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profsmudge.bsky.social
ProfSmudge
@profsmudge.bsky.social
350 followers 200 following 690 posts
School maths should be more than tables and algorithms. I try to write materials that show that. Dietmar Küchemann
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 10h
#MathsUntangle Probably the best fractions task I've ever written (at least I thought so at 4 am this morning....)
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 11h
In #MathsToday I helped a Y11 student solve inequs like x2+2x–8 < 0, via graphs and factorising to find a range of values on the x-axis. We hammered out a procedure, but it seemed like a completely alien world, a bit like going through a latin mass. If she masters the procedures, what does it prove?
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 1d
Yes, hard is good!
profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 1d
#MathsToday Working with two Y11 students yesterday, we checked to see whether 121 was divisible by 3.
The division 121÷3 gave us 40 r1.
I suggested we could treat the remainder as 1÷3 which proved to be very challenging.
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 1d
They remind me of this ICCAMS lesson, though your tasks seem mindbogglingly more difficult!
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 1d
Thank you. I think they held to exactly that naive argument.
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 2d
In #MathsToday a Y11 pupil said she thought it would be easier to get a grade 5 GCSE on the Higher rather than the Foundation papers. Is there any truth in this??
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 3d
Nagelsmann nails it....
profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 3d
Manager of a not very good team annoyed by the suggestion that it's not a very good team....
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 3d
Thank you - though I'm not convinced! I'd have thought it might be easier to see when two angles are identical, when formed by parallel lines, than to see the '180-ness' of a triangle!
I suppose "Here's a conjecture, will we be able to prove it one day?" might excite some pupils!
profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 3d
Interesting....
Tearing up triangles tends to produce a horrible mess as it destroys the triangle, though if used carefully it could provoke the classic proof involving an exterior angle.
I did once meet a teacher who used triangle angle sum to deduce angles on a straight line, but....
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 3d
"Many courses put the triangle-interior-angle-sum before corres. & alter angles … "
Do they really?? Doesn't seem coherent! Don't we use parallel line properties to prove interior angle sum?
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 3d
Nice stuff. I was just thinking about this similar task, as part of some work on fractions
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 5d
I was hoping one could get away with a 'by symmetry' argument, as A'B' is parallel to CB, or would that jar with Euclid's chain of reasoning?!
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 6d
Here's the beginnings of a dynamic proof of this
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 7d
I asked whether he could have used common fractions: 1/2 ÷ 8.
He suggested the 'flip...' method, but having changed 1/2 ÷ 8 into the full-blown fractional form 1/2 x 1/8 he wanted to 'fllp' again.
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 7d
He changed 1/2 to 0.5 and then used the unitary method, but initially found 8÷0.5 where he recognised that the result, 16, didn't make sense.
He then got 0.0625 and 0.375 which he knew was 3/8.
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 7d
In #MathsToday I used the classic 'cream for 6 people' recipe task with a Y10 student.
'pints' threw him so I changed this to 'litres'.
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 7d
Taking the extreme cases, it looks like it should be 50....
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 8d
Nice. Reminds me of this (Durell, 1939, Geometry for Schools)
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 9d
It's German, Jim, but not as you know it
dzlm.bsky.social
Deutsches Zentrum für Lehrkräftebildung Mathematik @dzlm.bsky.social · 9d
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profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 14d
Dee La Warr Pavilion, Bexhill. A day at the seaside.
profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 14d
I've had another look at this. Given your algebraic solution, that the area = 4 = 2², then we must be able to show that the 'houses' fit on the two (red) squares on the sides of your green right-angled triangle with hypotenuse 2:
profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 15d
This is all a bit Alice in Wonderland. An 'independent review' says Oak need more funds to publicise their resources, on the strange notion that the resources are worth publicising
profsmudge.bsky.social
ProfSmudge @profsmudge.bsky.social · 17d
?!
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