#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!)