We revisited longitude and latitude today just prior to a quick quiz on Monday of elevation/depression, longitude/latitude and bearings problems.

Firstly the section that we did on angles(complementary/supplementary) and bearings seems to have resolved many of the angle addition/subtraction problems students encounter in longitude and latitude (this makes sense). The second was that teaching how to solve latitude problems before longitude problems is far easier than vice-versa (this was not expected).

Sequence used:

a) nomenclature & uses - great circles:longitude+equator, small circles:latitude

b) how to draw latitude problems - uses of front vs side views

c) find the radius of small circles - r(small circle) = r(great circle) cos (longitude)

d) how to find the circumference of small circles - C(small circle) = 2 x pi x r(small circle)

e) how to identify the angle travelled - reading diagrams carefully & common errors

f) how to calculate the distance travelled - angle / 360 x C(small circle)

The reasoning for the second finding is that students were happy to learn new skills (eg. solve latitude problems)...

... students were even happier to be told that longitude problems were easier than latitude problems (eg. remove step c), draw the diagram a little differently - front view edge marked)

.. rather than teach longitude first and say that latitude problems were more difficult (as you need to add step c) and have to think harder about the diagram).

All in all, it can be taught in a lesson to a good group in year 10, maybe a bit longer if proving step c), with practice for a couple of sessions. I never would have identified the second finding if I hadn't chosen the wrong question as an example. Nothing like a random event to improve your teaching and give an insight into student thinking.

r(small circle) = r(great circle) cos (latitude)

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