Mike Reed
pfm Member
One of the uses of the present simple tense is for stating facts; e.g. 'the Earth rotates around the Sun', or, 'geometry is mind-boggling'.
Maths teaser
- Thread starter Rodrat
- Start date
One of the uses of the present simple tense is for stating facts; e.g. 'the Earth rotates around the Sun', or, 'geometry is mind-boggling'.
The problem came from a maths problem solving book. It does state that after the loan books there are twice as many non fiction as fiction left in the library. It is beginning to look like the maths book got it wrong or it was printed incorrectly. No wonder none of the teachers at my daughters school could work it out.
droodzilla
pfm Member
That's shocking if true. It's a straightforward simultaneous equation problem in two unknowns. Any GCSE Maths teacher ought to be able to solve it in his or her sleep.
I concur.
Likewise, I wouldn't think it a stretch for similar to work out if and where the question was flawed.
droodzilla
pfm Member
OK, I'll let them off. Though now I wonder why such a problem would be posed at that level...
A quick rattle together in Excel (could easily be done on paper but Excel's neater) shows the workings. I'd be a bit surprised that primary school non-specialists couldn't tackle the arithmetic in play as it's simple algebra but in fairness I am not close enough to the primary teaching system to pass judgment in reality.
droodzilla
pfm Member
I'm no expert but I think you overestimate the mathematical abilities of most primary school teachers. Many of them will be Humanities graduates who haven't done "serious" maths since they were 16 and, even then, might not have been very good at it.
A quick rattle together in Excel (could easily be done on paper but Excel's neater) shows the workings. I'd be a bit surprised that primary school non-specialists couldn't tackle the arithmetic in play as it's simple algebra but in fairness I am not close enough to the primary teaching system to pass judgment in reality.
No disrespect to primary school teachers intended. It's a different skill set and I'm sure most of the maths experts I know would be hopeless at teaching young children.
Marchbanks
Hat and Beard member
I would imagine their problem would be coming up with an answer that made no sense and having insufficient confidence in their own abilities to challenge the question. If I had been presented with that problem in an O-level paper I don’t think I would have had the guts to write ‘this question is wrong, what you mean is...’ and then give the ‘sensible’ answer.
There is no way that a primary school pupil could be expected to solve a simultaneous equation, it's a nonsense. Teachers, maybe, it's GCSE maths, but they would have to be au fait with the techniques and may not have used it for many years. Designing a spreadsheet to crack it by iteration is easier and what I'd do. I do this sort of thing for work, say when homing in on a formulation for a food product. We need so many calories, so much fat, meat content better than X, off you go.
A few years ago I introduced my pals' then 10 year old daughter to the notion of density, mass and volume, by means of calculating how many tons of gravel would be required to resurface their drive to a depth of 1cm. Gravel is 2.5 tonnes a cubic m, off you go. We had a great time, drew a scale model, established that volume was independent of shape, so a driveway at 1cm could contain the same amount of gravel as was on a lorry to a depth of X, established that we needed about 1.2 cube, 3 tonnes, her comment was "this is just like a maths lesson but worse!" On the basis that density-mass-volume and "what volume of gravel is required to surface a driveway to 1cm deep?" is fairly taxing to a bright 10yo, you can imagine what they would make of a simultaneous equation.
The driveway answer BTW is 3 tonnes, but buy 5 because the delivery is the expensive bit and you can always lose a bit of excess in thicker layers at the edges that you later use to repair potholes. However such an exercise is a pipe dream until such time as the potholes become deep enough that the car's undercarriage scrapes on the ground when passing through them. The driveway is still a mudbath, said child is now studying A levels and is more interested in languages than maths.
A few years ago I introduced my pals' then 10 year old daughter to the notion of density, mass and volume, by means of calculating how many tons of gravel would be required to resurface their drive to a depth of 1cm. Gravel is 2.5 tonnes a cubic m, off you go. We had a great time, drew a scale model, established that volume was independent of shape, so a driveway at 1cm could contain the same amount of gravel as was on a lorry to a depth of X, established that we needed about 1.2 cube, 3 tonnes, her comment was "this is just like a maths lesson but worse!" On the basis that density-mass-volume and "what volume of gravel is required to surface a driveway to 1cm deep?" is fairly taxing to a bright 10yo, you can imagine what they would make of a simultaneous equation.
