I don’t like being too dependent on calculators. The future might bring an EMP (electromagnetic pulse) that would fry all such gadgets (and cell phones, cars, computers, etc.), and I want to be ready for a post-calculator world, if that happens.
My overarching strategy for doing math in my head is this: don’t have just one single strategy. Instead, devise one, on the fly, based on the problem you are trying to solve.
I do, however, use a few “go to” strategies for certain things, such as finding 25% of something, or multiplying by eight, or similar problems. This involves looking for, and take advantage of, powers of two, as well as their reciprocals. 25% is 1/4, which is simply halving twice, and multiplying by eight is three doublings, since 8 = 2³. With practice, doubling or halving numbers repeatedly and silently, in one’s head, becomes much faster and easier. If done out loud, it becomes easier still, and on paper, it’s extremely easy.
I intend to do more blog-posts in the future with calculator-free calculation strategies, but not all at once — instead, these techniques will be posted one at a time. However, these postings will stop immediately, in the event of an EMP.