Idle thought: Explain in a sentence why for any numbers n and s such that n>s, s²/n is closer to s than n is . #UKMathsChat

Idle thought: Explain geometrically why the square-root operator is distributive over multiplication. #UKMathsChat

Something I didn't know. #UKMathsChat

#poetry #poem Christian Wiman

An aide-memoire for right-angled trig?! … maybe not … but it's interesting how orientation affects our ability to remember relationships. In this orientation I find the symmetry of the relationships much clearer. If only all trig questions had horizontal hypotenuses ;-) #UKMathsChat #iTeachMaths

#poetry #poem Louise Glück.

An Ailles Rectangle problem. Find the value of a°. More an exercise in (trigonometry) language fluency than anything else. i.e. do you know how to interpret the terminology to be able to do it in your head. @davidkbutler.bsky.social #UKMathsChat #iTeachMaths

If … you broke trigonometry into smaller pieces … spread it over 3 years … and taught the basics of just sine in early Secondary … then you could play around with problems like this … without everyone collapsing in a heap. Gradual trigonometry. #UKMathsChat #iTeachMaths

Is there a good working definition of 'understanding' (c.f. knowledge) that people regularly turn to? (Apologies, not a #CogSciSky person, unfamiliar with the various schools of thought. Looking for something succinct).

If there was a cot button on calculators … I’d be one of the people that used it.

A sort of proto-trig task. No angle values required. Certainly no sin/cos/tan required. In one sense trigonometry was always two things: 1) building a table of values and 2) learning how to manipulate the results. This task concerns the latter. #UKMathsChat #iTeachMaths

#poetry #poem Mosab Abu Toha, from 'Forest of Noise'. There's a moment in each poem where he gently stops you in your tracks and shows you something you have never had to experience.

Strand curriculum. t.ly/v-JCL. Two different topic tasks per lesson. 15min HW+LSQ, 15min Task 1, 15min Task 2, 5min spare. Keeping to time and the right resources essential. Pros: Pupil focus, spacing. Cons: Time making resources. Intense 50min but I loved it. #UKMathsChat #iTeachMaths

#poetry #poem Anna Akhmatova, trans. Kunitz and Haywood. This grabbed me the first time I read it. O.M. is the exiled Osip Mandelstam. The still shaking earth. The chill of the last four lines.

0.38 × 72 − 0.72 × 38 The top set decided they needed a calculator :-( Everyday is a learning experience ;-) #UKMathsChat #iTeachMaths

Proof shamefully cribbed from @mathforge.org‬ … redrawn because I like my unit circle ;-) loopspace.mathforge.org/CountingOnMy... I like the way the identity is posed, not as a double angle question … but as 'what is tan x + cot x?!' … which feels a more natural question. #UKMathsChat #iTeachMaths

#poetry #poem Linda Gregg. For me it’s often just one line that draws me in.‘The quiet is in the idea of silence’.

A t-shirt design for mathforge.org. Thank you Andrew for helping me see differently. For Andrew's proof, see: loopspace.mathforge.org/CountingOnMy... #UKMathsChat #iTeachMaths

A task attempting to view Pythagoras' theorem through a purely geometric lens ... i.e. with a focus on areas rather than numerical lengths. (Are there already tasks out there like this? Maybe I've just not seen them.) #UKMathsChat #iTeachMaths

Thinking about the lenses we see Pythagoras through. I'm not arguing one is better than the other but I am struck how a geometric lens feels different to the other two ... also how hard it is to think exclusively through just one lens. Looking for a sounding board. #UKMathsChat #iTeachMaths

#poetry #poem Alice Oswald. ‘A greenwood through a blackwood/passes (like the moon’s halves/meet and go behind themselves)’.

Trying to get into the head of Varāhamihira (6th century, India). I think he saw sine 30° as the root of a one-quarter area and sine 60° as the root of a three-quarter area. The geometric partition into ¼ and ¾ will definitely stay with me. #UKMathsChat #iTeachMaths

I couldn't resist a go at this. A 'proof without words' using just Pythagoras' Theorem. Requires a bit of effort on the part of the reader (as PWWs do) but hopefully kept to a minimum. Wish I had a class actually that could talk through it and articulate the steps. #UKMathsChat #iTeachMaths

#poetry #poem Louise Glück. ‘You see again how far away/each thing is from every other thing.’

A starter for my class who have had one lesson of C≈3.14×d. 'Measure the diameter of each circle and calculate the circumference ... and stop bending the rulers.' #UKMathsChat #iTeachMaths

περιφέρεια – periphery Hence the letter π to denote 3.141592... 1706 William Jones I didn't know that. #UKMathsChat #iTeachMaths

The brilliance of Indian mathematics! Mādhavan is Mādhava (1340–1445) YB is the Yuktibhāsā of Jyeṣṭhadeva (1500–1575). New Years Resolution: Refer to the 'Mādhava Series for sine, cosine and arctangent.' From: link.springer.com/content/pdf/..., p423 #UKMathsChat #iTeachMaths

#poetry Osip Mandelstam. Two translations. I'm drawn to the first. From stale staircases and squares/palaces all walls and angles ... the gentle slowing of the last two lines. Written in exile, his shadow his diminished self, it alludes to Dante's own exile in 1302 and lines from Dante's Paradiso.

