Mark Dawes
@mdawesmdawes.bsky.social
I teach maths and play music. Runner since Feb 2016. Y aprendo español.
Creator of Quibans for Core Maths. https://quibans.blogspot.com/
Based near Cambridge, UK
Creator of Quibans for Core Maths. https://quibans.blogspot.com/
Based near Cambridge, UK
News story in the Times that says every secondary school will have to offer triple sciences at GCSE (though not all pupils will have to do them).
One of the images used to illustrate the story? The usual sort of nonsense...
One of the images used to illustrate the story? The usual sort of nonsense...
November 2, 2025 at 7:33 PM
News story in the Times that says every secondary school will have to offer triple sciences at GCSE (though not all pupils will have to do them).
One of the images used to illustrate the story? The usual sort of nonsense...
One of the images used to illustrate the story? The usual sort of nonsense...
Half marathon in Surrey today. 'The Hurt' was well named (not used to all the hills). But lots of fun.
October 11, 2025 at 5:45 PM
Half marathon in Surrey today. 'The Hurt' was well named (not used to all the hills). But lots of fun.
In #MathsToday (in fact, #MathsRightNow at the #RyderCup ), the official website shows the state of play and also gives predicted percentages for each possible result in each match.
Any comments on the predictions?
Any comments on the predictions?
September 26, 2025 at 7:12 PM
In #MathsToday (in fact, #MathsRightNow at the #RyderCup ), the official website shows the state of play and also gives predicted percentages for each possible result in each match.
Any comments on the predictions?
Any comments on the predictions?
@teachertapp.bsky.social sent me this.
Scary to realise hope much time I have spent on the app.
There are 1440 mins in a day. So if I have spent a minute each day Tapping then that's more than a full day in total. (Not that this realisation will make me stop, obvs!)
Scary to realise hope much time I have spent on the app.
There are 1440 mins in a day. So if I have spent a minute each day Tapping then that's more than a full day in total. (Not that this realisation will make me stop, obvs!)
July 23, 2025 at 3:11 PM
@teachertapp.bsky.social sent me this.
Scary to realise hope much time I have spent on the app.
There are 1440 mins in a day. So if I have spent a minute each day Tapping then that's more than a full day in total. (Not that this realisation will make me stop, obvs!)
Scary to realise hope much time I have spent on the app.
There are 1440 mins in a day. So if I have spent a minute each day Tapping then that's more than a full day in total. (Not that this realisation will make me stop, obvs!)
The @telegraphnews.bsky.social keeps using this graph showing private school fee increases.
According to their figures, from 1986 to 2024 (ignoring the 2025 increase) school fees have multiplied by 9.6
(so fees of £3000 in 1986 would be 3000 x 9.6 = £28,000 in 2024).
/1
According to their figures, from 1986 to 2024 (ignoring the 2025 increase) school fees have multiplied by 9.6
(so fees of £3000 in 1986 would be 3000 x 9.6 = £28,000 in 2024).
/1
June 15, 2025 at 7:04 PM
The @telegraphnews.bsky.social keeps using this graph showing private school fee increases.
According to their figures, from 1986 to 2024 (ignoring the 2025 increase) school fees have multiplied by 9.6
(so fees of £3000 in 1986 would be 3000 x 9.6 = £28,000 in 2024).
/1
According to their figures, from 1986 to 2024 (ignoring the 2025 increase) school fees have multiplied by 9.6
(so fees of £3000 in 1986 would be 3000 x 9.6 = £28,000 in 2024).
/1
Very lovely #CambridgeHalfMarathon today.
A great run in the sun!
A great run in the sun!
March 9, 2025 at 3:56 PM
Very lovely #CambridgeHalfMarathon today.
A great run in the sun!
A great run in the sun!
Just realised I have a 5-year streak on @teachertapp.bsky.social !
February 2, 2025 at 3:53 PM
Just realised I have a 5-year streak on @teachertapp.bsky.social !
How did you count the frying tomatoes?
#MathsToday
#MathsToday
January 1, 2025 at 3:34 PM
How did you count the frying tomatoes?
#MathsToday
#MathsToday
Nice one.
How do you manage to do the highlighted part? I get nerd-sniped. Every. Single. Time.
Can't possibly wait a week.
How do you manage to do the highlighted part? I get nerd-sniped. Every. Single. Time.
Can't possibly wait a week.
December 19, 2024 at 8:25 PM
Nice one.
How do you manage to do the highlighted part? I get nerd-sniped. Every. Single. Time.
Can't possibly wait a week.
How do you manage to do the highlighted part? I get nerd-sniped. Every. Single. Time.
Can't possibly wait a week.
In #MathsToday one of my #CoreMaths students sent me this photo he took in the local Co-op.
