29, 2025 at 10:01 AM
That took me a while to understand...
This came to me in a dream. Oh well!
December 26, 2025 at 12:06 PM
This came to me in a dream. Oh well!
How come it costs €1.20 to send a card from Germany, but £3.20 to send one back?!
December 23, 2025 at 12:32 PM
How come it costs €1.20 to send a card from Germany, but £3.20 to send one back?!
Clusters of mistletoe have suddenly appeared on our apple tree...
December 22, 2025 at 10:51 AM
Clusters of mistletoe have suddenly appeared on our apple tree...
#MathsToday Used this task with a group of Y10 students. They struggled to view the task structurally, even when their arithmetic produced the result 241.
But they gained some insight with 7x12 – 6x12.
But they gained some insight with 7x12 – 6x12.
December 18, 2025 at 2:36 PM
#MathsToday Used this task with a group of Y10 students. They struggled to view the task structurally, even when their arithmetic produced the result 241.
But they gained some insight with 7x12 – 6x12.
But they gained some insight with 7x12 – 6x12.
Just received my copy of MT 298, with my article on mathematical thinking
December 11, 2025 at 5:45 PM
Just received my copy of MT 298, with my article on mathematical thinking
#MathsToday Memories of Pythagoras
A Y11 pupil tells me he saw a video about Pythagoras' Theorem with diagrams like these:
A Y11 pupil tells me he saw a video about Pythagoras' Theorem with diagrams like these:
December 11, 2025 at 9:34 AM
#MathsToday Memories of Pythagoras
A Y11 pupil tells me he saw a video about Pythagoras' Theorem with diagrams like these:
A Y11 pupil tells me he saw a video about Pythagoras' Theorem with diagrams like these:
interesting thought? - as it rotates, what happens to the length of the segment through the centre of the pentagon that cuts the pentagon in two?
December 9, 2025 at 9:46 AM
interesting thought? - as it rotates, what happens to the length of the segment through the centre of the pentagon that cuts the pentagon in two?