## Tuesday, November 3, 2015

Once again the internet is abuzz with hysteria because of a third grade problem that was marked incorrect when, according to many, it was not.

The problem involved using  the repeated addition strategy to solve 5 x 3. When the student wrote 5 + 5 + 5 every one cried foul saying the student's answer was correct. The answer is clearly incorrect because it should be, as shown, 3+3+3+3+3+3.

Understanding the repeated addition concepts is one of the most important ideas in multiplication and division especially in problem solving. There are so many different skills wrapped up in this seemingly simple idea that we, as parents, owe it to our children to take the time to grapple with this issue and understand it so we can help our children and not dismiss  it out of hand becasue it is different fro the way we learned math.

In terms of a simple math procedure 5 x 3 is the same as 3 x 5 since they both = 15. This is called the commutative, or turn around, property of multiplication. But, if you apply this idea to real objects in real situations the two number sentences are not the same. One is three groups of 5 and the other is five groups of three. If you were working say with M&Ms 5 x 3 would be 5 groups of 3 M&Ms which looks quite different from 3 groups of 5 M&Ms. *****  *****  ***** or *** *** *** *** ***

Now, if you apply this to division, the reverse of multiplication, 15 M&Ms divided between 3 children is quite different from 15 M&Ms divided between 5 children. If we teach multiplication as repeated addition we can teach division as the reverse or repeated subtraction.

There are, of course, more concepts related to multiplcaiton and division but that's another story. So my advice to parents is don't knock something you might not understand just because it's different from what you learned 20 - 30 years ago. Take the time to learn it and you'll find that understanding math instead of just memorizing it is so much more rewarding and useful in the long run.