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 cannot even begin to describe how much you’ve taught and continue to teach me through your videos. I’m going into year 12 this year and I feel like your way of teaching is so ‘crystal clear’ to me so thank you so much! Too bad you can’t be my teacher I’ve recently watched you playlist for derivatives and those videos are amazing! … Continue to make awesome videos because you’re a legend.

Chelsea N (student, 2015, in private discussion about CCM YouTube videos, with permission)

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