How many non right-angled triangles are there?!

Yes, I think so!

Why not apply skills in a meaningful, purposeful way? But, yes, exploring shapes in the Cartesian plane can be a rich, engaging activity.

Well, yes, and there are exams. But I think we could think a lot harder about how to make school algebra meaningful.

In the case of the third triangle, if one removed the isosceles condition, one could ask questions like, 'What happens to the shape as the value of x increases?', 'When is it isosceles?', etc. Still artificial, but perhaps quite intriguing and throwing light on the (still arbitrary) expressions.

Yes, in school algebra we often come up with tasks that fail to show the 'purpose and utility' of algebra. Tasks like those, seemingly in a context but with algebraic expressions that seem to have no rationale, are prime examples.

Thank you. Yes, 'same or different' can be productive, but I couldn't get to grips with that particular example, especially regarding the heading, 'addressing misconceptions'.

OK, thank you (still seems very strange to me!)

I don't get this at all. What is the task trying to address?!

The Strait of Hormuz:
source of enriched Iranium

1/2 of 4/7 = 2/7
4/7 of 1/2 = 4/14

Who?!

I've experienced something similar and found it puzzling. I had thought using fractions to measure length, as on a ruler, would seem quite 'natural'.
Something is more than 2 cm but less than 3 cm, what could we call it? More than 2½ but less than 3...? More than 2½ but less than 2¾...?

How does this statement, from National Lottery CEO Andria Vidler, compute?

"Roman numerals have no zero"
Well, yes, why would they?!

Can you give an example of such a White Rose problem?

Hmm. Perhaps worth remembering that Gauß, for example, and Euler too I think, did a lot of 'practical' maths too.
As for 'beauty', if it does, on occasion, apply to a poem, a painting, a theorem, I doubt whether its meaning is the same.

@wandsworthlabour.bsky.social
In April 2023 I paid £175 for my annual parking permit.
In April 2024, 2025 and 2026 the price increased by 6.8%, 9.6% and 22%.
1. What does the permit cost now?
2. Should I be glad that these sly increases ameliorate the effect of the council's council tax freeze?

Glass half full,
or glass 7/8 empty?!

needless polarisation

Blessed are the Self Righteous.

The effects of a one way stretch

Starmer: What a cowardly man.

I'm trying to think of some two-sided singles.
Please release me?
You keep me hanging on?
Satisfaction?
There must be better ones.

Common numerators!
[very nice]

Shows my age... [ I heard him and his band in Croydon in about 1963...]

D E?

Ah! I hadn't seen it like that, but yes, difference of two squares!

Imagine replacing 90 in this item. For what other numbers would the item still work?