I was inspired by this post by Nathan Kraft (@nathankraft1) in which he engages his staff in a question about Oreo cookies. (Mr. Kraft was quick to inform me that Christopher Danielson (@Trianglemancsd) was the inspiration for his post. I do want to give credit where it’s due.)

I decided to see what my third hour students would do with it. So, last week Friday I showed them the picture and we started discussing the a variety of aspects of Oreos (some of which were more useful than others). Then, it happened. One students asked:

“Is the stuff of a Double Stuf *really* double of the stuff in a single stuff?”

The beauty of this activity is that the students were able to become involved in the formation of the solution process. They practically all had a prediction. First idea, would double the stuff be twice as tall?

The above image represents what multiple students observed. It was an awesome opportunity to discuss conclusions. What conclusion can we draw from the observation we just made?

Either it was double the stuff and it wasn’t manifesting itself in its height, or it wasn’t double the stuf. (Often, the student’s original predictions colored their conclusion to these observation.)

Next idea was mass. Gave in impromptu call to Mr. Corcoran, the chemistry teacher, who loaned us some scales. But what do we measure? The whole cookie? That opened up another important question? Is the same wafer used for both the standard and the double-stuff?

After some quick diameter and mass measurements, it seemed like there was no meaningful difference between the two. But, just to be safe, each student scraped the Stuf from a standard and a Double Stuf and set to the scale to get a mass measurement.

Then we compiled the results.

Each group took a moment to deliberate and concluded that, for the most part, it seems that the Double Stuf is appropriately named. Some groups seemed to think that, if anything, the Double Stuf contained more than double the Stuf.

This activity contained so much of what makes contextual, collaborative learning valuable. Authenticity, source of error, conclusions that were not clear, but needed to be discussed. Students needed to listen, speak and rephrase when others didn’t understand.

It also had the beautiful feature of me not knowing the answer and they knew it. So, there wasn’t the temptation to treat me like the math authority, as though all math learning begins and ends with the Teacher’s Edition.

And for an added bonus, the AP Stats class meets next door at the same time and so, we were able to strike a deal to rerun the trial with the guidance of the stats class for a broader, students-teaching-students experience.

I’ll report back with our findings.