Hmm that's interesting - I'd tend to round one of the numbers, whichever is closest to a '5' or '10', to make an 'easier' multiplication, then add / subtract the extra value lost / gained by rounding.

Example 9 x 14 = (<10> * 14) - ([1] * 14) = 140 - 14 = 126

key: <> easier rounded number [] deal with rounding 'error'

I've done that before too, but for whatever reason my mind just defaults to adding two numbers rather than subtracting. Probably either habit or I just find it easier.

Weird, I did it the other way - 9x10 + 9x4 = 90 + 36 = 126

You only have two sig figs at best for an engineering estimate you could get close by rounding up to 10x15 which is 150. The error on both terms is gonna round to about ten so subtract both error factors from the 1st order estimate and get about 150-10-10 aka a decent engineering estimate done in the head to two sig figs is 130. Thats not too far from a calculated answer, only a couple percent off, which is smaller than the measurement error.

The most important estimating still, after manipulation of sig figs is knowing which way to bend for the overall system. So say I'm tiling a kitchen floor or buying paver bricks for a modest sized patio. Well, some raw material is going to be too ugly to use and I'm going to screw up some of the trimming and cutting and I'm going to drop some, and the cost of the gasoline and time to drive out to the home center and buy one more (mismatched) tile or brick is very high, so in that scenario I'd buy the 10x15=150 tiles and hope thats enough (I'm feeling lucky today). On the other hand if I had 9 steel chains each rated (by whom? Static or dynamic loads? Point concentrations or perfectly (LOL) distributed?) to 1400 pounds each, I would round way down for safety's sake and not suspend more than 10 x 10 or 10000 pounds on that platform. Even if the chains are rated properly I only need to screw up or fail four of them and the thing crashes down.

Anyway for engineering purposes 9x14 is somewhere around 100 to 150.

I find (10x14) - (1x14) = 140 - 14 = 126 slightly quicker and less error prone than carrying the ten across the hundred boundary with 9x10 + 9x4 = 90 + 36 = 126, I'm not an educator though so there may be better ways taught now.

But this is wildly off topic, and in reality I'd rather someone knew how to use their calculator or excel or Python to do this sum than know how to do this sum in their heads.

It's important they know the rough answer in terms of scale and shape, so that any mistype or error is quickly recognised, but I don't think it is important to actually know how to quickly do long multiplication in one's head.

I do the same. However, recognizing you can do that is part of learning arithmetic and problem solving in general. I learned that method at an early age and it taught me that most big, scary problems in general are really just a bunch of small problems that can be identified and solved more easily.

This is how arithmetic is starting to be taught in elementary schools now, which unfortunately has resulted in those big Facebook blow ups about how "common core" math homework doesn't make sense anymore.

10 times 14 - 14.

(9* 7) * 2 :)