Ben L Sinclair

I've started to share the GCSE and A Level knowledge booklets that I use in my teaching. I am constantly updating them so any errors, feedback or questions are welcome :) I'll add the rest to the folder as and when I've recorded their study videos! drive.google.com/drive/folders/…

@DeeVijayan @mrsouthernmaths @Whitehughes @melissamaths This is my year 13 proof booklet: drive.google.com/drive/mobile/f… Similar principles: make sense with numbers before representing algebraically; scaffolded and faded steps; revision of definitions; famous proofs and conjectures from beyond the spec (1089, Collatz…)

any tried and tested methods/resources for teaching proof in year 12?Would scaffolding work when teaching proofs. I think proof is a way of thinking &the fact that every question can have a different starting point make it hard for Ss @mrsouthernmaths @Whitehughes @melissamaths

@MissThorburn @mathsjem @draustinmaths @MrTs_NQTs @mrbartonmaths @NCETMsecondary It can be considered as 1/2 ÷ 2/5 = 5/10 ÷ 4/10 = 5/4 (5 things / 4 things = 5/4). Still multiplying by 10, links to the 'common denominator approach' of addition, and feels less mechanical. I'd still always aspire for fluency and understanding of 'multiplying by the reciprocal'

I’d like to move away from KFC to teach dividing fractions and have thought about teaching it using equivalent fractions (see picture). Looking for feedback and advice! Please be honest @mathsjem @draustinmaths @MrTs_NQTs @mrbartonmaths @NCETMsecondary

@tm_maths In fact, it doesn't matter what the first set of primes are: A: The only primes are 2, 11, 31. B: What about 2x11x31+1 = 683? A: The only primes are 5 and 13. B: What about 5x13+1 = 66? 66 = 2x3x11 2,3 and 11 can't be in my original list (remainder 1) Each is a contradiction

@tm_maths You can play this game forever to show that there are infinitely many prime numbers to add to your collection. It won't result in all of the prime numbers, but that's not the point. In either case, you have contradicted person A's assumption that there can be finite primes.

no matter how many videos I'm watching of it or resources I'm looking at, I still don't understand the proof of there are an infinite number of primes. It's something I can memories the steps for but don't know what's going on.

@geomathsblog @Mathematical_A I use a horizontal one but call it a ‘coordinate table’ so they make the link. Don Steward uses vertical ones effectively: donsteward.blogspot.com/2013/11/4-in-l…

How do you set out your table of values? Discussed at dept meeting tonight. I've always used horizontal but vertical gives you the coordinates beautifully!

@JennyHillParker I made these taster booklets to use with them: drive.google.com/drive/u/0/mobi…

Q1 - Does your school run A level taster days/sessions for year 11 students, and if so what activities do you do with them? #mathscpdchat

This is my list updated list so far, anything missing?

@DrHelenDrury @AccomplishEdu @ProfSmudge @colinfoster77 @TFrancome Probably because I made it up! 🙈 I was thinking about the 'cusp' of a cardioid. (More appropriate name than what my year 13s call it...). You can then continue the maths/biology puns by calling the K angle 'bicuspid'... 🙃❤️

@mathsacharya @AccomplishEdu @ProfSmudge @colinfoster77 @TFrancome How fascinating! I don't think I've heard of 'cusp' angles before - thanks! Maybe slightly different definition though...is 'K' two different cusp angles?! oxfordreference.com/display/10.109…

We can define an angle but is there a name for the marking K? ⁦@ProfSmudge⁩ ⁦@DrHelenDrury⁩ ⁦@colinfoster77⁩ ⁦@TFrancome⁩

I'm conducting an exciting new research project, Maths ACTive, with @Warwick_Edu and looking for student volunteers! Please share and feel free to contact me for more info b.sinclair@warwick.ac.uk tinyurl.com/mathsactiveinfo @NCETMsecondary @mathsjem @colinfoster77 @Bobby_Seagull

@danicquinn @joboaler @DMR_Network @Mathematical_A @dr_tom_hunt @LearningMaths Thanks Dani. I've adapted the study for different schools - some have asked whole classes to complete it as homework, others have advertised it to students (strongly encouraging some to participate!) and the rest have used it 1-on-1. I'm open to whatever each school needs/prefers

@mathsacharya @joboaler @DMR_Network @Mathematical_A @dr_tom_hunt @LearningMaths Something like this feels funny to make “compulsory” as homework, despite being (presumably!) beneficial, as it is a weird message and could also mean some low grade engagement. If it is optional/encouraged homework, with lower take-up, is that ok for the study?

@Whitehughes Quite! I was trying to come up with conceptually interesting approaches. Also played with using a circle inside the parabola, and using small angle approximations… not much luck there though!

@Whitehughes Generalise and you a perverse proof of x = -b/2a !

@Whitehughes I just use integration 🙃 If I'm being really lazy, I let delta=1...

@missweeks1001 And the number of petals is probably a Fibonacci number! 1, 2, 3, 5, 8, 13, 21, 34... gofiguremath.org/natures-favori…

Is there a mathematical name for this kind of natural symmetry?

@SStreaterMaths @GemmaHeald @JamesRawlins90 They look good, Sian - I’d be interested in taking a look at your approach and comparing it to mine if you have copies! twitter.com/mathsacharya/s…

Teaching through booklets- is it the way to go? I like it in my classroom but all classrooms are different! Thank you to @GemmaHeald and @JamesRawlins90 for all the advice. So lucky that I have a team who have opted to test these this term to see if they benefit our students!

@Ridermeister So a quadratic will only have real roots if all the coefficients are real, and it’s Disc ≥ 0.

@Ridermeister Inequalities in complex numbers don’t work the same (need to compare magnitudes instead), so ‘non-negative’ isn’t really a thing Square root a im num, you get an im num Instead, if Disc=0 -> one repeated complex root; if Disc≠0 -> two distinct roots (both complex or both real)