Thank you. I had a great time doing it.

Yep...not enough maths questions!

Un-Natural Numbers: 4 - Klein Groups, Harshad Numbers & Mod 4 YouTube video by Un-Natural Numbers

What's this? Oh it's episode 4 of #Un-NaturalNumbers

With the magnificent @steckl.es and @paddymaths.bsky.social.

Give it a watch if you're in the mood for Klein groups, Harshad numbers and Modulo 4 arithmetic.

#mathstalk
#mathschat
#talkingnumbers

youtu.be/RfNBjhHGJ54

Latest episode of Invasion of the Poddysnatchers is out now from me and @paddymaths.bsky.social, we watched Devil in a Blue Dress starring Denzel Washington and Don Cheadle from 1995.

open.spotify.com/episode/29Of...

The cover page for a set of Further Statistics 1 exam questions.

The cover page for a set of Core Pure exam questions.

The cover page for a set of Mechanics and Statistics exam questions.

The cover page for a set of Core Pure 2 exam questions.

I've also expanded my collection of A Level Further Maths 'Exam Question a Lesson' packs for the new half term.

Setting and marking three of these questions each lesson has been really helpful with Year 13 this year.

(As you can see, I've become a bit addicted to the Sagona font family!)

A PowerPoint slide with handwritten annotations. On the left are general strategies for conducting an investigation: 1. Get a sense of the problem Try lots of cases! → Systematic → different 2. Make a conjecture Look for pattems Make a prediction 3. Test your conjecture Try to break it! Weird example? 4. General argument Write n for "any number" Not specific cases 5. Extend What would a mathematician do next? On the right are examples of each step, all showing number pyramids with the same number along the bottom row. Example conjectures are: • The top number is 4 x bottom numbers • The two numbers on the second row will be the same • The top number is always even “If the bottom number is an integer” has been added to the last conjecture in a different colour. Suggested extensions are: • Subtract not add? multiply? divide? • 4 layers? 5 layers? n layers? • consecutive? sequence?

The same slide as before, but now with different annotations. The title at the top reads Investigate: bottom row is consecutive integers Some examples are shown on the right. There are three conjectures: Middle row all odd Top number is even Bottom middle number x4 = top number There are three general pyramids, one with bottom row odd-even-odd, one with even-odd-even and one with n-n+1-n+2

A spreadsheet showing the numbers 1 to 72 arranged as an array of 18 rows by 4 columns. The column headings A to D and row numbers 1 to 18 are visible. Square numbers have been highlighted in yellow - the highlighted cells are only in the first and last columns.

Students’ conjectures are written on a whiteboard: All square numbers are in column A or column D. Square numbers alternate between A and D. Gaps between two square numbers in the same column increase by 1 each time. 49 will be in column A , row 13. Square numbers in column D are in square rows. The gap from a square to the next one in its column is its square root. Odd squares are in column A, even are in column D.

I’ve ended up with a few spare lessons with Y8 (unknown for me, I’m usually behind!) so we’ve been doing investigations. They came up with loads of things I’d never thought of! I particularly liked one student’s justification of why even squares appear in square numbered rows. #MathsToday

In #MathsToday we will be playing lobster pots. I bloody love this game, and my version has become ridiculously complicated, with weather forecasts, pirates and extra places to go fishing. Here is a simple version:

www.google.com/url?sa=t&sou...

Do you want an article you have written to appear in Chalkdust issue 21? If yes, the deadline for submissions is issue 21. We're looking forward to reading what you send us!

Exciting Project Revealed |100 Days To Go Revision Books from Corbettmaths YouTube video by corbettmaths

Exciting Project Revealed!
100 DAYS TO GO REVISION BOOKS 📚✅🎉
www.youtube.com/watch?v=bDTH...

A puzzle drawn in black and blue felt tip pen. In the bottom left is a square with area 5. Lined up on top of this original square is the second square, which is exactly the same size. Touching these two on their right is a larger third square, which is as tall as the first two put together. And on the right of the third square is the fourth and largest square - we can’t tell exactly how large this one is compared to the others. The following three points are joined to create the blue triangle: the top left corner of the original square, the top right corner of the second square, and the top right corner of the largest square.

Four squares. What’s the area of the blue triangle?

#geometrypuzzle

This is another of my all-time favourite puzzles. Written on a day when the weather was too bad to go outside, so it seems appropriate for today! How would you solve it?

One of the things we talked about yesterday was the importance of checking #ALevelMaths students know what makes a good sketch.

So in #MathsToday I showed Y8 what good and bad sketches look like. I then plotted some graphs on @desmos.com and got them to sketch on MWB. Might as well start early!

Dirty Dancing to The Muppet Show theme tune YouTube video by Pandamoanimum

A thread of silly videos I've made (most of which are over a minute long, so have to be posted via YouTube links)

The final dance in Dirty Dancing, but they’re dancing to The Muppet Show theme tune.
www.youtube.com/watch?v=V9v6...

