I went through and can't find the grading example that they had when I was dealing with this with my kids. If I can get the spacing right they showed the student's work as below, with the proper pen marks for 'carrying' if you were doing long hand multiplication:

37
*23
------
111
740
------
851

The marking guidelines stated that this was to be marked as INCORRECT, because the student was falling back and using the algorithm and the correct answer was to formulate multiple different strategies for solving the 'problem'.

A better answer would have been 10 times 37 is 370, so 20 times 37 is 740, then 3 times 37 is 111. So 740 plus 111 makes 851.

Even that though was NOT a good enough answer. No, the BEST answer was the above and then a second method like calculating 25 times 37 and subtracting 37 twice as an alternative solution.

@drradon: I agree with you 100% on teaching both and teaching basic arithmetic first and then leading on to proper math once that foundation is established.

@dannym3141,

I was first blindsided by it when my kids came home with multiplication homework and were adamant they couldn't answer it the way I was showing them because it would be marked wrong, it was the wrong way to do multiplication.

The link to the full Manitoba math curriculum is below. The worst sections are under 'Mental Math' with the idea being that you should be able to add/subtract/multiply/divide all numbers in your head with a dozen pages worth of tricks. The tricks being what newtboy was calling 'proofs'. Our curriculum calls them 'techniques' though and I've included an example from the Grade 3 curriculum verbatim after of how it is supposed to be 'taught'.

Overall Math curriculum:
http://www.edu.gov.mb.ca/k12/cur/math/index.html

Grade 3 example:
http://www.edu.gov.mb.ca/k12/cur/math/support_gr3/number.pdf

From page 56:
Describe a mental mathematics strategy that could be used to determine a given basic fact, such as
-doubles (e.g., for 6 + 8, think 7 + 7)
-doubles plus one (e.g., for 6 + 7, think 6 + 6 + 1)
-doubles take away one (e.g., for 6 + 7, think 7 + 7 – 1)
-doubles plus two (e.g., for 6 + 8, think 6 + 6 + 2)
-doubles take away two (e.g., for 6 + 8, think 8 + 8 – 2)
-making 10 (e.g., for 6 + 8, think 6 + 4 + 4 or 8 + 2 + 4)
-commutative property (e.g., for 3 + 9, think 9 + 3)
-addition to subtraction (e.g., for 13 – 7, think 7 + ? = 13)."

Now before you think me and observe there's nothing wrong with showing kids some extra tricks to help them, that is NOT how this is supposed to be used. If you read further, students are REQUIRED to "explore" multiple methods of calculating answers and must demonstrate they know and can use all these 'tricks'. So instead of providing assistance for difficult calculations as it should be, it's used to make ALL calculations difficult, and create extra work, AND makes kids just learning the concept completely overwhelmed with everything you MUST know to get a right answer to 2+2=4.

And here's the link to the Grade 11 review of the basic arithmetic:
http://www.edu.gov.mb.ca/k12/cur/math/ess_mm_gr11/full_doc.pdf

And for the Grade 11 students and teaching them to add/subtract/multiply and divide, the teacher's guide describes this like a subjective discovery process with quotes like this:
"Consequently, mental calculation activities should include periods for thought and discussion.
During these periods, the teacher should encourage students to
-suggest a variety of possible solutions to the same problem
-explain the different methods used to come to the correct answer and their
effectiveness
-explain the thought process that led to an incorrect answer"

An important note is we are not talking about solving complex word problems here or anything, but specifically for calculating a basic arithmetic operation with the different methods being those described from back in Grade 3 already outlined above.

Think you might have a typo there, newt.
5-4 = 1
not -1
I even checked it on a calculator

also in plenty of programming languages, "2" + "2" does equal "22"

Maybe there's no logical reason to have different systems but the reasons to have only one system are kind of thin. I am perfectly capable of using more than one system and I find that I prefer different systems for different uses. I can use imperial measurements when I build a shed and metric when I do engineering calculations. When I cook, I might use cups and tablespoons to make chili but I use grams to measure ingredients when I bake bread. And if you prefer one or the other, I can adapt. Humans are good at that. ;-)

Extend the argument and it's not logical for the world to speak more than one language. Translating between languages is a whole lot more work than translating temperature scales. We should all speak Mandarin, because it's the most spoken language in the world. But my best friend's 2 year old speaks Mandarin AND English. I suspect he'll be just fine.

Anyway, long story short, I agree we should all know how to use the metric system. That doesn't mean we all need to use it for everything.

when the narrator talks about how it sounds chaotic even though it's calculated (in this case) is what I think makes a ton of music great... thinking sloppy drunk punk, jazz and blues going any which direction, moments in most live performances...

In the limited times that I've been around skunks, it definitely seemed possible to watch them from a safe distance and be in basically no danger of being sprayed. If there's a dog around, that gets a lot riskier fast though.

There's definitely a risk vs reward calculation to be made there. I think the reward of seeing some nature first-hand would have been enough to keep me on the porch if I was the guy in the video, but I'd have been pretty cautious about it. And I can't fault him for opting for "NOPE" either.

