First impressions are lasting impressions. After the introductions and niceties are over during your first lecture to a new batch of students, you can try getting them to participate by posing an interesting general problem to solve. I have found the following problem to be a sure-fire way to break the ice and have used it with success on quite a few occasions.
I came across this poser entitled "Girdling the Earth" during my student days in a puzzle book published 60-70 years ago. I have not come across a similar problem subsequently which is quite surprising. Not so in the case of jokes. There is nothing like an original joke today. All jokes have been recycled over the years.
The problem went something like this:
Imagine that the Earth is a perfect sphere; no valleys and mountains. You are given the task of encircling the Earth from the North pole down to the South pole and back to the North pole, exactly one full circumference in all and touch both ends of the rope together. If all goes as planned, the rope will be hugging the Earth all round its polar circumference and to an observer in outer space it would appear that you have girdled the Earth.
Due to an error in calculation, it was found that you have 10 feet of extra rope after circling the Earth. When the two ends of the entire rope are made to touch, this extra length causes the rope to become loose all round the Earth and there will be a "gap" all round. It is therefore decided to make the rope tight all round the Earth's surface by packing a uniform thickness of sheets of paper.
What would be the thickness of the paper material required below the rope at any point?
The students would look at you incredulously as though wondering whether you are out of your mind and why you had posed such an inane problem to them. Invariably, all the students will say that the thickness of paper material is negligible since 10 feet is not going to make any difference when we consider an object like the Earth and not even an ant can crawl through the resulting gap. But you can surprise the students by showing with a simple calculation that the answer is close to 1.5 feet all round the Earth, enough for a normal-sized person to crawl through!
We can be ambidextrous when required!
It was around the year 1998 when I was teaching in the Department of Electronics and Communication Engineering, Osmania University, Hyderabad. I am a right hander and I happened to injure my right wrist and it was in a plaster cast.