Wednesday, January 11, 2006

factoring trinomials with children

Matthan, my 13 year old, is factoring trinomials again today in Algebra. Remember how to do that? If you are an average person who didn’t major in math or go into pipefitting, you might not remember much about your advanced math courses or factoring trinomials! Don’t worry, it’s perfectly normal to have taken a course in high school or college and then not remember a darn thing after you’ve lived your life in freedom for a few years. Factoring trinomials is when you have something that looks like this:

x(squared) + 6x + 9

and you have to make it look like this:


You will remember that a factor of 9 is 3? This is the same thing only with some parenthesis thrown in there just to trip you up. You are finding the multiples of a number only now the number has googely eyes and fangs.

When I asked Matthan, “What number gives you nine when multiplied by itself or 6 when you add it?” or “What numbers when multiplied give you 8 yet when added give you 6,” I realized how elementary basic Algebra really is. It’s all the other stuff that confuses me like the parenthesis and the ‘unknown variables.’ We can all add 3+3 and multiply 3 times 3; add 4 and 2 and multiply 4 and 2, so why do we get all tripped up when we see it in the context of Algebra?

I think I know why. When we were in elementary school we were taught that “X” means to multiply.


We were very impressionable and we accepted that fact and used it most of our little math lives. Then one day, we are told that the very symbol with which we have come to associate multiplication is now an unknown variable. “What?” Then we are told instead of using an “X” you can put 4 in a parenthesis and 2 in a parenthesis and that now means what the “X” meant all those years before. Oh, and your ABC’s are now coming to join us for math class – well, Algebra. We learn one thing and use it all of our lives and just when it becomes second nature we have to give new meaning to old symbols and learn all new ways to do the same old things. Algebra seems to be a whole new world and it’s not peaceful to some of us.

It shouldn’t be new or scary at all. In fact, it’s not new, it’s just playing around and rearranging and expressing numbers that we are familiar with in many different ways. Why did it feel different? Why did we learn that multiplication could be expressed by putting an “X” in between two numbers when the whole time we could have just put those numbers in parenthesis? If we are expecting children to grow up and learn Algebra why don’t we just start Algebra in third grade? Maybe I’ll figure the answer out one day. Until then, we are going to play around with Algebra from the get go.

When I asked Matthan, “What numbers when multiplied give you 8 and when added give you 6,” so that we could factor a trinomial, I looked at Kelsey and thought, “She could do what we are doing!” So, I wrote a trinomial out: “x(squared) + 6x + 9” and under it I wrote two parenthesis with an X in each one like this: (x + ) (x + ) and let her decide what numbers should go after the plus sign. She picked up on this pretty fast!

When I told her that she was doing high school Algebra she became very excited. Her confidence in Math was boosted. I hope that when Kelsey enters the world of Algebra and is greeted by my googely eyed monster, that it won’t be something frightening for her.

She can factor trinomials now because that takes basic elementary math! And of course, as her understanding of math expands so will the complexities of the trinomials.

A few years later, as my daughter was learning how to convert Fahrenheit into Celsius, my six year old was inspired to play around with equations and variables. Here is the post.

Too often we give children answers to remember rather than problems to solve. -Roger Lewin

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