richardtrimble.bsky.social
52 posts
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80 following
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When I see a big Sverdrup coming I just resign myself to going with the flow...
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For political reasons I am backing the Sievert (my wife works in Radiotherapy). However milliSieverts are much preferred!
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I really appreciated your best guess posts and the people who made the papers. My students did too and made a point of saying thank you too just before CP2.
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How about 'pure fraction' vs 'mixed number'?
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The analogy I use is climbing an infinite ladder 🪜.
I can get onto the first rung.
If I'm on a rung I can get to the next one up.
Therefore I can climb the whole (infinite) ladder.
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This is exactly right, they can only be issued to the student, not even the parent unless there is a prerequisite arranged letter authorising this from the student
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Can I recommend David Bressoud's book: Calculus Reordered: A History of the Big Ideas? A very strong case for the primacy of integration both historically and pedagogically.
press.princeton.edu/books/hardco...
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You've really wet my atmosphere...
I'll get my coat.
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This is definitely the easiest explanation to grasp intuitively for me.
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The error term is proportional to the fourth derivative of the function at some point in the interval so it is exact for cubics.
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Let's use induction, then I only need to know f_1, f_2, and f_8.
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Shame
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The word "Judeo-Christian" came into circulation following the Holocaust as Christian theologians tried to reset the church's teaching to acknowledge that Jesus was Jewish.
blogs.timesofisrael.com/antisemitism...
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I think all the values you are generating are similar because your criteria for a 'good fit', although all different, are strong enough to lead to very similar curves.
If you can think of a criteria whose best fit curve has power 1/√π your coincidence will be explained. I can't think of one ATM!
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The BYU version reminds me of Pentatonix which suggests it might be processing/mixing. I definitely prefer the second version you posted, not just because it sounds better but also because they look like they are having a great time!
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bsky.app/profile/benr...
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Love this!
Such a Simple bound!
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Ah you are reminding me of my favourite macro, I managed to cobble together some excel vba so I could enter numbers via the keypad WITHOUT PRESSING ENTER! Then Excel upgraded and it broke...
Cast out of paradise.
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I think maybe use your idea of, usual coordinates on the left, transformed coordinates (with all those parallelograms) on the right and just observe how a *single point* moves. That will emphasise the linearity, then it becomes obvious that every (small) square becomes a (small) parallelogram.
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Oh no! I hope that's not our board, we recently moved from MEI to edexcel and I'm still catching up!
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I much prefer concave up and concave down. misconceptions almost all eliminated with this language very clear link to second derivative. Make the switch, you won't regret it.
Leave convex for the physics people where objects have an inside and outside and it actually makes sense. Or polygons....
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Here is another one I can't resist sharing. We ask if two equal squares can equal another square. Number work galore, and hiding behind it all we get to approach the irrationality of sqrt 2. Can do this over two lessons.
docs.google.com/document/d/1...
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I forgot, the geometric magic squares is better if you have done a pentominoes investigation first! Lots of systematic searching, questions of how you know you have found them all etc.
Follow up with finding all possible tilings of a 3 by 5 rectangle and the reasoning to know you got them all
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2. Geometric magic squares, did you know over every number magic square there are loads of geometric ones! So much fun and creative problem solving, not to mention display work if you need that stuff!
docs.google.com/document/d/1...
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I'll give you a beautiful sequence of two lessons i used in a similar situation a few years ago.
1. Make 15, this is an number game that turns out to be isometric to noughts and crosses played on a magic square
docs.google.com/presentation...
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I guess you are teaching in the USA.
Sadly here in the UK we lost Euler's method from most syllabii in Secondary school in 2017. But, yes, I always started with spreadsheets too!
Great fun. Do you explore the error term being proportional to the square of the step size?
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geogebra.github.io/docs/manual/...
You might find the slopefield tool on geogebra easier. Together with SolveODE or NSolveODE you can investigate a lot of differential equations
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Preview y2 content in y1, refer back, recap, connect. It's not ideal.
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AS maths has a roughly 85% pass rate. Not generously marked, just AS not A Level. All our y1 students sit AS maths with passing as a prerequisite to y2. A substantial minority of our students have grade 6 or even 5 at GCSE, those who pass y1 almost always pass y2. It's objective, fair and useful.
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and one very wide low frequency density bar out around 2.5 standard deviations away from the mean. It will have the highest frequency but most certainly departs from the concept of mode being a measure of central tendency.
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Take an extreme example and you will see that frequency must be the wrong answer.
E.g. take a sample from some normal data, plot the histogram with lots of thin, low frequency, high frequency density bars in the central area near the mean ...
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Yes, thanks Colleen.
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We recently moved board from MEI to Edexcel and discovered they don't want us to plot negative r values for some reason! So I have an adapted plotter that allows you to show/hide negative values of r, which I think is necessary for the explanation.
www.geogebra.org/m/xcafkwpt
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Thanks!
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Do you have a 'go to' source for these sessions or is this a fabulous pulling together of ideas?
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'making my own graph paper' is where I'd draw the line.
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Glad you liked it!
I tried your gaussian elimination method with a class, not convinced yet but open to trying it again.
bsky.app/profile/rich...
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Yes it is - if going to bigger matrices. I want them to know the cross product in vectors though and I am doing surgery on their understanding of inverse matrices (not taught by me). I had intelligent students faced with
AB = (scalar) I
Not realising that B relates to A^-1 !
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My approach to this is via the vector product, the determinant as scalar triple product and flat parallelepipeds having volume 0.
( a b c)^T ( b×c -a×c a×b ) = (a.b×c) I
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When we academised our contracts were TUPEd over so there was no change except at the governance and financial level as we no longer had top slicing.
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It isn't a polyhedron so I'm not sure there question makes sense
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This feels like a lovely hack! It sits very nicely with compound interest 'minus 1 years'. Might be harder to motivate in the 'original price' context.
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Usually 'harder', there should be an explanation in the first 5/6 pages of the book buried somewhere...
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Here is an activity I used with a very able ks3 class on this very thing about 6 years ago. It is based on a special carpet diagram which I love.
docs.google.com/document/d/1...
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This bit is so much fun and so little known...
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I find the proofs of these converses sneaky I don't know one that doesn't somehow use the 'forwards' argument.
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Here is another one on a similar theme:
Prove that the locus of D with angle BDC fixed is a circular arc starting at B and ending at C.
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Or perhaps parallel lines, suppose the circle centre A radius AB intersects AD at D' possibly not equal to D.
Then BD'C is half BAC (forwards version). But BDC is the same angle so D'C and DC are parallel and, since D' and D lie on AD, D' and D must coincide.
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OK. When you say 'linearity of both ax + by + cz and of "being at right-angles to" gives the general result', I'm not sure I go with you on the second. If I project a right angle from 3 to 2D the image might not be right angled. I feel lifting up from 2 to 3D might be possible but not obvious!