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#14

(32F)U/2^N = L^U.4S(4/T)
4F(U/2ⁿ) = L^U3S(4/T)
F(U/2ⁿ) = L^US(4/T)
FU^N = L^UST 

Mathematics – GCSE level.

To begin with, the presentation is non-standard and quite sloppy. Firstly, numbers should go before letters, so for example the right hand side of the second line should read 3L^US(4/T). Secondly, all the parentheses are unnecessary as multiplication is associative – careful positioning of symbols next to fractions should obviate any confusion as to whether to multiply by the numerator or denominator. Thirdly, the 'N' on the left hand side changes to an 'n' and back again. Finally, it is more usual to use all lower case letters for unknowns. 

Algebra may mean ‘reunion of broken parts’, but there's no happy reconciliation for this equation. It is quite impossible to make FU^N=L^UST as there is an error in each step of the calculation. The basic rule of manipulating equations in this way is that whatever is done to one side of the equation must also be done to the other side.  This rule has not been followed: 

– At the second step, the left hand side has been divided by 8, but the right hand side by 4/3. 

– At the third step, the left hand side has been divided by 4, but the right hand side by 3. 

– At the final step, the left hand side has been multiplied by 2^NU^N-1, but the right hand side by T²/4.

Taking the first line as the starting point, the closest to FU^N equalling L^UST that can actually be achieved is FU/2^N-1 = L^US/T.

The teacher could have instead started with 2nu/ts = (2/f)l^u, which can be rearranged to show that fun=l^ust. (Although nuts flu does sound rather like something that may be a result of too much fun lust.)

If the teacher is looking for a way to show how fun algebra can be by making words out of the symbols, she might instead try asking her students what the volume of a circular pizza of radius z and height a is.

2/10 A nice try in engaging students, but riddled with errors. 

(Answer: pi.z.z.a – now that is fun!)

#13

SEAT
BELT

REMEMBER..
NO, NO, NO,
U-turns over
double yellow lines

10 2
Keep Hands
on wheel
10-2

           C

LeFT   B
Signal
           A

Driver’s Education

It is a promising start that the first thing on this blackboard is SEAT BELT as putting one on is the first thing one should do when getting into a car. Seatbelts have been a major contribution to road safety – they reduce the risk of fatal or serious injury in a collision by as much as 50%. Risk compensation theory, where drivers who feel safer in one way instead take risks in other ways, does muddy the statistics somewhat, but there is no doubt that it is better to wear one. Volvo’s decision to make the patent for their three-point system open and let other car manufacturers copy it for free should be applauded. (Drug companies, please take note.)

Anecdotes about car users who died terrible deaths because they were trapped by their seatbelts, or who miraculously survived a collision specifically by not wearing one abound, but whilst it is true that seatbelts may cause serious injury or death (or their non-use save lives) in particular accidents, these incidents are much rarer than those in which the use of seatbelts saves lives. The occurrence of these rare incidents is also usually much overstated, like referring to a 100-year-old who smokes 20 a day, but not mentioning the thousands who die young of lung cancer.

Cries of civil liberties regarding the mandatory use of seat belts should also be ignored – not wearing a seatbelt is not a victimless crime when an unrestrained body becomes a lethal missile for other car occupants. Even for accidents involving just a single driver the cost to society of more serious injury or death cannot be discounted. Clunk click every trip.

As a side note, another safety issue to note before even getting into a car is that bare or stockinged feet are not recommended behind the wheel. They are also unacceptable in a classroom situation and the teacher should enforce this for both theory and practical driving lessons.

It is also good that the dangers of U-turns over double yellow lines (the road marking indicating the division between oncoming lanes in this jurisdiction) are being highlighted. The chalk marks around ‘U-turn’ indicate a thorough demonstration of what a U-turn is with several such manoeuvres clearly shown. This kind of diagram, combined with the repetition of the drawing action can particularly help visual learners who might be struggling with the concept of ‘U’. There might indeed be another such demonstration below the words ‘double yellow lines’ to give extra reinforcement to the point, unless those are meant to be double yellow lines, in which case they are a rather poor effort, being neither yellow nor entirely double.

Whilst at one time ‘10 and 2’ was indeed the preferred position for hands on a steering wheel (although this diagram actually shows something closer to 10:30 and 1:30), the advent of power steering means that the extra leverage gained by beginning a turn with a larger downward movement is no longer necessary. Indeed, the advent of airbags means that ‘10 and 2’ is actually dangerous, with the airbag explosion turning the driver’s hands and forearms into face-seeking projectiles. ‘8 and 4’ or ‘9 and 3’ is now the recommended configuration – it is clearly time to update curriculum materials and send this teacher on a refresher course. Indeed the entire concept of using an analogue clock as a reference is rather outdated – perhaps iPod controls would be more relevant to this cohort, so instead of ‘hands at 9 and 3’ they would be taught ‘hands at skip back and skip forward’.

In the overtaking manoeuvre diagram, the curved arrows showing the overtaking vehicle’s path show that it approaches dangerously close to car B before swerving sharply into the oncoming lane, possibly even clipping the rear bumper. Such manoeuvres should be planned further in advance, executed more smoothly and not bring vehicles into dangerous proximity with each other.

The left signal (or ‘LeFT Signal’) also comes far too late to give other road users warning of the driver’s intentions. Remember: mirror, signal, manoeuvre, not manoeuvre, signal, learn how to use lower case letters.

It is also worth noting that 32% of jurisdictions drive on the left (and rising – the last right-to-left switch was in 2009, whilst the most recent left-to-right change was over 30 years before that), so in those parts of the world this last diagram would show an undertaker rather than an overtaker – something that the learner driver might need if she follows those arrows.

5/10 Good work on buckling up, but the rest of the ideas need bucking up.

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