Math in My Head!

Taking math classes really makes a person think about…well, math!  I am currently taking two math classes and one thing that I have noticed is how often I reach for the calculator.  Is this a good thing or is this a not so good thing?  Hmmm…

This left me thinking, “shouldn’t I be able to do more of this math in my head?”  If a person tries to Google “mental math strategies”, they come up with a pretty extensive list of methods for doing math in their head.  It seems a little overwhelming and my brain is already protesting not using a calculator.  So, here are just a couple of methods I learned about in math class.  These seem pretty straightforward and a good place to start.

Not just people are compatible…numbers are too!

Compatible numbers are numbers that easily go together to help solve a problem.  For starters, it can be helpful to look for numbers that make ten in a problem or multiples of ten.  These are easy to calculate.  Here is an example with addition:

7+9+3=

 I know that 7+3=10.  If I add those together first, then it is easy to add 10+9=19.

How about multiplication?

                (2x3)x(5x4)=
I know that 2x5=10.  This leaves me with 3x4=12.  Finally, I can solve the problem with 10x12=120.

OR I know that 5x4=20.  This leaves me with 2x3=6.  Finally, I can solve the problem with 20x6=120.

Here is a video, showing how this method could be helpful in teaching elementary students to solve problems mentally that require adding a long list of numbers.

 

Once students have mastered looking for 10’s, they can move on to looking for other number combinations that are compatible to help solve problems mentally.

If it looks too difficult to do in your head…just compensate!

Compensation is another technique which uses a form of compatible numbers.  It simply means that if there is not anything in the problem that looks compatible, we just substitute (or compensate) to make it compatible.  Here is an example with addition:

35+48=
I see that 48 is pretty close to 50.  So, I change it to 50 in my head.  Then it is easy to add 35+50=85.  Now, since I added 2 to the 48 to make 50, I simply take away 2 from my answer.  85-2=83.

How about multiplication?

9x14=

I see that 9 is close to 10.  So, I change it to 10 and multiply 10x14=140.  Now, since I multiplied by 10 instead of 9 (10 sets of 14 instead of 9 sets of 14), I subtract the extra set of 14 from my answer.  140-14=126.

There are many other techniques for doing math in our head and teaching elementary students to do math in their heads too.  I found this List  to be helpful.

Should I toss out my calculator?

Probably not!  It sure comes in handy for that math that I can’t do in my head…