Most vehicle side windows are made of tempered glass, compared to the laminated glass of the windscreen. The windshield is designed to "hold" its pieces upon severe impact due to the lamination process (a layer of plastic material sandwiched between two layers of glass) whereas the tempered side windows will shatter into small relatively harmless globules. Tempered glass is used due to it being roughly 4x the strength of non tempered glass, and cheaper to produce than laminated.

Most automotive side glass is typically between 3-6mm thick, depending on the region of origin, eg Europe, Japan, USA etc. That said, calculating the compression, tensile and sheer strength a particular window can sustain is not exactly simple. However as a simple baseline, a 2ftx2ftx5mm sheet of tempered glass, with supports 2ft apart can support roughly 160lbs of sustained weight. In the case of automotive design, window frame support, distance of supports, curvature etc will change the properties and strength of the glass.

Long story short, with the vehicles window fully rolled into the frame, that lion would need hundreds of pounds of force directed at a single point to reach the shatter point. Granted, I've never arm wrestled a lion, so maybe those folks were just a can of Vienna Sausage ready to open anyway. Best not to mess with the king.

I guess the hint for these is the rotational test that they show at the first.

1) A sticky object that would let go like a wall crawler that climbs down a wall would create this effect. (see below)
2) You can't. As you approach infinite speed it would get very close. (see below)
3) The bike will move forward. (see below)
4) The outside parts of the wheels that overlap the rail. Also if the train has a flywheel that is larger than the wheel size the bottom of the flywheel would also always move backwards faster than the train was moving.

1) He says "what object is inside?" so I'm not sure a liquid would count. Also a viscous liquid would flow a slow rate and would probably not stop and start. You might be able to get a viscous liquid to stop and start if you had fins, but that still might just move slowly or gain enough momentum to roll fast without any flow.

2) A little excel calculation shows that the average velocity approaches twice the initial but will never hit it.

attempted m/s - total time - average m/s
1 100 1
2 50 1.333333333
3 33.33333333 1.5
...
200 0.5 1.990049751
201 0.497512438 1.99009901

3) I'm not sure if the parameters of this experiment are explained sufficiently.

If it is allowed to slip then no matter the mechanical advantage a hard pull should always be able to get the bike to skid back and defeat friction.

If the bike is not allowed to slip on the ground then I don't understand how it could ever move backwards, the only options would be that it doesn't move at all or it moves forward.

If it can't slip then the ratio of the pedal to the wheel is what is in question. Bikes only have gear ratios higher than 1 and the crank is smaller than the tire so the tire will always rotate more than the crank thus the bike should move forward.

This line is incorrect Vavg = (V1+V2)/2. That only applies if you run at V1 and V2 FOR THE SAME AMOUNT OF TIME.

Speed is Distance divided by Time, so the formula for calculating average speed is Dtotal / Ttotal.

The problem is that that only works if your second lap can be longer than the first lap.

If they are the same distance, the maths are undefined.

V1 = D1/T1
V2 = D2/T2

Vavg = (D1+D2)/(T1+T2)
if (D1 = D2) then
Vavg = 2D1/(T1+T2)

if Vavg = 2V1 then
2D1/T1 = 2D1/(T1+T2)
then T2 = 0

therefore V2 = D1/0 .... cannot divide by 0 (and no, it's not infinity )

The track question seems really straightforward, so I must be missing something.

The question is how fast do you have to run the 2nd lap such that the average of the two laps (Vavg) is twice the velocity of the 1st lap (2V1); so Vavg = 2V1 (says right in the video). Unless I'm missing something, V2 has to equal 3V1:

Since the problem states that Vavg must be 2V1, we can substitute that in the average calculation below:

So, Vavg = (V1+V2)/2 becomes 2V1 = (V1+V2)/2

Now solve for V2:

V2 = 4V1-V1
of
V2 = 3V1

i.e. your 2nd lap must always be 3x faster than your 1st lap so that the average of the two laps is twice the velocity of the 1st lap.

No?

Watch further, particularly his videos on authoritarian regimes. His issue is that controlling language with force is a hallmark of classic far left regimes (ie. Lenin/Stalin's Russia, Mao's China etc), so his beef is not only with the uni, it's with the government and the deluded (or worse, calculated) morons who think that state sanctioned and enforced speech is a "good thing".

He has spent decades studying authoritarianism and makes compelling arguments as to why the current "SJWs" are almost identical to the precursors of other authoritarian regimes.

I don't ask anyone to take anything said at face value, but Peterson does the due diligence for his arguments, and will often defer answering a question if he doesn't think he can offer a well reasoned response. I've yet to see a single video where he has said anything negative about trans people (as opposed to saying negative things about a government law to force language), yet he is described as a homophobe because it's far easier to label him to discredit him than to actually listen to what he is saying.

She'd probably be ten to twenty percent more productive if she used a reverse polish calculator. I'm just saying.

Your video, Japanese people take their calculators very seriously., has made it into the Top 15 New Videos listing. Congratulations on your achievement. For your contribution you have been awarded 1 Power Point.

So, is there a gameshow yet that tests calculator speed and accuracy whilst being fellated?

Thanks I didn't work out how they calculated it either.