Paper and Pencil or Mental Math?
What the common core ALSO asks students to become proficient at are strategies that allow students to more readily peform MENTAL arithmetic. As an example, consider this problem:
31 – 19
To perform this subtration on paper, one would almost certainly use the traditional algorithm of “borrowing” (another post will have to address this term) 10 ones from the 30, to make 11 ones. Then one can subtract, just as we’ve all been taught with the traditional algorithm.
However, what if you are NOT doing this on paper, but are doing it mentally? Personally, I find myself counting up from 19. It looks like this:
19 + 1 gives me 20
Adding 10 more gets me to 30.
I need one more to get to 31.
That’s a total of 12 (1 + 10 + 1) that I have added on, so 31 – 19 = 12.
Becoming fluent in the ability to do mental arithmetic is important. But we delude ourselves if we think that this means the traditional algorithm is the best way to teach mental arithmetic. Having multiple strategies, that work for a variety of types of problems, becomes increasingly important as students progress through their learning.
For a more detailed look at this, please take a look at this article on Common Core Subtraction.
What are some of the different strategies that you use for mental arithmetic? Feel free to comment below with some examples.