My Parallel Academy offers free online maths tutoring for 250 students. Just recruited 450 more! Preparing bright state school kids for UKMT maths challenges. We need more superstar maths teachers/tutors who offer 8+ hrs/wk evenings/weekends, £27.50/h. Email CV & note to tom@goodthinkingsociety.org

In #MathsToday I was trying to explain how to manipulate numbers in standard form so that you could add them. The class was properly struggling with the concept until one of the kids went, "one gets big, the other gets small. How is this even difficult?" 😂

Whammageddon!

Got done by a year 8 watching TikTok on his phone. Confiscated the phone in revenge, obviously.😂

My Y12 class has been solving trig equations this week, and in our first lesson calculators were banned! Here are the new resources I made for using exact values:
✨Exact Trigonometric Values Sort It Out
✨Solving Trigonometric Equations with Exact Values Crack the Code
#UKMathsChat #ALevelMaths

Two identical 2 x 5 rectangles. One is laying on its 5 unit side. The other is immediately to the right and is standing on its 2 unit side. An orange quadrilateral is formed by drawing a line from the top left corner of the lying down rectangle to the top left corner of the standing up rectangle. Another line is formed by connecting the bottom left corner of the lying down rectangle to the upper right corner of the standing rectangle. The two remaining sides are formed by the original two rectangles. What is the area of the orange quadrilateral?

#RecreationalMath #iTeachMath #MathSky

I’m giving away a 4K UHD / Blu-ray edition of Criterion’s stunning I WALKED WITH A ZOMBIE / THE SEVENTH VICTIM

All you have to do it LIKE this, REPOST, and FOLLOW

The winner will be chosen at random on 5th Dec! To enter twice, sign up at at Patreon via the link in the bio!

Good luck!

In U6 #MathsToday we're starting off with a concrete example of finding the values of a and b that minimise the sum of the squares of the residuals for our linear model.

#ALevelMaths

In #MathsToday we were making Sierpinski Tetrahedrons (Green so they can approximate a Christmas 🎄 tree)

These two quiet students loved it being called
"Sir Pink C"
They decided it needed to be a handsome hat.

#ITeachMaths #MTBOS

Mission accomplished! Last school year, I was inspired by another post to curate and organize 180 math tasks on Google Slides. Here is the link: bit.ly/180daysmath

I'm #mathstoday we did some calculating b^2-4ac on whiteboards to iron out some negative number issues before using the quadratic formula to solve quadratics

Gradient-point-line structure #mathstoday #alevelmaths

Transcript of the xkcd comic, from explainxkcd.com Two flow charts are shown. The first flow chart has four steps in simple order, one with multiple recommendations. DIFFERENTIATION Start Try applying Chain Rule Power Rule Quotient Rule Product Rule Etc. Done? No Arrow returns to "Try applying" step. Yes Done! The second flow chart begins like the first, then descends into chaos. INTEGRATION Start Try applying Integration by Parts Substitution Done? Haha, Nope! Chaos, Roughly from left to right, top to bottom, direction arrows not included. Cauchy's Formula???????!???????? Partial Fractions??? Install Mathematica? Riemann Integration Stokes' Theorem???? Risch Algorithm??? Sad face???????? What the heck is a Bessel Function?? Phone calls to mathematicians Oh No Burn the Evidence More arrows pointing out of the image to suggest more steps.

Just finished differentiation with my #ALevelMaths students, and started integration. I'm reminded of this excellent xkcd comic...
#MathsToday xkcd.com/2117/

Twin Proofs for Twin Primes - Numberphile YouTube video by Numberphile

In March 2022 I discussed a property of twin primes with Brady on Numberphile
youtu.be/n4gmYjyI3vo?...
Pick a pair of large twin primes. Multiply. Find digital root. It's 8.

I seem to remember I was first set this as a puzzle by Colin Wright (though that's true of many a thing...)

A PowerPoint slide titled ‘Some nice little puzzles’ Text reads: app.dwo.nl/en/se/ Log in as 'Guest' Select 'SE Lower Grades' Select 'Cube buildings' Select 'Building using three views 1' For each puzzle, you need to build the 3D shape so that it matches the plans and elevations. But! the fewer bricks you use, the more points you score. There is a screenshot from the website, showing the top, front and side views of a 3D shape. The shape has been partially built, from yellow cubes sitting on a grey base.

An absolute classic for Y9 #MathsToday. I don’t think I’ve ever seen them so engaged on a Wednesday afternoon.

Polypad – The Mathematical Playground Unleash your creativity with the world’s best virtual manipulatives!

Teaching year 8 about polygons in #MathsToday and they were exploring why only some shapes tesselate.

Using the Polypad online manipulatives was brilliant and they had a great time creating some "exciting" tiling patterns.

polypad.amplify.com/p#polygons

I do it like this with Y11 students.