December 17, 2024 at 11:40 PM
In #MathsToday one of my #CoreMaths students sent me this photo he took in the local Co-op.
Well this is lovely!
I've put some labels on the diagram.
The shaded area is equivalent to the area of the triangle ACD (which is (1/2)b(g+h) ) subtract the area of BCD ((1/2)bg)
This gives (1/2)bh as required.
Nice!
I've put some labels on the diagram.
The shaded area is equivalent to the area of the triangle ACD (which is (1/2)b(g+h) ) subtract the area of BCD ((1/2)bg)
This gives (1/2)bh as required.
Nice!
December 10, 2024 at 11:57 AM
Well this is lovely!
I've put some labels on the diagram.
The shaded area is equivalent to the area of the triangle ACD (which is (1/2)b(g+h) ) subtract the area of BCD ((1/2)bg)
This gives (1/2)bh as required.
Nice!
I've put some labels on the diagram.
The shaded area is equivalent to the area of the triangle ACD (which is (1/2)b(g+h) ) subtract the area of BCD ((1/2)bg)
This gives (1/2)bh as required.
Nice!
A real privilege to accompany a choral concert this afternoon (playing an organ I was previously unfamiliar with).
Nice floor tiles too...
Are the black tiles all the same size? If not, which are bigger?
#mathstoday
Nice floor tiles too...
Are the black tiles all the same size? If not, which are bigger?
#mathstoday
December 8, 2024 at 9:10 PM
A real privilege to accompany a choral concert this afternoon (playing an organ I was previously unfamiliar with).
Nice floor tiles too...
Are the black tiles all the same size? If not, which are bigger?
#mathstoday
Nice floor tiles too...
Are the black tiles all the same size? If not, which are bigger?
#mathstoday
The subtraction versions are ... interesting.
Almost no-one seems to have ever used the second one here.
Almost no-one seems to have ever used the second one here.
December 8, 2024 at 9:07 PM
The subtraction versions are ... interesting.
Almost no-one seems to have ever used the second one here.
Almost no-one seems to have ever used the second one here.
I _was_ taught them, early 1980s.
Have you seen the 'official' methods, in Appendix 1 of the Maths national curriculum?
assets.publishing.service.gov.uk/media/5a7c5b...
Here's the long multiplication example.
Have you seen the 'official' methods, in Appendix 1 of the Maths national curriculum?
assets.publishing.service.gov.uk/media/5a7c5b...
Here's the long multiplication example.
December 8, 2024 at 9:05 PM
I _was_ taught them, early 1980s.
Have you seen the 'official' methods, in Appendix 1 of the Maths national curriculum?
assets.publishing.service.gov.uk/media/5a7c5b...
Here's the long multiplication example.
Have you seen the 'official' methods, in Appendix 1 of the Maths national curriculum?
assets.publishing.service.gov.uk/media/5a7c5b...
Here's the long multiplication example.
As I understand it, if they follow the 'standard algorithm' but have a numerical slip they get the marks. Unfortunately the markscheme explicitly mentions putting the zeroes in! I suspect that Henslowe would have lost both marks (where I would want to give one!)
December 8, 2024 at 8:54 PM
As I understand it, if they follow the 'standard algorithm' but have a numerical slip they get the marks. Unfortunately the markscheme explicitly mentions putting the zeroes in! I suspect that Henslowe would have lost both marks (where I would want to give one!)
Half Marathon this morning (Carver Barracks nr Saffron Walden).
Brilliant organisation.
Much faster than expected too (84 min 2 sec).
Very pleased.
#EduRunners
Brilliant organisation.
Much faster than expected too (84 min 2 sec).
Very pleased.
#EduRunners
November 9, 2024 at 12:30 PM
Half Marathon this morning (Carver Barracks nr Saffron Walden).
Brilliant organisation.
Much faster than expected too (84 min 2 sec).
Very pleased.
#EduRunners
Brilliant organisation.
Much faster than expected too (84 min 2 sec).
Very pleased.
#EduRunners
I'm enjoying my running. Less fond of the darker evenings though!
October 29, 2024 at 10:11 PM
I'm enjoying my running. Less fond of the darker evenings though!
Today’s run. Lovely views. Lovely weather.
October 12, 2024 at 7:08 PM
Today’s run. Lovely views. Lovely weather.
My method was very different from yours.
A surprisingly nice-looking solution, though!
A surprisingly nice-looking solution, though!
September 5, 2024 at 11:53 AM
My method was very different from yours.
A surprisingly nice-looking solution, though!
A surprisingly nice-looking solution, though!
