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Secondary Magazine - Issue 120: Sixth Sense

Created on 10 March 2015 by ncetm_administrator
Updated on 29 April 2015 by ncetm_administrator


Secondary Magazine Issue 120'SIX' by Richard Gray (adapted), some rights reserved

Sixth Sense

John Partridge, Assistant Head at King's College London Mathematics School, writes:

Towards the end of last term, an NQT-colleague asked me “How do I start the revision process with my mechanics class?” He was keen to discuss more exciting options than those based on his own memory of preparing for exams: could he do something other than dig out some past papers, and the mark schemes, and let the students get stuck in pretty much by themselves? After a little discussion we agreed that giving out a paper and letting the students attempt it in class would probably not be a fruitful use of valuable revision time: they’ve seen so many new ideas in Mechanics this year, and previous experience suggests that every question on the paper would soon become a whole group discussion … lament … along the lines of “what, I have to remember the suvat formulae?!”; “to find the force up the slope do I use cos or sin?”; “but surely the weight is equal to the tension…”

Instead, we decided that concentrating on one topic at a time made sense, and chose to begin with a long (and hence difficult in the eyes of many students!) question on forces. Given that students often find the pure mathematics involved in solving mechanics problems challenging, we thought we would separate the two processes. Consequently, we took a highly structured question and removed the structure, to create an “aide-memoire/starter” question. Here’s an example:

In the diagram, the sledge is held in equilibrium by the string.  If I told you the tension in the string, how would you go about finding the normal reaction?

[inspiration: MEI Mechanics 1 January 2011, q6]

  diagram of sledge held in equilibrium

Presented with this, what might your students say, and what might you say to them? By removing the value of the tension, you prevent calculation: students have to discuss and develop their plan in words, but they cannot get distracted by – or bogged down by – the numerical manipulation.

Hopefully, the following “recipe” for finding the normal reaction will soon (re-)materialise:

  1. draw a force diagram showing all the forces acting on the sledge
  2. split forces into well-chosen (meaning?) components where necessary
  3. use equilibrium parallel to the slope to find \theta
  4. use equilibrium perpendicular to the slope to find the normal reaction

If you now tell the students that the tension in the string is 25N, each of these small steps is approachable and “do-able”, and can be discussed with individuals or in small groups if further consolidation is needed. The “pure” skills can be honed now that the mechanics is essentially “done”.

Having got this far, you could ask some extension questions of the students – “How do I make this question harder” [it could be accelerating] “or easier” [the string could be parallel to the slope] – and hopefully this starts to remind them of all the work done [pun fully intended!] on forces and Newton’s Laws earlier in the year. Asking the class to “find the speed after 5 seconds if the string is removed and the sledge is released from rest” gives an excuse to get (collectively) the constant acceleration formulae up on the board, and learned before they’re needed next lesson!

Now tell them that they’ve essentially worked their way through a 17 mark question without panicking – indeed, they could see the full version at this point, and asking them to do it should boost their confidence and morale.

Later, my colleague reported back that the 20 minutes of “recipe building” had been very productive, and that after the students got past the scary diagram, they were pleased to have come up with a plan that would get them such a big chunk of their M1 marks. The next lesson was then valuably spent working through whole questions selected from other papers on the same topic (a couple of hours literally “cutting and pasting” a few papers into topics is time very well spent – and you only have to do it once before re-using year after year!) and my colleague is now thinking how to plan the next few revision lessons to be structured similarly but on different M1 topics. For example:

Two ships P and Q are moving with constant velocities. Ship P moves with velocity (2i – 3j)kmh-1 and ship Q moves with velocity (3i + 4j)kmh-1. At 2pm, ship P is at the point with position vector (i + j)km and ship Q is at the point with position vector (-2j)km. (Edited from Edexcel, June 2011, q7)

You have 3 minutes to write down what the question might go on to ask you to do.

This could lead to a think-pair-share discussion and collectively students might agree on some specific questions such as:

  • Find the bearing on which each ship is moving
  • Find the position of each ship at 3pm
  • Find the distance between the ships at 5pm
  • Find the bearing of P from Q (or Q from P) at 4pm

You could encourage them to answer these, before requesting more general questions (ideally with answers!):

  • Where are the ships t hours later?
  • When is Q due north of P?

Or, for example, a picture like this (from AQA, June 2013, q5):

3kg mass suspended

should prompt the students to ask themselves (a) what happens when I let this go? (b) how long until the 3kg mass hits the ground? (c) how high does the 1kg mass go after the 3kg mass hits the ground?

Although this does delay the lesson when you do hand out a whole past paper to do, I’d suggest that it makes that lesson much more valuable for the students (and much less traumatic for them too!) because all the preparation has been done recently. The students have been thinking what questions they might get asked, so when these questions are indeed the ones that are asked, the students tackle them with confidence, enthusiasm, and success.

How do you support your students to revise? Let us know @NCETMsecondary or email to info@ncetm.org.uk.

Image credit
Page header by Richard Gray (adapted), some rights reserved



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