In answer to several questions:

It has been many years since I did any teaching so it will take a few
days for me to get up to speed on it.

I used 7700 lbs of water because that is the empty displacement of my
boat.
The captain of the sinking vessel knew what displacement meant and
about concepts of buoyancy.
I inadvertantly gave a problem that was too easy,
I have no knowledge of coast guard pump capacities but only intended
for him to show he knew how to do such a problem.
I have read both the Patrick Obrien and CS Forester novels multiple
times and consider Obrien too verbose and detail oriented for a 14 yr
old.
I have him do some steering, actually I make my kids do a lot of
steering in and out of port although the auto-pilot does most of in
transit.
I make him do coastal piloting by taking bearing on markers and
markings LOPs on the chart.
The "Reward" thing really hasn't been an issue. We are both sure he
could pass the end of 8th grade tests now but I told him I wanted him
to be more educated than that. I explained that most of us are of
average intelligence and the only way we can do better than seriously
intelligent people is to simply know how to do more things than them
and to be more determined.

today's lesson:

This involved compass variation and I got out a globe and showed him
how it occurs because the magnetic and geographic poles are far
separated. I also explained that the magnetic poles wander to make
annual variation increases.

First, I had him do some conversions of a position like 23 deg. 30 min
to degrees and fractions of a degree (23.5 degrees).
Then, I explained that on short trips, I never have to account for
compass variation because it is only about 2 degrees in our local
waters. Then, I gave him a chart from 1983 of the NE Gulf of Mexico
with its variation and annual increase marked. I then asked him how
much I would be in error today if I steered strictly by compass from
Cedar key to our next destination; Tarpon Springs (about 60 miles).
The correct answer is about 5 miles if you account for the variation in
1983 and add the annual variation increase. He was surprised at this
and thought he had done something wrong at first so i guess he learned
something.

Tomorrow, I will ask "Why do we use only the latitude scale on a chart
to measure nautical miles? Why cant we use the longitude scale?" He
ought to be looking at the globe for this one.

I will also ask, how many right angles can a triangle on a plane have?
How many right angles can a triangle on the surface of a sphere have?