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Angles Questions - Give A Reason Why

Discussion in 'Mathematics' started by Skillsheets, Nov 3, 2015.

  1. Skillsheets

    Skillsheets Occasional commenter

    I find this topic one of the trickiest ones to get students to understand fully how to set out their answers to questions. I work as a private tutor and would appreciate any tips people have on how to get them to set their reasoning out logically. I dread them asking for help with circle angles as I find I rarely get them to where they need to be. Yes they can be taught the facts ( and sometimes stop saying 'the angles in a triangle ARE 180° ) but rarely do I find a student who can convince me that they can communicate their reasons in a coherent fashion which is surely the whole reason for including circle angles in the syllabus.

    Please advise. ( And give reasons for your answers )
     
  2. Piranha

    Piranha Star commenter

    I would advise writing a short version of the rule next to the place it is used. Sorry, I don't know how to do the proper notation on this forum:

    A = 90 (angles in a semicircle)
    B = 180 - 90 - 55 = 35 (interior angles of a triangle)
    D = B = 35 (angles in the same segment)

    I think that it is clear that way. Do others think that more is needed?

    Now, if that is the answer, what was the question?
     
    colinbillett and Skillsheets like this.
  3. colinbillett

    colinbillett Occasional commenter

    As I understand it, the reason for doing geometry is to give the learners experience in deductive reasoning - following steps from one to another, and as you say, giving reasons along the way. And the GCSE has been updated to include marks for quality of written communication. But those QWC marks aren't always for geometry questions, and the learners are sometimes asked to give reasons, and sometimes not. What you need to do is familiarise yourself with GCSE mark schemes, so you can see how the marks are awarded on geometry questions. It doesn't need to be in a 'correct' statement, because often the mark scheme only needs to have sight of specific words, such as 'alternate angles'. The learners often think by giving a calculation they have given a reason, but this isn't the case. Piranha give clear examples above. i give them card matching activities, when they've had some experience, and they match the theorem to the picture. Then they can keep those, or a side or two of A4 with the corresponding pictures and statements so they can check what they are looking for, or what they think they have found. Plus I lead them in gradually, building up familiarity and confidence - so start with easy designs, on which the learners can fill in all the visible angles, and explain to me how they are deducing each one - easy with 1-to-1 tuition. Then build up to the harder ones.
    All the stuff I use is on TES, and they work for me. I'm afraid the big sets will cost you a quid each, but there are a couple still on the free resources - presentations of the required statements and some exam questions, but as I say, I don't start there, I start with matching cards.
    And vocabulary is often lacking, so you might like to start with this (free) one:
    https://www.tes.com/teaching-resource/the-circle-names-and-parts-of-a-circle-6335606
    These are also free:
    https://www.tes.com/teaching-resource/gsce-maths-geometry-statements-revision-6086774
    https://www.tes.com/teaching-resource/maths-three-assorted-worksheets-on-gcse-geometry-6268513
    And these are a quid each, but lots of files in each.
    https://www.tes.com/teaching-resour...activity-co-operation-and-discussion-11042866
    https://www.tes.com/teaching-resour...for-hands-on-activity-and-discussion-11042894
    Hoping that helps, Colin
     
    Skillsheets likes this.
  4. Skillsheets

    Skillsheets Occasional commenter

    Thanks Colin, I will add those to my own collection. I try to insist on ' The angle in a semicircle is 90°', 'Angles in a triangle ADD UP TO 180°' etc. I have tried a new approach of getting them to do the calculation followed by BECAUSE then giving the reason. I do work through the reasons and vocabulary with them but they still don't get it. Also I find they often really don't get ideas like angles being 'in the same segment'. I remember being taught that angles subtended by the same chord at the circumference were equal. This may seem a lot more complicated but it contains a better visualisation of the set up.
     
    colinbillett likes this.
  5. zithobilezee

    zithobilezee New commenter

     

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