The driveway answer BTW is 3 tonnes, but buy 5 because the delivery is the expensive bit and you can always lose a bit of excess in thicker layers at the edges that you later use to repair potholes. However such an exercise is a pipe dream until such time as the potholes become deep enough that the car's undercarriage scrapes on the ground when passing through them. The driveway is still a mudbath, said child is now studying A levels and is more interested in languages than maths.
Thanks for posting. My workings as follows (assuming wording switched in last sentence):
4F total
3F fiction, F non fiction
3F-120 = (F-24)*2 (after removing books)
3F-120=2F-48 (expand RHS)
3F=2F-48+120
3F=2F+72
F=72 (subtract 2F from both sides)
T=4*72=288 (Total books in library)
fiction = 72*3=216, non fiction=72
after removing books:
fiction=216-120=96
non fiction=72-24=48
4F total
3F fiction, F non fiction
3F-120 = (F-24)*2 (after removing books)
3F-120=2F-48 (expand RHS)
3F=2F-48+120
3F=2F+72
F=72 (subtract 2F from both sides)
T=4*72=288 (Total books in library)
fiction = 72*3=216, non fiction=72
after removing books:
fiction=216-120=96
non fiction=72-24=48
Marchbanks
Hat and Beard member
Maybe it is, if you are au fait with the techniques and have done it for many years. Personally, I find solving a simultaneous equation a doddle but wouldn’t have a clue how to set up an iterative method of solution in Excel.
Aha!
droodzilla
pfm Member
I was thinking the same thing.
Graphically, you're looking for the point where two lines cross. You can imagine moving from one line, across to a point on the other, then up or down to a point on the first line and so on, making a kind of cobweb that converges on the point you want.
I suppose an Excel spreadsheet could be used to model this convergence process.
Graphically, you're looking for the point where two lines cross. You can imagine moving from one line, across to a point on the other, then up or down to a point on the first line and so on, making a kind of cobweb that converges on the point you want.
I suppose an Excel spreadsheet could be used to model this convergence process.
Dowser
Learning to bodge again..
That’s pretty much what I do when I cannot see an obvious way of creating a formula (more often than I admit!) - with 3 real world examples you can quickly correlate which direction is the right one, and just edge towards to correct answer. I like the earlier description best - a brute force attempt at solving the problem
To be fair I'm no Excel guru, I just set it up to do the sums and then chuck numbers at it until the solution drops out. I'm sure you could get the spreadsheet to do something clever but I don't know how. However I can, as can most people if they set their minds to it, and certainly people who can still remember how to solve simultaneous equations, set up a table, populate it with every possible start point, then just scan the solutions until I get one I like. It's inelegant but effective. It reminds me of an engineering solution for a cap sorter. It's a chute that picks up bottle caps on a stepped conveyor. They all need to be one way up. Devising a means of picking up the caps only one way is a pig so the engineering solution is just to have a slot in the chute with an airline set up to flip out inverted caps. The pickup runs fast enough that even if 90% of your caps are the wrong way it still works. It's crude and inelegant but it's robust, simple and effective. Sometimes crude just works.
gavreid
Pretty Words...
I would certainly expect all teachers at any level to have a decent attempt at this, and with pencil and paper. This is significantly below GCSE Maths, which is still required for entry to pretty well every University in the country. It's not as though the solution even comes out as a quadratic or somesuch. It's a trivial bit of algebra in the end, that requires some problem solving ability, which should be expected of all graduates. I can just image, for example the Today programme presenters, laughing and joking collectively about being unable to do it themselves, while in the next breath reeling in horror that somebody might not know the difference between David Walliams and William Shakespeare. It exemplfies the problem we face in the way being poor at maths is socially acceptable, while being poorly read is not - dumbing down has led to scientific fact being presented as debatable opinion.
droodzilla
pfm Member
Not true. It's approximate/graphical solutions only at KS3. The algebraic approach only comes at KS4 (GCSE level):
https://www.gov.uk/government/uploa...CONDARY_national_curriculum_-_Mathematics.pdf
https://www.gov.uk/government/uploa...ta/file/331882/KS4_maths_PoS_FINAL_170714.pdf
As for solving simultaneous equations being a doddle - that's only true if you find them a doddle. I've always been extremely good at maths and am currently doing a PhD in theoretical physics but I tutor GCSE maths students to earn a bit of extra cash and I can assure you many of them struggle even with relatively basic algebra. Maths is a cruel subject: it can be an absolute delight if you're good at it but if you're not it's a very hard, dispiriting slog.