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FMSP Mechanics Session Birmingham

It’s been a pretty full on term so far, as it always seems to be, so it was lovely to have a break yesterday evening and do some maths for ourselves! We were fortunate enough to welcome Trevor Starbuck to the first Birmingham and Solihull Further Maths Support Programme network meeting hosted at John Willmott School. The intention of these network meetings is to bring together teachers from across the city who have an interest in meeting with other teachers to explore issues relating to the teaching and learning of mathematics and further mathematics at A Level.

Trevor had spent part of the afternoon talking with some of the higher achieving Year 11s, and then turned his attention after school to a small but very enthusiastic group of willing maths teachers. Not having had the privilege of teaching A Level, and still holding a passion for all the mechanics modules I chose at Uni oh so many years ago, I was really looking forward to this session.

The classroom we were meeting in had been transformed into a den of mechanics experiments. Trevor’s enthusiasm for the subject was radiating from him as he introduced the two experiments we were to undertake. These involved, amongst other things, half pipes, marbles, clamp stands, metre rulers and timers.

The curve shows a quadratic relationship between the distance and the time.

The curve shows a quadratic relationship between the distance and the time.

Firstly, there was timing a marble rolling some given distances. The metre long pipe, marked into 20cm segments, was kept as shallow as possible for the marble to roll. It was then timed 3 times each for rolling each distance from 20cm to 1m and the mean value taken. Results plugged into Autograph and the following graph was produced:

The second experiment involved the the rolling of a marble across a tilted table. Our job was to track its path as accurately as we could, to gather data on its path, distance and time. image  We first set the pipe and clamp stand so the marble could travel a decent path up and across the tilted table. Next was to identify the end point of the path, which crated the x-axis.  This path was timed (at least 5 times, and a mean value taken) and the axis was then split into 8 equal parts.  Rolling the marble as consistently as possible, we tracked when it passed each division (again, 5 times for each, taking the median of the points we had plotted on the division lines).


We ended up, as you would expect, with a lovely parabola. The final two measurements to take were the height of the middle division – the point where the marble started its downward journey, and, using a bit of trigonometry, the degree of inclination of the table.image

These experiments were reminiscent of those undertook by Galileo in the late 16th Century.  Ofcourse, he didn’t have electronic timers, so we were quite relieved when Trevor didn’t insist on use using a water hour glass timer, similar to what Galileo would have used.  imageAs well as rolling balls across inclined planes and measuring their distance, Galileo also used the Tower of Pisa to give him a vertical height from which to drop objects.  He was able to demonstrate that a body dropped from height starts at zero velocity and increases his speed over time (rather than the constant velocity, that was larger the more the body weighed, assumed by those before him). This also involved his discovery that the velocity of a falling body is independent to its weight and the mathematical expression that, the speed of an object increases as the square of the time, hence our quadratic graph from the results of the first experiment.

Fast forward 100 years and armed with Newton’s Second Law of Motion, we are now able to form some calcualtions from our data.


And so we have it; practical experiments and calculation enabling us to derive a (very approximate) value of gravity.  There is of course discussion time here for all the aspects not taken into consideration, the main one being air resistence, but our time had come to an end.

The Birmingham and Solihull FMSP network hope to meet at least termly. It was a really enjoyable, practical session; a chance for us teachers to focus on mathematics, from those of us who would like to brush up on our A Level to those who have been teaching it for many moons!  Each meeting will have a specific focus such as this, but there will always be time for discussion of other matters according to teachers’ interests and concerns.  I do encourage any local teachers who are interested in A Level maths (you don’t have to be teaching it) to get involved with the network.  For more information, please contact:

Martyn Quigley
FMSP Coordinator for Birmingham and Solihull
School of Mathematics
University of Birmingham
B15 2TT
0121 414 4800

Mock Exam Follow up

Our year 11s have completed another mock paper, and I wanted a more robust way of each pupil working on a topic which they shouldn’t have lost marks on, along the idea of @just_maths oops sheets.  I knew which topics I wanted to target, and whilst looking at the PRET homework that @mathsjem and @DIRT_expert collated, I put together worksheets with a model solution to the target question, the memory box for revision, skills practice and exam question practice.  I’m so grateful to the resources that fellow maths teachers put online, as I was able to quickly find appropriate questions from the PRET homeworks (thanks to @_rhi_rhi, @AdamGoodridge18)

The worksheets are all below, remembering the credit going to the above folks.

Mar13 2H 05Circl

Mar13 2H 11ExpandFactorise

Mar13 2H 13Pythagoras

Mar13 2H 13Trigonometry

Mar13 2H 15SimilarShapes

Learning Journey

With a new timetable for the last 3 weeks, I thought it would be a great chance to try some new resources.  So with my middle 8s an bottom 9s, I have used a learning journey for their unit of work, following discovering  I just adapted for my groups and unit of work.  It involves an initial assessment, with peer assessment, so pupils can see what they can already do and then set targets for what they would like to achieve from the objectives.  I just asked them to think of one thing they’d particularly like to be able to do, but emphasising it’s not the only thing they’ll be doing!  At the end of each lesson, they write what they have learnt (on their journey!).  Hopefully it will help them see their progress over time.

Learning Journey Numeracy

oops! Upside down photo!





Let’s start blogging

I’ve recently discovered how much wealth of knowledge, discussion and resources are shared by maths bloggers and tweeters.  Having now been teaching for over 5 years, I’ve started to build up my own library of resources which I can share (some of which has been “pinched” from websites such as Tes).  I’m also very much enjoying trying out different ideas and developing these.  So one place to share is on my own blog!  Happy blogging 🙂