There's a lot about math and basic arithmetic that is NOT explicitly taught, such as approximation: having an idea of what the answer should be before you even do the calculation, as a way to help double-check the answer. As a simple example, if you are multiplying a two-digit and a three digit number, you should already know that the answer is going to be at least 1,000 (ten times a hundred) and less than 100,000 (a hundred times a thousand). If it's a practical problem, there are usually other ways to check if the answer is reasonable or makes sense, as in the swimming pool quote below.
I've always thought of the sliderule as a good teaching tool because you have to figure out the magnitude yourself, as well as be able to read the scales accurately to get a good answer.
I just read this blogpost on a calculator that you have to give a good approximation to the answer before it gives you the precise answer:
http://mathforlove.com/2016/06/qama-the-calculator-that-wont-make-you-lazy/
As the following quote below as well as the previous post indicates (with virtually the same calculation), using calculators for trivial calculations (and blindly accepting any result) is legion.
I've often bought Subway "Fresh Value" meals, and sometimes the cashiers ... I usually pay with exact change, or back when it was $4 (plus tax), a dollar over. When the total is $4.23 I'd pay with a $5 bill, two dimes and three pennies, and almost every cashier immediately knows what to do and gives back a dollar. One poor teen used a calculator to figure out he owed me a dollar (the CASH REGISTER already does this!), taking about a minute to do it. I saw him do this twice in one week, then didn't see him any more. Another guy haughtily said "It's FOUR twenty three," pushed back the change, took the five and then gave me three quarters and two pennies. I didn't say anything, especially as his supervisor (who clearly knew better) was standing right there. I never saw him again, but I hope he got an earful, just so he'd know he wasn't doing the right thing and it would be easier to just take the change and give back a dollar bill.
I’ve seen eighth graders reach for a calculator to solve 100 – 98. I’ve seen college students accept total gibberish from their calculator after mis-keying, without considering whether the answer makes sense on a gut level. (“The swimming pool costs… 53 billion dollars.”)
I could rant about this for as long as the OP (about this CC thing, when you're learning numbers, addition and subtraction and multiplication tables, you don't need to learn the theory behind arithmetic - leave that for at least the fifth grade or so, as a prerequisite to algebra), but I'm resisting...