Mental Multiplication: Useful Facts and Exercises

a) The value of knowing your first 100 squares has been discussed pretty thoroughly and the high percentage of coverage that can be had through knowing simple differences of squares and the binomial theorem gives a large coverage of the space for little investment.

b) Advancing multiplication tables up to 20 or so has also been quite productive in terms of raw speed. (I will continue with this mostly as a matter of becoming more familiar through practice in calculation).

c) Practicing basic addition and substraction 1/2/3 digit has also been helping. Both getting very comfortable with carries AND learning how to use complements to avoid carries.

d) Learning how to “read” a multiplication as opposed to calculating it. (Somewhere between calculation and memorization)

I’m looking for my next bit of rote memorization to help me along the way…

Has anyone tried focusing on learning the Prime factors and their multiplicands to 10,000 /1000/100 ??? and using them as pivot points for mental calculation? It seem like factoring via primes should provide a strong alternative method for calculation but I’ve never found it recommended anywhere. If you have how did you go about it? Was it productive? Fun? Simply another entertaining way of thinking about calculation while you waited for your brain to catch up with your ego?

Any other suggestions for calculating fun? I don’t want to spread myself to thin but I don’t want to burn out on a single set of drills either.

thanks,
R :slight_smile:

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So there are 70 nontrivial composites and 168 primes between 0 and 1000

https://zieglerk.wordpress.com/2009/07/12/recognize-your-primes/

I suspect that internalizing the common divisibility rule up into the teens would be useful…

Kinma recently pointed out casting out nines and elevens was pretty darn useful for checking your work.

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Ulama spirals… This way lies madness.

There are so many. Better find a general algorithm imho.

Lol! Beatiful pictures though.

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There is a general algorithm for this, but it doesn’t appear that anybody on this forum has written about it before. Hope I still get a chance today, but if not over the next couple of days, I’ll post about it.

EDIT: post on general algorithm here…