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…  

Hooray for the Array!

While studying sets and whole number operations and properties this week in my summer Math for Elementary Teachers class, the topic of the rectangular array was broached.  Arrays can be used starting in the early elementary years to help students understand a variety of number concepts and operations.  As a teacher of elementary students, it is beneficial to understand different ways that arrays can be used to help teach math.  The possibilities are endless.  Only limited by how creative you are willing to be.   

Aren’t arrays just for teaching multiplication?
Of course not!  How boring would that be?  Before students learn multiplication, arrays can be used to teach many other number concepts.  A few of them are…

• Equal /Not Equal
• Odd/Even
• Sorting
• Skip Counting

Some of these concepts are related to multiplication but younger students will probably not notice this connection until later.  Arrays can be used to teach many things and exposing students to them early in their education will help to build links to prior knowledge for future learning.

How can arrays be used for multiplication?
Arrays are an excellent way to help students understand multiplication.  Breaking number sentences into rows and columns helps to give them a visual representation of the problem.  Besides this arrays can be used to explore and demonstrate other concepts that go along with multiplication.

• Factors/Primes/Squares
• Properties of Multiplication
• InverseOperation of Multiplication - Division 

How can we get creative with arrays?
Even though graph paper and a pencil work just fine for making arrays, that does not mean that we are limited to using only this method.  Arrays are all around us (muffin pans, legos, tiles on a floor, and eggs in a carton) and students should be encouraged to explore them in many different forms.  Students can be given grids and various types of materials (buttons, blocks, candies, and coins) to use in making arrays.  Arrays can be a great method of visual and hands-on learning. 

Hooray for the array!   

More information on arrays can be found at:

More about arrays!