Ben L Sinclair

Maths Teacher, Educator and Learner.
PhD student

[Ben L Sinclair @mathsacharya]

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!
https://t.co/tFksx1LJdT

[Ben L Sinclair @mathsacharya]

@DeeVijayan @mrsouthernmaths @Whitehughes @melissamaths This is my year 13 proof booklet: https://t.co/W7IRGjhGm9

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…)

[Ben L Sinclair @mathsacharya]

@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'

[Ben L Sinclair @mathsacharya]

@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

[Ben L Sinclair @mathsacharya]

@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.

[Ben L Sinclair @mathsacharya]

@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: https://t.co/oXpIoNnN5W

[Ben L Sinclair @mathsacharya]

@JennyHillParker I made these taster booklets to use with them:
https://t.co/8fyk4HlOSV

[Ben L Sinclair @mathsacharya]

@MrTaylorMaths2

[Ben L Sinclair @mathsacharya]

@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'... 🙃❤️

[Ben L Sinclair @mathsacharya]

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 [email protected]
https://t.co/ptTKduzOvC

@NCETMsecondary @mathsjem @colinfoster77 @Bobby_Seagull

[Ben L Sinclair @mathsacharya]

@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

[Ben L Sinclair @mathsacharya]

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 [email protected]
https://t.co/ptTKduzOvC

@NCETMsecondary @mathsjem @colinfoster77 @Bobby_Seagull

[Ben L Sinclair @mathsacharya]

@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!

[Ben L Sinclair @mathsacharya]

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

[Ben L Sinclair @mathsacharya]

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

[Ben L Sinclair @mathsacharya]

@missweeks1001 And the number of petals is probably a Fibonacci number! 1, 2, 3, 5, 8, 13, 21, 34...

https://t.co/wY58cQgF7I

[Ben L Sinclair @mathsacharya]

@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!
https://t.co/sh03ogJds7

[Ben L Sinclair @mathsacharya]

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!
https://t.co/tFksx1LJdT

[Ben L Sinclair @mathsacharya]

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

[Ben L Sinclair @mathsacharya]

@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)