gerard mcn
@germinalmaths.bsky.social
I teach maths in a Scottish state-sector secondary school.
From “Sciencia”, published by Wooden Books. Or the shorter QED, by the same publisher.
November 30, 2025 at 12:22 PM
From “Sciencia”, published by Wooden Books. Or the shorter QED, by the same publisher.
Very nice. Thank you!
November 28, 2025 at 9:18 PM
Very nice. Thank you!
Very elegant!
I was, in fact, thinking initially of a quantitative (Pythagorean) approach- hence the choice of the 3-4-5 r.a.t.
If understand your argument, the difference in perimeter is
3 - sqrt5?
I was, in fact, thinking initially of a quantitative (Pythagorean) approach- hence the choice of the 3-4-5 r.a.t.
If understand your argument, the difference in perimeter is
3 - sqrt5?
November 28, 2025 at 9:17 PM
Very elegant!
I was, in fact, thinking initially of a quantitative (Pythagorean) approach- hence the choice of the 3-4-5 r.a.t.
If understand your argument, the difference in perimeter is
3 - sqrt5?
I was, in fact, thinking initially of a quantitative (Pythagorean) approach- hence the choice of the 3-4-5 r.a.t.
If understand your argument, the difference in perimeter is
3 - sqrt5?
Same area (not perceptually obvious) but different perimeters, which can increase without limit.
Conceptually hard?
I would say so.
Conceptually hard?
I would say so.
November 27, 2025 at 5:55 PM
Same area (not perceptually obvious) but different perimeters, which can increase without limit.
Conceptually hard?
I would say so.
Conceptually hard?
I would say so.
These may help convince you of the utility of my original suggestion regarding triangles. They’ve helped convince me!
November 26, 2025 at 9:38 PM
These may help convince you of the utility of my original suggestion regarding triangles. They’ve helped convince me!
Rhombus and kite.
November 26, 2025 at 9:34 PM
Rhombus and kite.
Similar approach for parallelograms
November 26, 2025 at 9:29 PM
Similar approach for parallelograms
These images - with thanks to @studymaths.bsky.social (geoboard on Mathsbot.com) - show that a rectangle where one side is the mean of the two parallel sides and the other the height of the trapezium - may be of use.
November 26, 2025 at 9:19 PM
These images - with thanks to @studymaths.bsky.social (geoboard on Mathsbot.com) - show that a rectangle where one side is the mean of the two parallel sides and the other the height of the trapezium - may be of use.
This usually results in easier processing, which some pupils may benefit from.
November 26, 2025 at 6:24 PM
This usually results in easier processing, which some pupils may benefit from.
1. The act of reconstructing the (smaller) rectangle from the triangle may help establish a stronger memory trace.
2. Numerically, I tend to halve one (preferably even) side-length before performing the multiplication, as opposed to halving the product of the sides.
2. Numerically, I tend to halve one (preferably even) side-length before performing the multiplication, as opposed to halving the product of the sides.
November 26, 2025 at 6:23 PM
1. The act of reconstructing the (smaller) rectangle from the triangle may help establish a stronger memory trace.
2. Numerically, I tend to halve one (preferably even) side-length before performing the multiplication, as opposed to halving the product of the sides.
2. Numerically, I tend to halve one (preferably even) side-length before performing the multiplication, as opposed to halving the product of the sides.
I believe the ancient Greeks (and others?) calculated areas by constructing a rectangle with an area equivalent to that of the shape in question. So there is a historical justification for this approach. Some other points in its favour:
November 26, 2025 at 6:21 PM
I believe the ancient Greeks (and others?) calculated areas by constructing a rectangle with an area equivalent to that of the shape in question. So there is a historical justification for this approach. Some other points in its favour:
Like you, I’ve always derived the formula by halving a “parent” rectangle, but found many pupils don’t retain this approach over time. Your post prompted me to seek an alternative - thank you! Whether this one is more effective, I don’t know, but it may be worth a try given the retention issue.
November 26, 2025 at 6:21 PM
Like you, I’ve always derived the formula by halving a “parent” rectangle, but found many pupils don’t retain this approach over time. Your post prompted me to seek an alternative - thank you! Whether this one is more effective, I don’t know, but it may be worth a try given the retention issue.
I’ve been thinking about this. My experience chimes with yours -poor retention of the formula for area of a triangle is a real issue. What if we halved one side of the rectangle? These images could be cut up or coloured to highlight equal areas.
November 25, 2025 at 6:59 PM
I’ve been thinking about this. My experience chimes with yours -poor retention of the formula for area of a triangle is a real issue. What if we halved one side of the rectangle? These images could be cut up or coloured to highlight equal areas.
Three squared equals six.
November 23, 2025 at 2:31 AM
Three squared equals six.
Coming Up For Ayr.
November 12, 2025 at 7:02 PM
Coming Up For Ayr.
Stuck in the middle with Hughes.
November 8, 2025 at 1:04 PM
Stuck in the middle with Hughes.
A colleague from Health and Food Technology observed my S1 lesson on multiplying and dividing integers this week. One pupil had been told (in maths) he must say negative 3 and not minus 3. My colleague said HFT teachers would never use “negative“ to refer to a temperature. I can’t disagree.
November 7, 2025 at 5:50 PM
A colleague from Health and Food Technology observed my S1 lesson on multiplying and dividing integers this week. One pupil had been told (in maths) he must say negative 3 and not minus 3. My colleague said HFT teachers would never use “negative“ to refer to a temperature. I can’t disagree.
I would hope a lot of mathematical concepts have been met “for the first time” before pupils even know what maths is.
November 7, 2025 at 5:40 PM
I would hope a lot of mathematical concepts have been met “for the first time” before pupils even know what maths is.
