[sidlls]

Mainly the list you stated.

Practicing basic arithmetic and judicious application of the distributive property (much like decomposing complicated problems into smaller subproblems) will take one very far in this sort of thing.

I was introduced to dimensional analysis in my high school physics class. We generated an expression off by just a constant for some property (which I don't recall) of a large scale dust cloud simply by identifying pertinent quantities (e.g. density, the classical gravitational constant) and resolving the powers each quantity must have in order to yield the correct units (corrected due to below comments; thanks) of the property. It made an impression on me, and I used the technique often as a guesstimate to "motivate" or provide a calibration for a solution to various problems all the way through grad school. It's not infallible, and can even be wildly misleading, but it's a fantastic tool.

[chairleader]

Good point. Dimensional analysis is a great "space" to traverse to get answers. It's a great grounding for your thinking, in addition to helping you get to within the right order of magnitude.

I suppose I was wondering if there are any good drills, exercises or puzzles to help internalize these skills. Instead of a daily crossword, maybe there's a daily estimation puzzle somewhere.

[konschubert]

However, dimensional analysis is for when you need to figure out the formula.

"Estimating" is when you have the formula and fill it with estimates to obtain a combined estimate.

[imcoconut]

Could you elaborate on this? By "resolving the powers" do you mean magnitude of interacting forces? And by correct dimensions do you mean spatial dimensions?

[btouellette]

By dimensions he means units. So taking into account the units of density/the gravitational constant (and any other pertinent quantities) and the units of the quantity you are calculating for you can derive an approximate formula just by looking at it and saying okay this unit needs ^2 and this one needs ^-1 and this one needs ^-3 for the end units to work out.

https://en.wikipedia.org/wiki/Dimensional_analysis