A man sits on a park bench surrounded by a large crowd of pigeons and ibises. He peels the coating off a piece KFC chicken one small fragment at a time and throws the fragments to the birds.

A man sits on a park bench surrounded by a large crowd of pigeons and ibises. He peels the coating off a piece KFC chicken one small fragment at a time and throws the fragments to the birds.

Wordle 1,768 3/6.

1: b b b b b …
2: G b Y b b …
3: G G G G G …

I was enjoying this game and then it was suddenly over.

So #MathSky #iTeachMath, submissions for workshops for my local maths teacher association conference are due shortly, so I am making my yearly request for what things you would have me run a 50-minute session on. (Even if you can’t come, you can imagine what you’d love to be part of if you could.)

This Is Just To Say

I have turned off
the AI features
that were in
the update

and which
you were probably
hoping
to monetize

Fuck you
they were stupid
so unnecessary
and so annoying

Ooh Operation Tower. Never thought of doing a session on that. VERY interesting idea!

I'm sorry, but that's just a list with dot points under headings. Drawing it in concentric circles does not make it a model.

So #MathSky #iTeachMath, submissions for workshops for my local maths teacher association conference are due shortly, so I am making my yearly request for what things you would have me run a 50-minute session on. (Even if you can’t come, you can imagine what you’d love to be part of if you could.)

7/12+-2/12=5/12
7/12 * -2/12 = -7/12*1/6=-7/72≈-1/10, not low enough

8/12+-3/12=5/12
8/12*-3/12=2/3*-1/4=-1/6, not low enough

9/12+ -4/12 = 5/12
9/12 * -4/12 = 3/4 * -1/3 = -1/4 YAY!

So it's 12(x+3/4)(x-1/3).

How about one more?
Factorise 12x^2+5x-3.

12x^2+5x-3
=12(x^2+5/12 x-3/12)
=12(x^2+5/12 x -1/4)

We need to add to 5/12 and multiply to -1/4.
One + and one - is what I need.

6/12+ -1/12=5/12
6/12 * -1/12=1/2 * -1/12 = -1/24 not low enough

Someone has shown it to me before, but I can never remember the trick (and hence it is a trick).

Though the original writer was probably going for (4x-3)(5x-2), but I like mine better.

16/20+7/20, yeah that 7 will be a problem

15/20+8/20
15/20*8/20 = 3/4*4/10=3/10 YAY!

So it's 20(x... wait. I was doing it with +23/30 in the middle. No worries. It will work fine if I change them both to minus.

20(x^2-23/10 x+6/20)
= 20(x-3/4)(x-2/5)
Nice.

20x^2-23x+6
=20(x^2-23/20x+6/20)
Things that add to 23/20 and multiply to give 6/20 = 3/10.

First instinct is 20/20+3/20=23/20.
20/20*3/20 = 3/20. Too small.

21/20+2/20
21/20*2/20=21/200≈1/10, even smaller.

18/20+5/20
18/20*5/20=9/10*1/4=9/40=2.25/10, closer

I feel like doing another quadratic.
Factorise 20x²-23x+6 (from corbetmaths.com)

Bahahaha! How many 50's go into 833? Well there would be 16 in 800, and then not quite a whole one for the 33. How many short are we to get the 17 50's in 850? Ah 17 exactly. So it's 17×50-17 = 17×49.

Multiples of seven I just don't have much of a feel for, but that means they can give me these sorts of surprises. Take 833, for example. Take 700 to get 133, then add 7 to get 140. Lovely.

I really like netball. I found it a very enjoyable game to play, and it's also mathematically interesting in several different ways.

A man walks three dogs, who are in sequence along multiple dimensions: small, medium, large; stub tail, short tail, long tail; smooth hair, fluffy hair, curly hair; white, tan, brown.

A man walks three dogs, who are in sequence along multiple dimensions: small, medium, large; stub tail, short tail, long tail; smooth hair, fluffy hair, curly hair; white, tan, brown.

In the park, a young girl sits in the middle of the the path with her feet out and her takeaway chicken nuggets and chips between her legs. The other six members of her family sit at the picnic table on the lawn five metres away.

During the course of a normal lesson, absolutely ask them what they notice! I agree this is a very good and important thing, as long as you are actually interested in what they personally say, rather than waiting for a specific response and declaring everything else wrong or not quite there.

Don’t care. You should never ask “what do you notice?” as a formal assessment because if you’re looking for a specific response, then you’re not wanting to know what they notice.

What goes into 833?
833/7=119 oh that’s a surprise
119/7=17 oh wow it’s got a 7^2 in it
833=17×7^2
√833=7√17
q=-31/16±7√17/16
Doesn’t really give me any better of a feel for it. I mean I know it’s really close to 30/8 and 1/8 and that’s good enough for me.

If I completed the square, I’d halve the middle coefficient to get 31/16, so I’d need to add and subtract 961/256, and when combined with the 1/2 = 128/256, that would make it in 256ths 961-128=833
So I’d get
(q+31/16)^2=833/256
q+31/16=±√833/16
q=-31/16±√833/16
Sure.

What happens with the +4 though?

8q^2+31q+4=0
q^2+31/8 q +1/2=0

31/8+0=31/8. 31/8×0=0
30/8+1/8=31/8. 30/8×1/8=15/32 remarkably close but too low!
29/8+2/8=31/8. 29/8×2/8=29/32 way too high.
So there’s an answer somewhere in between.
It’s probably irrational isn’t it?

So I was right:

8q^2+31q-4=0
q^2+31/8 q -1/2=0

4+-1/8=31/8
4×-1/8=-1/2

(q+4)(q-1/8)=0
q=-4 or 1/8

Just checking the original question again and it was indeed
8q^2+31q-4=0
and not
8q^2+31q+4=0

8q^2+31q+4=0
q^2+31/8 q +1/2=0

I need numbers that multiply to 1/2 and add to give 31/8. Hmm.

31/8 = 32/8-1/8 = 4-1/8
Ah and 4×1/8 is indeed 1/2. Lovely.

No wait. That’s 4 and -1/8 which multiply to -1/2. Damn.

Saw a quadratic equation go past and I want to solve it.

8q^2+31q+4=0