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Real life application of maths topics

Discussion in 'Mathematics' started by teacherres, Mar 25, 2007.

  1. Can you direct me to a resource that shows how the NC relates to real life scenarios. So that i can answer the questions like "Where will we ever use surds".
  2. Can you direct me to a resource that shows how the NC relates to real life scenarios. So that i can answer the questions like "Where will we ever use surds".
  3. Goodness...

    I know you want real life applications for different topics, however, you can surely come up with them for surds. Do kids/you, really think that cars, rockets, tower blocks, London Eye etc. have been made using only integer/rational values of measurement?

    I am not attempting to be fly with you, just making a point.

  4. When manufacturing the London Eye at what point did the designers knowingly use surds. When the parts were manufactured were the sizes given as surds or decimal values with a given tolerence.
    Can we be a bit more specific, I can see that when we design a circular ****** that trigonomerty and pythagoras will be useful to determine the position of the holes from a datum point but where is the practical use for surds???????
  5. Ok, you like pythagoras, use pythagoras. What size is the hypotenuse when both 'short' sides are 1? Surely you could make up a story with that.
  6. Absolutely,

    I always start the teaching of surds with the unit square. Talk about the history of Pythagoras and the pythagoreans. The practicality bit is the fact that some time ago people did not have calculators to round numbers to x decimal places.....lead into the Egytians using 22/7 for pi.

    As for your original question, I don't know of any websites! be intersting to find some, even if for posters on the wall.

    Practical use of surds-----> it is practical to show trigonometric ratios as surds. In fact, if they are a decent group why not go into how the trigonmetric ratios are formed for certain angle, side ratios i.e. the unit square or the Equilateral triangle for 30, 60 and 90 degrees.

  8. Drawn the short straw and have had to teach maths?
    What is your specialist subject? I know I would have problems explaining why we learn parts of French orHistory for example
    NCEMT website has some good resources and th MoD ones (wherever a link is to them)
  9. PaulDG

    PaulDG Occasional commenter

    I'm not aware of any practical use of surds - essentially, for all practical purposes, all irrational numbers must be approximated.
    Surds are, as I see it, an easy bit of pure maths dropped in the GCSE spec for those who may go on to higher study of maths.
    Recognising that surds are irrational and what that means whenever you get a surd in a practical situation (that it can only be approximated) is useful, but being able to simplify surds (esp when a £5 fx-83DT calculator can do the job very, very well) isn't something that, AFAIK has "practical" purpose.
    But... do the kids care? I used to think they did, but I'm increasingly of the opinion that the "what would we ever use this for?" question is only really a distraction technique - the answer "you'll need to do it in your GCSE and in your A level if you carry on with maths in the 6th form" is almost certainly the only answer they actually need.
  10. Informant

    Informant New commenter

    Persisting with use of surds prior to a final answer avoids propagation of accuracy errors. eg root 2 x root3 x root 2 x root 3 = 1.414 x 1.732 x 1.414 x 1.732 = 5.998684 compared with correct answer of 6. This is important for permitted tolerances in engineering or margins of error in science.
    Actually pupil interest usually increases if you mention that Pythagoras reputedly had Hippasus drowned for proving the existence of irrational numbers as he had thought this an impossibility (cue discussion using a number line and what values fill the spaces between the integers....lots of fractions of course and irrational numbers for gaps still remaining).
    For quadratics you can mention the shape of the curve is a parabola, used in (car headlight) reflectors and satellite (TV) dishes to focus parallel rays at a single point. Also it's the same shape of a conic section and the path of a projectile (I throw a pen across the room at this point, but have lost one in the light fittings....pupils remembered that very clearly).
    For trial and improvement explain some solutions cannot be determined exactly (eg irrational roots!), but quoting motion of planets as cause of tides and the need only to predict high tide to within a minute or a second brings realism to a real problem.
    Hope that helps (so far).
  11. I'm very much in the same boat after just a year and two terms in teaching. I used to try and give them really detailed real life situations ... but now I don't bother trying to manufacture something that ends up being totally unreal.
    What happened to a quest for understanding? It struck me earlier today when I was sat in the garden, enjoying the sun before going back to work tomorrow ... I'm sure I and my peers got satisfaction from understanding things. The "thing" may have been, in itself, quite boring but that didn't matter. Whether it was a CDT teacher explaining HOW a slip-diff worked, a science teacher explaining WHY sodium+water=fun (not that my chemistry teacher would have put it like that), or a French teacher telling us why "elle a une belle vue du balcon" meant what it meant (look it up - it's a corker!!), or any other setting.
    Maths, in my very humble but admittedly very biased opinion, gives more opportunities to understand more things than most subjects, and, what's more, it is the key to understanding so many other things. English Lit will help you analyse texts ... maths will help you understand what analyse really means!
    Period 1 ... here I come!
  12. I love teaching maths history too - but i only teach the interested, so i don't have the op's problem
    but btw - the Egyptian formula for the area of a circle was:
    If the diameter is d, then the area is d - (1/9)d, all multiplied by itself
    This gives a value for pi of 256/81 - see my wonderful (ahem) resource on Egyptian maths
    as far as i'm aware, the 22/7 value came first came from archimedes, who did not share pythagoras' horror of the irrational number, and used the inscribed/circumscribed polygon method to get 223/71 < pi < 22/7
    think it's time for bed [​IMG]


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