GCF (greatest common factor) and spending ‘too much time’ on math topics. These are the middle school math ideas I’m thinking about today.

There were times during the school year when I’d think I had spend too much time on a math topicโฆ.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 Iโd run out of time (I’m sure you know the feeling!).

So, spending more time than I was โsupposed toโ occasionally stressed me out.ย But most of the time, I was glad I spent so much time on some concepts, even though I appeared to be โbehindโ when talking with other teachers about where we were in the curriculum.

- When I say that I spent more time, itโs
**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.

**Day 1 of Reviewing How to Find GCF**

1)ย Partner up (using the equivalent expressionsย partnering cards for extra reinforcement of that concept!) and

2) Write short paragraphs to explain each method (and include their own examples).

- That activity took most of the math class (after our warm up and reviewingโฆ.only a 40 minute class).ย

**Day 2 of Reviewing How to Find GCF**

- listย factors
- findย GCF of given numbers
- solve quite a few GCF word problemsย

The students in the first class period didnโt even get half-way through the task cards, and I started thinking, โOh, no, now we have to use **another** day to finish this tomorrowโฆor maybe we shouldnโt finish, we should just move on.โ

BUT, as I listened to my studentsโ discussions, class after class, I decided that weย __definitely__ย 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 confirmedย that spending this time is ** what’s best for them**. I heard:

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

- Students helping one another by pointing out one anotherโs mistakes (politely) โ which means they can identify mistakes in work!ย

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 turningย to each other for help and trulyย tryingย 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 discussionsย continually improved throughout the year, as did their collaborative thinking skills.

โ

Was the extra time I spent on GCF and other math topics worth it? Absolutely!

**GCF Task Cards**

โGCF & Factors Footloose Task Cards