Random Thoughts XIV: Pizza, Pomegranate Juice, and Shreddies

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What ever do you mean?
Did you not see it? He twitched his leg! (or maybe it was his foot? :hmm:) :faint:

Or maybe it just looked like it due to the low quality of the recording. :dunno:

Or maybe some women just really love deep-voiced singers (I prefer tenor myself, mostly; for instance, my favorite Rockapella singer is the short blond guy, Scott Leonard).

At any rate, I suppose I should have used this: :sarcasm:
 
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When i think of singers with deep vocals i think of the lead singer from Crash Test Dummies.
 
following up in tumblr is done by clicking on posters' names and that might quickly take one to those not safe for work/NSFW pages . But this account on itself seems to be concentrating on nothing but architecture and the like with many pictures seeming to be of real stuff . At least one Ben Myhre , too , as far as ı have noticed . You might scroll down a bit and right click(?) on pictures to open them in a new tab to download before the site calls on you to join/log in .


31-01-2024.jpg
 
following up in tumblr is done by clicking on posters' names and that might quickly take one to those not safe for work/NSFW pages . But this account on itself seems to be concentrating on nothing but architecture and the like with many pictures seeming to be of real stuff . At least one Ben Myhre , too , as far as ı have noticed . You might scroll down a bit and right click(?) on pictures to open them in a new tab to download before the site calls on you to join/log in .


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Did you mean to link to the OP? It doesn't relate to the rest of your post.

Love the above room, though. If it was real and if I was still able to do stairs, I'd be comfortable in it. With fewer plants, of course (there are reasons why I don't have house plants, and they have to do with over-enthusiastic cats and a couple of science fiction books by Alan Dean Foster).
 
can not manage to link to people so that it would show in the alerts . A trick to multiply browsing the archives is adding date after ...

...archive/2024/01 would show the recent posts and re-writing it to 2023/12 would allow you to see more posts without the ever present "wall" that calls on you to join/login .
 
the city nearby seems to be offended again . Because of my reference to a page in some thread that ı apparently edited after some ransomware attack . Even if reference to it probably involves the American prodding and permission for New Turkey to declare a "Blue Country" in the seas around . Which of course would annul some previous freeze or whatever that was agreed to in 1976 when this country was surprisingly once more ready to go to war against the Greeks , this time over their attempts to stop oil exploration and stuff in the Aegean . The city nearby might have even noticed the Greeks are supposedly sending ships to the Red Sea and off Yemen ; which is payment for Americans to send a Patriot battery to replace the missiles the Greeks have been forced to donate to Ukraine . While this in itself is not much , the talk is the Americans will be based on some island in the Aegean , moving around another freeze that forced the S-300 batteries to Crete , minimising their participation in any likely scenario of short duration clashes in the Aegean . Like the city would have noticed the trolling that has netted me , to my detriment and all , a claim of having had an affair with a some other Russian ; like strange at a time they are so close to being defeated by the West totally and incredibly . The same West that's supposed to be pushing something called the Seville Map and stuff . Against this , the Phantoms were offered as what people should think about . Because whatever made them passable back in 2019 naturally still stands in 2024 , to be really chanced against Patriots and not just in Crete , too . Have a been a patriot , the people of the city nearby , before quite a few of you were even born . Ignore stuff , be happy , don't interfere/anlamadığınız işe karışmayın.
 
There was some discussion today on my FB feed, on the following math homework question, given to 9-10 year old kids here in some school (or perhaps it is part of the official book for that grade - don't know).

1707241686402.png


The question tells you that a student rolled the dice 5 times, getting the numbers 2,6,4,6,3, and that he will roll the dice two times more. And asks what numbers he should get in the two final rolls if the average value of all rolls is to be a natural number.

Personally (I took some part in the discussion) I am of the view that it is good that such questions are asked so early - ok, not all the kids will get the answer, but some may actually find the search captivating and develop a love of math.
I assume that the method expected to be used would be along the lines of: the 5 rolls he already got give a total of 21, with the 2 final rolls it will be 7 rolls, the average of the value of all rolls is (21+A+B)/7 => if the average is a natural number (or even an integer...) 21+A+B should be perfectly divisible by 7, but since 21 is already perfectly divisible by it, it follows that A+B should also be perfectly divisible by 7 => a,b (order interchangeable) are 1,6 or 2,5 or 3,4.

Some in the thread argued that it is just too hard on the majority of the kids, who may feel nervous. I agree. But imo there's also a lot to gain for those who will feel attracted to math so early on, so I like it was a question in class :)
 
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There was some discussion today on my FB feed, on the following math homework question, given to 9-10 year old kids here in some school (or perhaps it is part of the official book for that grade - don't know).

