Student engagement is a funny thing.

On twitter I’ve been pretty critical about using extrinsic rewards to increase student engagement.

Me to extrinsic rewards for engagement. I just can’t get behind it, but open to being wrong https://t.co/jFviTCJZdN pic.twitter.com/nJeRISGREN

— Andrew Gael (@bkdidact) March 1, 2016

Today was our 100th day of school (as calculated by our students!) To celebrate we made 100 piece trail mix. Our trail mix included: cheerios, chex, raisins, and M&Ms. Candy! Talk about extrinsic student engagement! Before we dove in to the ~~rewards~~ food, I gave my class the following problem:

We have 4 ingredients to make trail mix. How many different combinations of ingredients can we have if our trail mix only has 100 total pieces?

The students persisted through their work on this *word problem*, until they arrived at various solutions based on their calculations and personal taste. For instance, one student is allergic to nuts and could only eat the cheerios and raisins, so that impacted his work on the problem. The students worked diligently and happily ate the trail mix once they had arrived at a reasonable solution.

However, after class I channeled Graham Fletcher and Dan Meyer to try to make this mathematical experience a more rich one for the students. So, here is a preview of the 3-act task we will be doing tomorrow in class…