# Pendulum studies- estimating the answers to calculations with a swinging mug on a string…

I was thinking of how to jazz up the topic of estimating the answers to calculations (by rounding first) for a KS3 class when it occurred to me that a bit of physics could provide just the opportunity. The lesson is about pendulums and calculating the speed at which they swing.

Start by giving the class mini-whiteboards and tell them they are not, under any circumstances to use their calculator in the lesson today.

Hang a mug, or similar weight from a piece of string from the ceiling such that it nearly touches the floor, forming a long pendulum.

The period of oscillation (time for one complete swing forward and back), T seconds for a pendulum of length L metres is:

T = 2 X pi X square root (L/g)

g is the gravitational acceleration and equal to 9.81 m/s/s.

Get a pupil up to the front of the class to measure the length of the pendulum and then ask the class to estimate what they think the period of time, T, for one oscillation will be. To do this they need to round the values in the equation to 1 sig fig and then calculate T. For example, 2 X pi becomes 6, g becomes 10 and a pendulum of length 2.8m is entered as 3m long. They estimate T = 6 X square root (0.3) = 6 X 0.5 = 3 seconds. (Assuming square root of 0.3 is 0.5 as 0.5 squared is 0.25 which is very close). Then swing your mug pendulum and get them to time the period for one oscillation with the stopwatches on their phones. When I did it with a class, the time of the real life oscillation matched the estimation very well and the class were delighted.

Then you ask the question, how long does the pendulum need to be to have an oscillation of 2 seconds? A bit of changing the subject of the formula and some more estimation later they can give you an estimate of the pendulum length required. We found this to be approximately 1m and when we built and tested it the oscillation was 2 seconds bang on.

Pupils seemed to be really engaged with the lesson and the learning was good too. They told me they got a real sense of why estimation by rounding is important and were surprised we they could predict the movement of the pendulum so accurately without using a calculator.

Definitely one to try out. Do you have any ideas of other science links that we could bring into our maths classrooms?

what a great demonstration of the power of estimation. My find of 2012 was the QAMA calculator that doesn’t deliver the answer to a problem unless the user has input a suitable estimate first. http://www.qamacalculator.com

So the skill being applied here (and in so many of our students – and teachers? – this skill is completely lost) can be continued in all lessons.

then estimation isn’t just a topic to be covered, but a way of life!

and as for other links, there are always the Bowland resources. http://www.bowlandmaths.org.uk