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Paddy MacMahon @paddymacmahon.com · 16h

I couldn't make this one unfortunately... Next time!

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Paddy MacMahon @paddymacmahon.com · 1d

This ☝️

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Reposted by Paddy MacMahon

Steve Walker @stevemaths.bsky.social · 2d

Here's our #OCRMathsPuzzle to end this week. 🙂

The vertices of a square just touch four edges of a regular octagon, as below.
The area of the square is 32 cm^2.

Work out the area of the regular octagon.

#MathsToday #UKMathsChat #RecreationalMath #geometry #area

Image describes the geometric problem.
The vertices of a square just touch four edges of a regular octagon. The area of the square is 32 cm squared. Work out the area of the regular octagon.

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Paddy MacMahon @paddymacmahon.com · 3d

...and unfortunately for some functions the derivatives are 'nested too deeply', so some of the d_s list will need to be deleted...

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Paddy MacMahon @paddymacmahon.com · 3d

Maclaurin Series in #ALevelMaths #FurtherMaths #MathsToday, so we're building animations using @desmos.com. Here's my effort:

www.desmos.com/calculator/z...

maclaurin animator

www.desmos.com

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Paddy MacMahon @paddymacmahon.com · 3d

A bonus area problem for the end of the week, inspired by a post by @mrlevmaths.bsky.social.

Important info from the alt-text: the curve is a parabola.

#ALevelMaths #MathsToday

Paddy MacMahon @paddymacmahon.com · 3d

I saw your labels and thought these represented the actual areas (as in the area of region 1 is 1 unit, of region 2 is 2 units, etc...) which got me thinking that that sort of thing might make a nice problem. Impossible to get regions with those areas using a parabola, but I came up with this:

A parabola passing through the origin and a positive value on the x-axis, with a maximum point in the first quadrant. A straight line with positive gradient intersects the parabola at 2 points in the first quadrant. Vertical line segments are drawn from each of these intersection points to the x-axis, so the area enclosed by the parabola and the x-axis is divided into 4 regions. The left hand region has area 13, the right hand region has area 44 and the top region has area 8. The final region is labelled with a question mark.

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Paddy MacMahon @paddymacmahon.com · 3d

I saw your labels and thought these represented the actual areas (as in the area of region 1 is 1 unit, of region 2 is 2 units, etc...) which got me thinking that that sort of thing might make a nice problem. Impossible to get regions with those areas using a parabola, but I came up with this:

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Reposted by Paddy MacMahon

Peter Rowlett @peterrowlett.net · 4d

The call for peer reviewers is very real - if you teach maths at the upper end of school through to early university and are interested in maths content useful to people like you, please get in touch via [email protected] - thanks!

#MathsToday #UKMathsChat #ALevelMaths #MathToday #MathSky

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Reposted by Paddy MacMahon

Catriona Agg @catrionaagg.bsky.social · 4d

In #MathsToday I made 40 A Level teachers colour in representations of the binomial distribution.

This is your regular reminder that if you teach #ALevelMaths you should definitely try to join your local Maths Hub’s A Level Pedagogy group. There is some brilliant stuff going on all over England.

A quartet of representations of the binomial distributions. Screenshots from https://www.desmos.com/calculator/3ea50eafbc

X ~B (10, 0.4)
Shade the diagrams to represent the probability
P(3 ≤X <6)
and draw a numberline.

X~B(10,0.4)
Shade the diagrams to represent the probability P(3 ≤ X < 6) and draw a
numberline.

X ~ B(8, 0.7)
Which is larger:
P(X < 5) or P(X = 6)?

X~B(12,0.36)
P(X ≥ c) < 0.5
What is the smallest possible value of c?

X~B(10,0.4)
Calculate the interquartile range of this distribution.
What is the mode?

X~B(8, 0.7)
P(X ≤ a) < 0.1
What is the largest possible value of a?
P(X ≥ b) < 0.1
What is the smallest possible value of b?

X~B(12,0.36)
P(X ≤ a) < 0.2
What is the largest possible value of a?
P(X ≥ b) < 0.2
What is the smallest possible value of b?

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Paddy MacMahon @paddymacmahon.com · 5d

Lots of SMC practice in #MathsToday.

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Reposted by Paddy MacMahon

Jed @jedediyah.com · 6d

First @NCTM.org yearbook (1926) here: catalog.hathitrust.org/Record/00006...

An interesting take on quadratics!

