Aaron Paquet-Smith

A grid of empty boxes with the headings: A is the point, B is the point,Midpoint of AB, Length of AB. Gradient of a parallel and perpendicular line. y-intercept, x intercept, equation of the line and sketch.

(Yet) another "Blank is Best" slide used in #MathsToday.

I made up the coordinates of A and B and Y10 had to try and fill the rest.

What was it that was hard about finding the horizontal and vertical distances? Knowing where to start counting from and to?

A task I liked from this week: instead of directly teaching the inclusion-exclusion formula, we treated finding probabilities as a puzzle to be solved with a Venn diagram. Then I showed them the formula and let them choose which they preferred to use. #mathstoday

If you wish your students had better number sense, then you'll love the estimation tasks from Andrew Stadel on Estimation 180. Here are the first twenty to get you started.

estimation180.com/days-1-20/

#MathsToday We did gradient of line segments in Year 9 by considering a rescaling of the overall countable change. No change in y over change in x, or rise over run.

Would anyone know where I might find a matching task for algebraic, trigonometric and exponential form of complex numbers? #Mathstoday #Alevelmaths

Adding some extra tasks for when I teach inverse trigonometric functions. When do arcsin, arccos and arctan behave, and when do we need to be careful? #mathstoday #Alevelmaths

What a great headline to use as a prompt right before teaching second derivative tests.

News headline "Flu hospital cases rising in England, but rate of increase slows"

My old friend the second derivative, we've been expecting you...

I also really struggled with core maths for grade 4 and 5 students. Glad to see others in the same boat here!

Thanks! What is the rotational thing, exactly? If you don't mind sharing!

Thank you, Andrew, for your detailed response. This is exactly the sort of rich discussion I am hoping to have on here!

What do you mean exactly by this second lie? If I have understood correctly, this would follow by the uniqueness to the ODE which I agree we can be happy to gloss over.

I agree this is nice maths. And the final result you mention here we can also get from compound angle formulae?

Are you referring to the unproven uniqueness of the solution to the ODE?

Thank you, this is interesting! This is also how the French book I am referring to has motivated it. But how would we justify the form e^ix and not some other constant e^kx? This is where I was feeling a bit unconvinced.

ChatGPT has given me that if f(x) = cos(x) + i*sin(x), then f'(x) = i f(x). The only function satisfying this is ke^ix, but using f(0) = 1 sets k = 1. This is quite neat.

v^2 = u^2 + 2as is also canonical in the sense that we get the work-energy principle from it. Or vice versa, depending on your start point.

Yes, and this is how I learned it too. But I will be teaching this in the French curriculum and they won't have encountered Taylor or Maclaurin expansions so I am hoping to find an alternative.

Yes, exactly!

Question for #ALevelMaths teachers. When teaching the exponential form of a complex number, how do you motivate this intuitively? I will (soon) be teaching this and interested in the various ways of doing it. #MathsToday #UKMathsChat

Y=ax²+bx+c in an attic

You've heard of elf on the shelf but have you heard of

Scrolling down, would the questions from these topic-by-topic practice booklets help? www.mathsgenie.co.uk/statistics.php

I suppose, a priori, no! But it can be hard to keep the hour productive and not feel like the holiday may as well already have started.

It would also be refreshing to not, again, leave stats until the end of the year.

Yes, I might need to re-think the teaching schedule! I was trying to do volume and surface area which may have been too 'boring'. Two-way tables have the benefit of feeling more like a fun puzzle!

This is a good idea. You don't find the motivation is too low from practice being too distant?

In Year 11 foundation #mathstoday we're doing just a past paper. Energy has waned and getting new content across so close to the holiday (we break up tomorrow) is really tough. Any tips for keeping new learning going before the holidays?

A simple, but one of my favourite, worksheets from mathspad today. I like the way the jumbled answers are in terms of pi or written to two decimal places. It forces the learners to be conscious about the distinction between the two. #MathsToday

Are Hungarian frames specifically for the recognition of 5 or also of other numbers? As a secondary specialist, these are new to me.

#MathsToday Same but different parametric equations to match to their graphs. We had a lovely 15 minute discussion based on this task, plus lots of Desmos animated particles to help us think about the x- and y-coordinates changing at different rates.