Multiplication Strategies

This year in math, we've been looking at solving problems differently.  We've really opened up dialogue with students about ways to look at numbers.

For example: 73

• 7 tens and 3 ones
• Round it up to 75 to make it a friendly number
• Round it down to 70 to make it a ten

Students have been able to talk about numbers just like this and this has given them a deeper understanding of place value and what we call "decomposing" the numbers or breaking them down to make them easy to use.

Recently, we have been studying multiplication.  I know many parents out there are just like me: we all learned the algorithm.  That's the fancy way of saying we learned multiplication like this:

                34
             x 72
          ---------
                68
       +   238
          ---------
           2,448

Now, I didn't put the little 2 above the 3 when I was multiplying 4 and 7, but if I was doing it on paper, I would have.  We learned multiplication this way.  We learned how to multiply digits upon digits.  What we failed to learn, was "what is really happening in this math equation?"  or "Why?"

Maybe I shouldn't assume that we all didn't learn the reasoning behind it, but I know I did not and I'm not alone.  Using the algorithm alone and just going through the motions is just that--going through the motions.  I know that we, as parents, can find ourselves saying--"If it was good enough for me, then it's good enough for them (my children)."  Whichever way you look at it, our children aren't being raised in the same world that we were brought up in.  They are competing in a world economy, where the person competing for your job isn't your neighbor, it could be someone in another country.  By developing the "why" and giving a greater meaning to something is much more meaningful than just going through the motions.

How does this apply to math?  Students are using methods in which they decompose the factors of a multiplication problem and then using basic facts to solve.

Let's use the same problem shown above.
   34 x 72
Let's decompose the 72.  It's 70 and a 2.
Now, let's use the distributive property and distribute the 34 to both of those numbers.
We have 34 x 70 and 34 x 2.
An easy strategy to solve 34 x 70, is to break it down to 30 x 70 and 4 x 70.
                                                                                   2100            280
What do we have left to multiply?  The 34 x 2.  I may already know from our mental math Number Talks that 35 x 2 = 70, so I'm going to do that and then subtract 2 from 70 because I added 2 ones on.  70-2= 68
Now let's add up all of our products: 2100 + 280 + 68 = 2,448

(this is just one method we've learning)

I won't pretend that methods like this aren't longer, because they are much longer.  But the comprehension of the numbers and how to manipulate them is so crucial and astounding to witness.
We've been working at developing these strategies in our classroom and the processing that you see happening is a little slow, but good thinking.  This is what I must emphasize: These strategies provide good thinking.

Teaching like this is necessary for the Common Core curriculum, which Iowa has adopted.  I appreciate your questions and I need your willingness to be open to your child learning new strategies, which may seem foreign to you. :o)