"Nor should we expect to have all the pupils able to factor ax^2+bx+c (a useless accomplishment for most people)"

"If the subject is to be valuable, the learning should be a pleasure"

As a result of this view of the reason for teaching algebra, we have come to see that we should not expect everyone to solve two simultaneous quadratic equations, although out of an entire class there will be found a few who can do so. Nor should we expect to have all the pupils able to factor ax^2+bx+c (a useless accomplishment for most people),

a considerable number will take pleasure in performing such a task and will thereby acquire some special skill which they may find useful in later work. The purpose of teaching algebra is found in none of these details: it consists in giving to everyone a general idea of the meaning of algebra, together with a few definite and useful applications which everyone is likely to meet. If the subject is to be valuable, the learning should be a pleasure, and it may properly be expected that this pleasure will carry the pupil into such manipulations of algebraic expressions as will fix the habit of using algebra in the cases to which it can be applied.

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Reposted by Paddy MacMahon

Kate Devlin 🎃👻🍂 @drkatedevlin.bsky.social · 6d

Am off to Kraków soon for a talk on Thursday as part of @unsoundfestival.bsky.social — awesome music festival (with talking bits too). www.unsound.pl/en/unsound-w...

Kate Devlin
IDISCOURSE PROGRAMME]
09.10
13:15
Patac Krzysztofory - Sala Miedziana
Discussion:
Future Sex
unsound. [web]
7-12October
Kraków

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Reposted by Paddy MacMahon

MEI @meimaths.bsky.social · 7d

We are proud to be sponsoring 10 places to attend the teacher day at ICTMT17 in London on 22 Oct buff.ly/piLruty

Take part in workshops, meet sector leaders, hear MEI’s Tom Button & Natalie Vernon on using Desmos

Apply: buff.ly/mnzr2N5

#ICTMT17 #MathsEd

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Paddy MacMahon @paddymacmahon.com · 6d

45% of 40 is 40% of 45.

40% is two-fifths, and one fifth of 45 is 9. So 18.

Paddy MacMahon @paddymacmahon.com · 6d

Yeah, I thought this was at the easier end of the spectrum. Although I needed some pen and paper working...!

Gemini pro made a hash of it...

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Paddy MacMahon @paddymacmahon.com · 7d

#ALevelMaths #MathsToday

Monday area problem. Find the exact value of the green area.

The graph of y=x² is in red, together with the point (sqrt3 / 2, 3/4) highlighted and labelled in blue. Also in red is a circle, tangent to the x-axis and touching the curve at the blue point. The region enclosed by the curve, the circle and the x-axis is shaded green.

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Paddy MacMahon @paddymacmahon.com · 8d

Something like: 2x³+ax²-4x+12 has a repeated root. Find a.

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Paddy MacMahon @paddymacmahon.com · 10d

Very proud of our girls in #MathsToday. 19 distinctions and 19 merits in the UKMT Mathematical Competition for Girls.

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Paddy MacMahon @paddymacmahon.com · 10d

I try never to use the word integral until we're talking about areas.

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Reposted by Paddy MacMahon

Darren Macey @darrenmacey.bsky.social · 10d

For more ideas for teaching statistics, check out our new lesson activities designed for Maths Week Scotland. rss.org.uk/resources/ed...

#MathsWeekScot

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Paddy MacMahon @paddymacmahon.com · 10d

It was this matrix transformations investigator:

www.desmos.com/calculator/c...

Referring to it as a graph doesn't quite seem right. Applet? Program?

Matrix transformations III

www.desmos.com

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Paddy MacMahon @paddymacmahon.com · 10d

I like this. I often pronounce desmos as if it were in French, so I reckon I can adapt to this.

"Use this desmo to investigate matrix transformations."

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Paddy MacMahon @paddymacmahon.com · 10d

In #MathsToday I'm wondering how to refer to a single @desmos.com instance.

Should I tell pupils to 'use this desmos to investigate' or 'use this desmos sheet...' or something else...? Should they 'make a desmos' to illustrate a graph?

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Reposted by Paddy MacMahon

Raj Raizada @rajraizada.bsky.social · 12d

I think my geometry students will enjoy making an infinite zoom effect, using the dilation tool in @desmos.com Geometry. Here's an initial attempt. Don't stare at it for too long! 😀
www.desmos.com/geometry/x46...
#iTeachMath

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Paddy MacMahon @paddymacmahon.com · 12d

In #ALevelMaths #MathsToday we started looking at transformations in terms of how you change the coordinates, using @desmos.com. Next time: encoding (some of) them with matrices.

www.desmos.com/calculator/j...

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