Two slides for my S1 on Monday; an upgrade of something I had on the old site. For the blue-red one I'll be looking for the answers 3/15, ¼, ¾ and 3/1. Thanks to @dpfl.bsky.social for prompting the last question type. #UKMathsChat #iTeachMaths

My school is going down the route of Bloom and ‘meta skills’ to promote thinking about thinking. I’m resistant naturally ;-) … and I think I prefer this. I like the questions (eg What am I curious about?) and can see myself using them. As a framework it seems less … well, contrived. #UKMathsChat

Initial thoughts for a lesson on relative areas. Choose a diagram, label the smallest region X, label the remaining regions in terms of X (e.g. 2X, 3X, whatever they are), add up the Xs, work out the fractions. Feels like a magic power once you know how to do it! #UKMathsChat #iTeachMaths

#poetry John Burnside ... 'on the borders of dunlin and tern' has stayed in my mind for years. The last line (from what I understand) is ... uisge; aran; oidhche; gealach; teine /ɯʃgʲə/, /aran/, /ɤ̃ĩçə/, /gʲaLəx/, /tʲenə/ oosh-ka, a-ran, oy-sha, gee-al-ach, chin-eh water, bread, night, moon, fire

This has been occupying me for the last few days. There are some nice moments in it, which in themselves would make for an interesting couple of lessons. Prompted by a post by @berniewestacott.bsky.social. #UKMathsChat #iTeachMaths

Osip Mandelstam, trans. Greene. McKane & McKane translate the first two lines as: 'Today is a little yellow round the beak, I cannot understand it –'. Does anyone know what the yellow would have symbolised in Russia in the 30s? #poetry

Anna Akhmatova, trans. Kunitz and Haywood. Kunitz writes: 'Her poems exist in the purity and exactness of their diction, the authority of their tone, the subtlety of their rhythmic modulations, the integrity of their form ... The only way to translate Akhmatova is by writing well.' #poetry

two-fifths is to three-sevenths as two-thirds is to five-sevenths Swapping the 5 and the 3 maintains the proportion. I don't think I intrinsically had a sense that this was true. Still a lot to learn, obviously! #UKMathsChat #iTeachMaths

Questions for a class: What do you notice? What does it equal? Make another like it with the same answer. If the numerator was 11/13 over 17/23, what would the denominator need to be? How would you type it into a calculator? Why does 2/3 ÷ 5/7 equal 2/5 ÷ 3/7 ? #UKMathsChat #iTeachMaths

Carolyn Forché, for Ilya Kaminsky. ‘… the tram to a stop where it is no longer possible to get off, …’ #poetry

Short sorting task. My S2s are struggling to realise that while 5/7 ÷ 2 is happily 5/14, 6/7 ÷ 2 is more easily 3/7 (rather than 6/14). They're fine with one process (acting on the denominator) but having two possible processes to choose from is upsetting the applecart. #UKMathsChat #iTeachMaths

Anna Akhmatova, trans. Kunitz. I’ve been reading and re-reading this all day. A moment, beautifully understated and at peace with itself. #poetry

#iTeachMaths #UKMathsChat

The two smaller angles in a right-angled triangle are complementary. Would you say this is something that is generally taught in UK schools? #iTeachMaths #UKMathsChat

Is there a notation for marking corresponding sides on similar triangles? #iTeachMaths #ukMathsChat

“Teaching is a performance profession. You need to be on your A-game every single day of the week and that’s difficult. My approach has always been that we need to treat teachers like elite athletes. They are given the best treatment. They are looked after and they’re cared for.” #UKMathsChat

I’m also being sold Bloom communicated every lesson. Do any maths departments do this? Is it useful? In what way? #ukMathschat #iTeachMaths

They’re trying to sell me ‘meta skills’ for mathematics. They want courses with clearly defined meta skills communicated every lesson. It feels the latest fad to me. Has anyone found this to be useful at Secondary level? #ukMathschat #iTeachMaths

On one level I’m frustrated. On another, saddened – you wouldn’t want this for anyone. And on yet another, annoyed that we’ve let them get this far thinking this. #iTeachMaths, #UKMathsChat

Lovely breakdown of addition & subtraction strategies. #iTeachMaths #UKMathsChat

The nice thing about GeoGebra 3D is that it does actually work. Adopt a ‘ruler & compass construction’ mind set and it all goes swimmingly. Todays efforts: first steps in the trigonometry of the diurnal motion of the sun. #iTeachMaths #UKMathsChat

ChatGPT. I give up. 'The six o'clock circle as referred to in the context of traditional Indian astronomy, does not go through the east-west points on the horizon.' 'In summary, the six o'clock circle in this context does indeed pass through the east and west points on the horizon.' Sigh.