View attachment 684122

The question tells you that a student rolled the dice 5 times, getting the numbers 2,6,4,6,3, and that he will roll the dice two times more. And asks what numbers he should get in the two final rolls if the average value of all rolls is to be a natural number.

Personally (I took some part in the discussion) I am of the view that it is good that such questions are asked so early - ok, not all the kids will get the answer, but some may actually find the search captivating and develop a love of math.
I expect that the method expected to be used would be along the lines of: the 5 rolls he already got give a total of 21, with the 2 final rolls it will be 7 rolls, the average of the value of all rolls is (21+A+B)/7 => if the average is a natural number (or even an integer...) 21+A+B should be perfectly divisible by 7, but since 21 is already perfectly divisible by it follows that A+B should also be perfectly divisible by 7 => a,b (order interchangeable) are 1,6 or 2,5 or 3,5.

Some in the thread argued that it is just too hard on the majority of the kids, who may feel nervous. I agree. But imo there's also a lot to gain for those who will feel attracted to math so early on, so I like it was a question in class :)
It was a very long time ago, but I cannot remember doing anything beyond arithmetic as maths at that age.
 
It was a very long time ago, but I cannot remember doing anything beyond arithmetic as maths at that age.
I was in a (supposedly - not really) prestigious elementary school, and in some final exams you'd see something along those lines.But there it was very clearly meant to fish for the mathematically inclined, not be a standard question.
 
There was some discussion today on my FB feed, on the following math homework question, given to 9-10 year old kids here in some school (or perhaps it is part of the official book for that grade - don't know).

View attachment 684122

The question tells you that a student rolled the dice 5 times, getting the numbers 2,6,4,6,3, and that he will roll the dice two times more. And asks what numbers he should get in the two final rolls if the average value of all rolls is to be a natural number.

Personally (I took some part in the discussion) I am of the view that it is good that such questions are asked so early - ok, not all the kids will get the answer, but some may actually find the search captivating and develop a love of math.
I expect that the method expected to be used would be along the lines of: the 5 rolls he already got give a total of 21, with the 2 final rolls it will be 7 rolls, the average of the value of all rolls is (21+A+B)/7 => if the average is a natural number (or even an integer...) 21+A+B should be perfectly divisible by 7, but since 21 is already perfectly divisible by it, it follows that A+B should also be perfectly divisible by 7 => a,b (order interchangeable) are 1,6 or 2,5 or 3,4.

Some in the thread argued that it is just too hard on the majority of the kids, who may feel nervous. I agree. But imo there's also a lot to gain for those who will feel attracted to math so early on, so I like it was a question in class :)
That is more advanced than what we did in that grade, but I do remember that we had similarly challenging bonus problems that were not from the syllabus, but probably not up to the difficulty/complexity level of this particular problem. (But then we didn't learn Probability until O-levels)
 
^Some of the math teachers in the thread suggested that at times such problems are given simply to have the kids try and then discuss any partial answer they may arrive at. I personally am in favor of it.
Some other math teachers in the thread expressed thoughts on the complexity making them and the kids nervous.

It could have been a lot worse. They could have asked for a general formula for any number of rolls of the dice ^^

The 9 year old should use the binomial theorem - the good 9 year old, the rest will be thrown off the cliff at mount Taygetos.
 
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This is a straight-forward problem that only requires knowing what "the average" means. It shouldn't be hard for 9-10 year olds, which would be 4th or 5th graders here. Averaging is typically taught in 3rd grade.

The average is 1, 2, 3, 4, 5, or 6. There are 7 rolls, and the total is the average times the number of rolls, so the total is 7, 14, 21, 28, 35, or 42. We already have a total of 21, so the last two rolls have to bring us to 28, 35, or 42. Since we can't roll more than a 6 or less than a 1 each time, 28 is the only possibility. We need a total of 7 on our last two rolls. What adds up to 7? 1&6, 2&5, 3&4.
 
^Yes, that's the other method I thought of too. But it is slightly less formalized (<=> more reliant on natural language explanations and particulars of the case, instead of a general scheme/progression). Can't have that for kids, bad habits ^^
 
I assume that the method expected to be used would be along the lines of: the 5 rolls he already got give a total of 21, with the 2 final rolls it will be 7 rolls, the average of the value of all rolls is (21+A+B)/7 => if the average is a natural number (or even an integer...) 21+A+B should be perfectly divisible by 7, but since 21 is already perfectly divisible by it, it follows that A+B should also be perfectly divisible by 7 => a,b (order interchangeable) are 1,6 or 2,5 or 3,4.
I worked it out with my rudimentary arithmetical knowledge that the easiest number would be 28 and I'm glad to see that somebody else got to the same number. What did other people say?
 
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