[kqr]

On the topic of memorising arithmetic, I have found it surprisingly useful to memorise a few base ten logarithms. While most people have a good sense of numbers as an arithmetic progression, the geometric perspective is often more useful. (Things like how 3 is halfway from 1 to 10, but 10 is halfway from 1 to 100. (This is just the square root, of course, since that is a power of a half. But it's also useful to know that 2 is one-third of the way to 10, and 1.6 is a tenth of the way to 100. I.e. knowing some logarithms, you can mentally compute arbitrary fractional powers in your head.))

For the curious, I write a little more about it here: https://two-wrongs.com/learning-some-logarithms.html