Home > Assessment, Exams, GCSE, Maths, Teaching > “Next Level” question

“Next Level” question

Back in November I wrote this post outlining the changes to the new GCSE maths curriculum and included some questions I had enjoyed from the SAMs and some that I had thought were less good.

One of my Y13 students had read the post and had had a go at some of the questions, he came to me in school and told me that he’d seen a “next level” question on my blog, that it had taken him ages to realise how to do it and that he couldn’t believe it was on the new foundation GCSE. I asked him which question it was and he said it was this one:

image

I considered the question. A shows a sector of a circle with an angle of pi/2 radians. I should say 90 degrees I suppose, as it’s a GCSE question. B shows the same square but this time there are 4 sectors, each with the same angle, again pi/2 radians 90 degrees. There are no lengths marked on.

image

This question is relatively straightforward once you pick up the key piece of information, that the squares are the same. You don’t even need to use the angles to work out the sectors as we are dealing with as they are quarter circles. You assign a value for side length and work through each one, showing the areas are the same.

I think it’s a great question, and I love the fact that these two shading arrangements give the same area. I did, however, wonder how future foundation students would cope with it given that a Y13, who scored a good A in maths AS and As in his other 3 ASs in Y12, referred to it as “Next Level”.

When discussing it with said student it turned out that the maths wasn’t the issue, it was that there was no lengths marked on, and he hadn’t realised straight away that you could assign a variable to work though.

I assume this is down to the nature of the current examinations, and their tendency to give scaffolding all the way through. I like the rigour of the new qualifications, and the fact they are designed to build mathematical thinking all the way through, but I fear that for some teachers ensuring this is built in will take some getting used to.

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  1. December 15, 2014 at 9:12 pm

    Reblogged this on The Echo Chamber.

  2. December 17, 2014 at 10:40 am

    For square b your initial equation is wrong. The shaded area is simply pi(r/2)^2 or to match the next line of your working 4 [(pi(r/2)^2)/4]

    • December 17, 2014 at 10:48 am

      Ah yes, i haven’t stated the /4. The sort of lazy working that infurates me. Oops.

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