I call this activity the “Candy Challenge”, so as not to give away the GCF way of finding the solution. I give the students this scenario:

*“I have 90 tootsie rolls and 120 smarties. I want to put together as many bags as I can with an equal amount of candies in each bag. Every bag should have the same number of Tootsie Rolls. Every bag should have the same number of Smarties.”*

Their task:

- Figure out how many Tootsie rolls and Smarties each bag would contain.
- Figure out how many total bags there would.

I reminded them that there should be no candy left over.

I placed students into teams of 4 and told them to come up with a solution and a reasoning behind that solution. At first I didn’t give them much to go off of. I wanted to see what they could come up with on their own. However, as I saw some confusion from some students, I decided to help out each class. I gave them this scenario: What if we only used 2 bags? How many tootsie rolls would be in each? (45) How many smarties would be in each? (60) I drew out the bags and labeled them with 45 Tootsie Rolls and 60 Smarties in each. I told them that this is a good answer…the bags are equal and no candy is left over, but 2 bags is not the most I can make. I want the MOST number of bags possible.

I left it to them to figure out the rest, and they did an awesome job at that! I was so impressed by the different methods and thinking that came from each of the groups. (Many without even the hint from me.) What was so great, was they were all talking about the “greatest common factor” without actually using that phrase.

I heard,

*“You want the highest number that can go into both.”*

*“We took all the factors and circled the biggest one that was in both of them.”*

*“We divided 120 and 90 by the same numbers, like 2, 3, 5, 6, etc. and realized 30 was the highest number that could be divided into both.”*

Perfect! Most got it.

I use this activity before introducing the Greatest Common Factor, so it will now hopefully make that much more sense. They seemed to enjoy it (possibly for the Smarties they each got!)

Tomorrow students will share their group work with the class and then we will continue with a lesson of Greatest Common Factor.

## About Gretchen Simmerson

Middle School math teacher living in Austin, Texas.