In this version x = 2/tan(α)
The area of the triangle is ½ × 2 × 2/tan(α)
The volume is therefore 12/tan(α)
/7
The area of the triangle is ½ × 2 × 2/tan(α)
The volume is therefore 12/tan(α)
/7
September 1, 2024 at 7:20 PM
In this version x = 2/tan(α)
The area of the triangle is ½ × 2 × 2/tan(α)
The volume is therefore 12/tan(α)
/7
The area of the triangle is ½ × 2 × 2/tan(α)
The volume is therefore 12/tan(α)
/7
In this version, I did the area of the rectangle subtract the area of the triangle.
y = 3tan(α)
Blue area is 6 – ½ × 3 × 3tan(α)
Multiply by the length to get 36 – 27tan(α)
/6
September 1, 2024 at 7:18 PM
In this version, I did the area of the rectangle subtract the area of the triangle.
y = 3tan(α)
Blue area is 6 – ½ × 3 × 3tan(α)
Multiply by the length to get 36 – 27tan(α)
/6
Problem 2
This is a brilliant problem, because it requires two cases to be considered.
/5
This is a brilliant problem, because it requires two cases to be considered.
/5
September 1, 2024 at 7:16 PM
Problem 2
This is a brilliant problem, because it requires two cases to be considered.
/5
This is a brilliant problem, because it requires two cases to be considered.
/5
This helped me find a new-to-me proof of the sine double-angle formula.
Area of isosceles triangle is ½absinC, which is ½sin(2α)
Right-hand right-angled triangle has area ½bxh, which is ½sin(α)cos(α). Area of isos triangle is twice this, giving ½sin(2α) = sin(α)cos(α) so
sin(2α) = 2sin(α)cos(α)
/4
Area of isosceles triangle is ½absinC, which is ½sin(2α)
Right-hand right-angled triangle has area ½bxh, which is ½sin(α)cos(α). Area of isos triangle is twice this, giving ½sin(2α) = sin(α)cos(α) so
sin(2α) = 2sin(α)cos(α)
/4
September 1, 2024 at 7:13 PM
This helped me find a new-to-me proof of the sine double-angle formula.
Area of isosceles triangle is ½absinC, which is ½sin(2α)
Right-hand right-angled triangle has area ½bxh, which is ½sin(α)cos(α). Area of isos triangle is twice this, giving ½sin(2α) = sin(α)cos(α) so
sin(2α) = 2sin(α)cos(α)
/4
Area of isosceles triangle is ½absinC, which is ½sin(2α)
Right-hand right-angled triangle has area ½bxh, which is ½sin(α)cos(α). Area of isos triangle is twice this, giving ½sin(2α) = sin(α)cos(α) so
sin(2α) = 2sin(α)cos(α)
/4
Angle C is (π – 2α).
The area of the sector, using ½r²θ is ½(π – 2α).
The area of the triangle, using ½absinC is ½sin(π – 2α).
Sine of (π – 2α) is equal to the sine of 2α.
The area of the blue segment is therefore ½(π – 2α) – ½sin(2α)
/2
The area of the sector, using ½r²θ is ½(π – 2α).
The area of the triangle, using ½absinC is ½sin(π – 2α).
Sine of (π – 2α) is equal to the sine of 2α.
The area of the blue segment is therefore ½(π – 2α) – ½sin(2α)
/2
September 1, 2024 at 7:10 PM
Angle C is (π – 2α).
The area of the sector, using ½r²θ is ½(π – 2α).
The area of the triangle, using ½absinC is ½sin(π – 2α).
Sine of (π – 2α) is equal to the sine of 2α.
The area of the blue segment is therefore ½(π – 2α) – ½sin(2α)
/2
The area of the sector, using ½r²θ is ½(π – 2α).
The area of the triangle, using ½absinC is ½sin(π – 2α).
Sine of (π – 2α) is equal to the sine of 2α.
The area of the blue segment is therefore ½(π – 2α) – ½sin(2α)
/2
Problem 1
I decided to work in radians because it made the calculations less messy, so assumed an A-level class, but it works for a high-attaining GCSE group in degrees too.
First I needed to understand the diagram. I thought of it like the first image, and then added another line.
/1
I decided to work in radians because it made the calculations less messy, so assumed an A-level class, but it works for a high-attaining GCSE group in degrees too.
First I needed to understand the diagram. I thought of it like the first image, and then added another line.
/1
September 1, 2024 at 7:08 PM
Problem 1
I decided to work in radians because it made the calculations less messy, so assumed an A-level class, but it works for a high-attaining GCSE group in degrees too.
First I needed to understand the diagram. I thought of it like the first image, and then added another line.
/1
I decided to work in radians because it made the calculations less messy, so assumed an A-level class, but it works for a high-attaining GCSE group in degrees too.
First I needed to understand the diagram. I thought of it like the first image, and then added another line.
/1