How do we count more rapidly?
If we have five buns and are given three more, we can add them to our total … six, seven, eight. If the numbers are larger, however, that method becomes impractical. For example, adding 120 in this way, even if you could add an extra two numbers per second, the exercise would take you one minute! Larger additions would take even longer.
To overcome this problem, people rapidly learned to use calculating tools … fingers, sticks, and pebbles in order to calculate. In fact, our word calculate comes from the Latin word calculus (meaning small pebble) because that is what citizens of the Roman Empire used at one stage for adding figures. Later, the abacus was invented and used extensively in many parts of the world. In time, many other calculating tools were created as well … Napier’s Bones, Genaille-Lucas Rulers, logarithms, and mechanical and electronic calculating devices (and others).
People also tried to calculate mentally or using marks on paper. These methods were more abstract and often required learning ‘tables’ of common calculations. For example, memorising 5 + 3 = 8 would make the exercise of adding the buns very much more rapid!
Eventually, algorithms (strategies or methods) were developed for rapid calculation using all four operations (and more). You will learn about a variety of those (mental and paper-based) algorithms here.
Adding and Subtracting Integers (Whole Numbers)
Powers, Indices, Roots, Radicals and Surds
I have been watching your “Integration technique” videos with high expectation and excitement. They never fail to give me a lot of joy and much pleasure. You must have been one hell of teacher at your time! … just continue making highly enjoyable and intellectually stimulating videos. … Unfortunately, what you learn at the university, you hardly ever see again in your office job. That is why I try to repeat some thing I learned: to enjoy it a bit more, to marvel upon beauty, and to keep my brain sharp. There is where your videos come in perfectly: interesting, amusing and thought provoking problems neatly presented. … You do your best to share your passion, knowledge and experience. The least I can do is to say an honest “Thank you!” As I said, your videos give me much pleasure. You may freely let other people know that. … Rest assured that I shall be watching your videos in the future. With joy and excitement. And I shall comment on them from time to time. You just continue making them.
Zoran V (in private correspondence via YouTube, quoted with permission)
See all Testimonials
