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Completing the square vs the quadratic formula

Discussion in 'Mathematics' started by pencho, Apr 20, 2011.

  1. pencho

    pencho New commenter

    For what my opinion is worth
    AQA have asked about completting the square a = 1 and b is even. They occasionally have had a second part which says hence or otherwise solve it (give your answer in the form p + q rt(...)). You would get credit if you went back to the formula. AQA have also had the question about finding minimum from a quadratic. Some nice questions.
    I would not teach completing the sqaure with a > 1 even when b is a muliple of a to a GCSE higher group - unless they are super intelligent. I would save this for a-level.
    Just my thoughtss
     
  2. bombaysapphire

    bombaysapphire Star commenter

  3. Yes it was swapped in 2008 from completing the square to completing the benefits claim form as it was more functional.
    Completing the square:
    (1) ensure in the correct form and take half the coefficient from the x term into a set of brackets
    (2) Square that, subtract the number from the expression and collect constants
    One completed square
    Now take the estimated mean from grouped data as a C grade question on foundation where its the sum of (fx)/sum of f
    That to me is a far harder concept surely?...strange what is deemed to be hard these days. Completing the square was B grade and to solve may have slipped into the A grade material in ~2005
    Edexcel are excluding vector notation from the foundation syllabus now [​IMG]
    Back to completing the square. I teach it to the top kids regardless as it saves wading through it in C1 and is a fairly straight forward concept.
    I believe revision should not stop new learning for future qualifications
     
  4. Now this is an interesting one - I hadn't considered this before (because I have never done OCR GCSE).
    In a linear GCSE higher tier exam 50% of the content must be at C or D grade (as I understand it), so very little of the paper can be A* stuff. This means that any single, difficult topic has a very low probability of cropping up on the paper. So when my pupils ask "how likely is this topic to occur in the exam" I have to say that it is very unlikely to crop up ... but that every A* topic is very unlikely to appear too.
    If you have M10 that is just A and A* material then I suppose more of the harder topics can be tested.
    Sounds like a good plan to me (which probably means this specification is going to be cancelled, no?).
     
  5. What is interesting here is that those candidates who have learned a rule (halve that number, subtract the square of this from that, add your shoe-size, etc) are less likely to be able to answer the "what is the minimum value" part.
     
  6. strawbs

    strawbs Occasional commenter

    It has been.......[​IMG]
     
  7. Kevin
    Is there any advantage for pupils opting for the M10 in terms of recognition/UCAS points/GCSE value or is it purely for those who want to do it (and presumably like maths ?)
     
  8. strawbs

    strawbs Occasional commenter

    If you don't do M10 it is much much harder to get an A*. Common route for those who get A* is to do M8 (target B) in Jan/Mar year 10, then M9 (target A) either June year 10 or Jan year 11, then M10 (target A*) in Mar year 11.
    Those aiming for A/B might do M7 then M8 then M9 etc.
    It operates like a ladder system where each module targets a higher grade than the one before. So a bottom end Foundation pupil would do M1, M2, M3 (and terminal) to get an F maybe.
    50* of the overall mark comes from terminal paper which covers the whole content of the course, and grades D-A*, and then 50% from the best 2 module scores.
    At the school where I taught where they did it, all the ex-pupils who came back for a visit said that they were "well ahead"at A level due to spending most of year 11 just on A/A* material.
    It worked well.....but it's going as it wasn't deemed suitable under the new re-jigging. Shame!
     
  9. Strawbs
    Thanks for that
    We have had the joys of edexcel cookie cutter one size fits all higher papers.
    Shame things change....
     
  10. Yes - which is why I had to look back three years to find a similar question on linear. There are approximately 25 A/A* marks on any given 100 mark higher tier paper, but it's all 50 of the marks on M10.
    Yes, if that question comes up and a learner hasn't seen it before, it's quite a good test of their understanding. If it comes up every other series, then it could just become another 'trick'.
    At the end of the day, it's *just* a modular maths GCSE - but a different way of cutting the content (into levels rather than topics) - so it's worth the same as any other. The key, as strawbs has said, is in the way you can target it, so those expecting a grade G/F can do very basic modules and those targeting A/A* can do the tougher ones, and anything in between.
    The A level prep comment is one I've heard a lot in the last few years as C1 follows quite nicely from M9/M10. You also get the A* on the modules for showing "competence at that level" (score around 60% on M9 and M10), rather than 90%+ accuracy on D/C/B questions. That suits quite a lot of students. It's why, this summer, over 65% of candidates are doing the higher tier, and the most popular modules are M9 and M10.
    Obviously I agree it's a real shame it wasn't re-accredited by Ofqual. When it was rejected, I tried to maintain the 'ladder' of stages as a teaching option and we got it accredited as a linear spec (Maths B). The textbooks mirror this approach as well, so the levels/stages still exist but not as a component of the GCSE grade, just for teaching and monitoring.
    Kevin
     
  11. Piranha

    Piranha Lead commenter

    I think I recall seeing questions asking you to complete the square and "hence or otherwise" solve the equation, in whch case you might as well carry on using completed square form. (BTW, would you get follow through from a wrongly completed square?) Otherwise, I am content for students to choose what to do. I have seen questions asking you to factorise, so they need to be able to do that.
    We do AQA, and are used to questions asking about the minimum. I try to get them to understand why it works, but when they come to the exam, they only need to remember to write down their value of b to get an easy mark. If you don't do this, or use it to solve quadratics, why bother to teach completing the square at all?
    The one case I strongly recommend completing the square is with simultaneous equations with a circle and a line such as y=3, as eliminating y gives an equation in completed square form. I haven't seen this at GCSE, but I have in C1 (MEI).
     
  12. Hasn't Gove expressed a wish to see GSCE/A level linear only? Or has that been brushed off. Also, I would be interested to know how well students are doing based on whether they follow modular or linear. Are there such stats?
     
  13. Not so much a reply as to if completeing the square should be used but a shout on a resource I've found useful when starting to teach this topic, and it's from our very own TES resources:

    https://www.tes.co.uk/teaching-resource/GCSE-Algebra-Completing-the-Square-6045142/
    It takes a visual approach that I'd not seen before and can easily be extended to other (more difficult) examples.

    Hope that helps!

     

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