Adding and Subtracting Five is Easy I will frequently use the term "five's conjugate". The word conjugate means yoked together or coupled. The five's conjugate are pairs of numbers whose difference is five—that's the coupling. The five’s conjugate of 1 is 6, of 2 is 7, of 3 is 8, etc. The five's conjugate of 6 is 1, of 7 is 2, of 8 is 3, etc.  The easiest way to think of the five's conjugate is with your hands. Each hand has a relative finger count (1-5). Both hands combined have an absolute finger count (1-10). Martian mathematics is largely single-digit mathematics, so we are mostly interested in the single-digits (0-9); therefore, we think of ten as zero. Let's say you want the five's conjugate of 7. Hold up both hands with the left hand's fingers fully extended. That is five. On the right hand, extend the thumb and index finger. You now have seven fingers. Now, make your left hand into a fist. You are left with only two...

Martian Mathematics  I call this Martian mathematics because if you saw someone doing math this way, you would probably think they were from Mars.  87 × 8, no problem. That's just 670 + 26.  Weird, huh? Not everything here is "out of this world," but a good bit of it will seem strange at first. With that said, I developed this system of mental mathematics for my children. Innumeracy is a growing problem worldwide and dependence on machines for calculation is the rate-limiting step in analytical thinking. These shortcomings are what I hope to alleviate with my system. In short, the methods you will find here are intended to unshackle mathematics from pen and paper. I am, of course, not the first person to do mental mathematics. There is much to be learned from Arthur Benjamin, Scott Flansburg, and Jakow Trachtenberg. I will visit them here as well. You should follow this blog if you are interested in fast mental math or homeschooling your children in mathematics. ...