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equations vs formulae (vs expressions/identities) - Help please!!

Discussion in 'Mathematics' started by TeasMad, Feb 9, 2012.

  1. Could anyone who teaches OCR GCSE maths be kind enough to clarify for me how this part of the syllabus is supposed to be taught?
    Just found a question in a recent OCR paper requiring you to classify the following as either formula, expression, equation or identity:
    P = 2W + 2L
    2(W+L) = 2W + 2L
    The mark scheme (predictably enough) wants the answers formula and identity, but won't accept 'equation' as an alternative answer.
    What is wrong with defining an equation as "a statement that the values of two mathematical expressions are equal, indicated by the equals sign (=)"
    (and thus all formulae are equations, even if the reverse is not true)
    Surely you can't teach a student that P=2W+2L is not an equation! What is y=mx+c supposed to be?
    thanks
    T

     
  2. Could anyone who teaches OCR GCSE maths be kind enough to clarify for me how this part of the syllabus is supposed to be taught?
    Just found a question in a recent OCR paper requiring you to classify the following as either formula, expression, equation or identity:
    P = 2W + 2L
    2(W+L) = 2W + 2L
    The mark scheme (predictably enough) wants the answers formula and identity, but won't accept 'equation' as an alternative answer.
    What is wrong with defining an equation as "a statement that the values of two mathematical expressions are equal, indicated by the equals sign (=)"
    (and thus all formulae are equations, even if the reverse is not true)
    Surely you can't teach a student that P=2W+2L is not an equation! What is y=mx+c supposed to be?
    thanks
    T

     
  3. An identity is true for all values of the variables you put in; i.e. an algebraic truth. 2(x+y)=2x+2y.
    An equation tends to be in one variable only (x, say) and be true for only some values of x. x+3=4.
    A formula is an equation connecting one variable to another. F=ma.
    But all of them are 'equations', but they have more specific names is one is being pedantic.
     
  4. mmmmmaths

    mmmmmaths New commenter

    P=2w+2L is a formula. P is the subject of the formula. The rhs is a rule that tells you how to work out the value of the subject.

    Y=mx+c is the formula that tells you how to work out the value of y given the value of x. Y is the subject of the formula.

    an equation can be solved to find one or more solutions.

    An identity is just one algebraic expression written in a different form on the other side of the equality sign (those three line signs). Hence rhs will equal lhs for all values of the variables.

    My foundation class are now good at these.......they also know that an expression is just a 'chunk' of algebra with no equals sign.
     
  5. Maths_Mike

    Maths_Mike New commenter

    While I agree in general with your definitions, I think we would all say y=mx+c is the equation of a straight line.
    In any case I hate these pedantic questions that really determine very little about a students mathematical abilty.
     
  6. Maths_Mike

    Maths_Mike New commenter

     
  7. I'm pretty sure I know what OCR expect of students but still feel that this is a bit of an OCR speciality which isn't a sensible use of valuable marks in exams. Surely they can find another 2 or 3 mark question which tests students on something useful.
    To complicate matters, I am pretty sure that in some maths texts, particularly American, the things we call identities are referred to as identity equations. I have also seen a learned article about Abel's Differential Equation Identity on the Wolfram site.
    Perhaps OCR will ask questions next year on whether -1 is a directed number or an operation???

    Hopefully someone from OCR visits this site. If they do, I still like you and your Board but don't like these questions. Except for the fact that I can probably train chimpanzees to get them right!
     
  8. 3x+ 2y = 12 has an infinite number of solutions that are probably best shown as a straight line graph. If it is combined with 4x- 2y = 2 it becomes a pair of simultaneous equations which can be solved with particular values of x and y.
    Does an equation have to have only 1 variable? Diophantine equations have 2 variables but only a limited number of solutions once we restrict the possible solutions to positive integers.
    It just seems to me that 3x +2y =12 is a different sort of thing to 3x+2 = 12 or some higher order equation in x which may have several solutions. Okay, it may be that my head is getting befuddled with my glass of beer, but it does seem that perhaps it really is not clear what an equation is. I suspect that is why in America they are all called equations but some have qualifiers such as identity equation (formula equation?)
     
  9. Andrew Jeffrey

    Andrew Jeffrey New commenter

    Curiously enough, I rather like this American idea of 'identity equations' in the same way that I like 'decimal fractions' to try to convince children that decimals are just a type of fraction, but I agree it can sound pedantic to talk about your 'poodle dog' all the time.
    But for a question to imply that identities are not equations (they are) smacks to me of the worksheet for reception children where they are asked to sort shapes into circles, triangles, squares and rectangles. Grrrrrrrrr...
     
  10. Piranha

    Piranha Star commenter

    Try marking MEI C3 Coursework. y=x^2-4 is a function; x^2-4 = 0 is an equation. It is pedantic, but OCR are not the only ones to use an equation as meaning something with particular answers while a formula allows you to find one variable based on others. I agree that it shows little understanding of Maths - it strikes me as a "teach to the test" topic, which I don't like doing.
     
  11. Hi mathsteacher1953
    Halfway down page 5 of the Ofqual subject criteria for GCSE mathematics specifications, "distinguish in meaning between the words equation, formula, identity and expression" so it's a requirement in all accredited maths GCSEs.
    http://www.ofqual.gov.uk/downloads/category/192-gcse-subject-criteria?download=1250%3Agcse-subject-criteria-for-mathematics-november-2011
     
  12. Nazard

    Nazard New commenter

    In both cases it would seem possible to ask an exam question that goes something like: "write down all of the words that can be used to describe ..."
    If there is then a picture of a square (with sides marked as being equal and right angles shown) then it would be necessary to draw lines from all of: square, rectangle, parallelogram, rhombus, kite. [I would also include trapezium, but that is a different can of worms ...]
    To return to the original question in this thread, <u>all</u> of the correct ones (formula, equation, etc) would need to be included for full marks.
    Sigh - another thing to put on the list for when I become President of the Universe.
     

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