Sure. I'll go with that. Farmer Bob can be a part of a case study. We start off simple.
Farmer Bob buys exactly as many posts as necessary... then he discovers shrinkage/theft/errors
The next project, Farmer Bob uses linear extrapolation from the past 5 projects and buys X% extra posts... but then he discovers new employees break things
The next project Farmer Bob uses Linear Regression, broken down into key variables (like # of new employees)
I think we can get a book deal with this!
At first kids just learn how many fence posts and fence is gonna be there in the end. I.e. how much do you need to buy ignoring some things. Like you ignore friction losses in physics in many cases, especially in school.
Extrapolation and Linear regression you learn later on to solve the same problem better! Love it!
Similar thing happens (or at least happened when I was in school) in chemistry. We learned the Bohr model and it could be used to explain everything that we learned about. Towards the end we learned that there are some things that model can't explain and that there's another model that can explain those things and so we learned about that and also that it's totally fine to keep using the Bohr model for a lot of stuff as it's easier. Like ignoring friction losses in physics and the predictions/calculations come close enough in most cases that it's still useful but much easier to comprehend and calculate than if you had to take them into account.
"Farmer Bob would be pretty stupid to drive an hour to the hardware store to buy 20 fence posts and 100m of fence, because Murphy's Law and what if one happens to be bad or someone cuts wrong and we're short 2m of fence?"
yes, growing up on construction sites does that to you, the problem is badly phrased if it's saying "should buy" instead of "needs" ;)