“Ms. Mathinaz has 25 lollipops, 10 Tootsie Rolls, and 15 Smarties. She wants to divide them into identical treat bags for her students. What is the greatest number of bags she can make?”
Last year, I taught this kind of problem the straightforward way. We listed the factors, found the greatest common factor, and were done with it. If the question instead asked how many Tootsie Rolls were in each bag, we hopefully divided by the GCF. Unfortunately, this went poorly. My kids struggle to read, struggle to understand word problems, struggle to recognize that this is a GCF problem, struggle to find the GCF, and struggle with whether or not that’s the final answer. It’s already a difficult situation and I was trying to force a strategy they didn’t understand. I mean, if you’re reading this and not exceptional at math, can you describe to me exactly why GCF gives you the answer here? Because I have this feeling it isn’t just my kids who don’t fully get that.
So this year, I tried it differently. I didn’t tell my kids how to do it. I had them list factors beforehand, but they didn’t know what it was for and then we set them aside. Then I gave them a bag of pre-counted candy and a stack of cups to split them into. The kids split the lollipops in all possible ways and listed them. They repeated for the Tootsie Rolls. They repeated for the Smarties. Then they tried it with all three. They found the largest number of cups and wrote it down. After we did a couple activities like that, I asked them to check out the factor list we made at the beginning (the numbers were the same as the candy problems) and see if they saw a pattern.
*GASP!* The list we made is the same as the factors! The number of cups is the GCF! Ms. Mathinaz, I found a shortcut! We could have just found the GCF instead of doing all that work!
Yessssssssssssss conceptual understanding! It’s so much harder to teach than algorithms, but it’s something I’m committed to working on this year. I know that means I’ve got some bad lessons ahead of me (my principal wasn’t overjoyed by my LCM lesson, which did not run this well), but I think this one was a success and it makes me hopeful.
And the best part? I gave my kids a ton of delicious candy. I let them play with it for an hour. At the end of class, they returned it to me. Every single piece, and yes, I counted. Yay for trust and honesty. (And yay for extremely explicit expectations and a detailed plan for rewards and consequences if the candy plan went well or poorly.) Huge win. I love my kids.