How to Find GCF and Spending Time in Middle School Math

There were times during the school year when I’d think I had spend too much time on a math topic….not because the kids seemed bored with it or anything like that, but because I had to get so many concepts covered that I was afraid I’d run out of time (I’m sure you know the feeling!).
So, spending more time than I was “supposed to” occasionally stressed me out. But most of the time, I was glad I spent so much time on some concepts, even though I appeared to be “behind” when talking with other teachers about where we were in the curriculum.

• When I say that I spent more time, it’s not that I made the students do worksheet after worksheet; instead, we’d practice/interact with the same skills in several different ways.

For example, before a holiday break one year, we worked on finding GCF (greatest common factor). Prior to 6th grade, most of the students had only been taught one method to find GCF: listing out the factors.

• When I taught GCF, I also taught students the prime factorization method and the ladder method (you may already know that I LOVE the ladder method, for most sets of numbers:-).

So, we worked on finding GCF, and then we had the holiday break.

• That activity took most of the math class (after our warm up and reviewing….only a 40 minute class). 

• list factors
• find GCF of given numbers
• solve quite a few GCF word problems 

The students in the first class period didn’t even get half-way through the task cards, and I started thinking, “Oh, no, now we have to use another day to finish this tomorrow…or maybe we shouldn’t finish, we should just move on.”

BUT, as I listened to my students’ discussions, class after class, I decided that we definitely needed to finish the next day.
And I definitely needed to continue to spend the same amount of time on topics that I had been spending, in all the different ways I employed, because what I heard from observing students confirmed that spending this time is what’s best for them. I heard:

• Quality math discussions 
• Students giving math advice to each other
• Students finding factors of larger numbers by testing divisibility rules (without me advising them to!)
• Students using different methods to confirm answers

• Students helping one another by pointing out one another’s mistakes (politely) – which means they can identify mistakes in work! 

I was so impressed with several things I observed during these days:

• Students’ ability to communicate about how to complete a problem
• Students’ ability to communicate disagreement with a partner
• Students turning to each other for help and truly trying to figure out the answer before asking me
• An increased use of math language!

I loved to walk around and listen to my students. I had my students work in partners and groups quite often throughout our studies of various math topics, and their discussions  continually improved throughout the year, as did their collaborative thinking skills.
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Was the extra time I spent on GCF and other math topics worth it? Absolutely!