ProfSmudge
@profsmudge.bsky.social
School maths should be more than tables and algorithms. I try to write materials that show that. Dietmar Küchemann
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.
I think this works, using enlargement and similarity rather than vectors:
January 23, 2026 at 11:04 AM
I think this works, using enlargement and similarity rather than vectors:
#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!
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'?
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...
Graph v Double number line
December 27, 2025 at 12:23 PM
Graph v Double number line
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...
Here too they immediately went for a rounding procedure, rather than trying to get some sense of the expression's value.
December 18, 2025 at 2:39 PM
Here too they immediately went for a rounding procedure, rather than trying to get some sense of the expression's value.
#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:
Does this make sense?
If only 2% give , what use is a donation of £2.75?
If only 2% give , what use is a donation of £2.75?
December 7, 2025 at 7:59 PM
Does this make sense?
If only 2% give , what use is a donation of £2.75?
If only 2% give , what use is a donation of £2.75?
Amazon-speak for
Package was left on doorstep
Package was left on doorstep
December 6, 2025 at 5:14 PM
Amazon-speak for
Package was left on doorstep
Package was left on doorstep
A simpler version, perhaps.
December 5, 2025 at 4:35 PM
A simpler version, perhaps.
Think of ways to solve this
December 5, 2025 at 9:43 AM
Think of ways to solve this
In #MathsToday
Varying an expression and thinking about what happens to its value;
and when that didn't work, varying the expression to be varied....
Varying an expression and thinking about what happens to its value;
and when that didn't work, varying the expression to be varied....
December 4, 2025 at 12:23 PM
In #MathsToday
Varying an expression and thinking about what happens to its value;
and when that didn't work, varying the expression to be varied....
Varying an expression and thinking about what happens to its value;
and when that didn't work, varying the expression to be varied....
Would you choose the same diagram or different diagrams for the two tasks?
December 2, 2025 at 1:33 PM
Would you choose the same diagram or different diagrams for the two tasks?
Actually, this makes A and B more equivalent
December 1, 2025 at 10:32 AM
Actually, this makes A and B more equivalent
Which diagram do you prefer here?
December 1, 2025 at 10:19 AM
Which diagram do you prefer here?