# Double Stuf Oreos: Are they really double the Stuf?

Double Stuf: A factual statement or clever marketing trick?

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?

It didn’t appear to be double by height.

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.)

Double by what measure? Mass?

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.

What math class looked like today.

Then we compiled the results.

The mass of the Stuf scraped off a sample of standard and Double Stuf Oreos.

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.

# Balancing Ruler Problem – A Surprising Solution, Part II

This is the last part of a multi-part series on balancing rulers. If you’d like, you can check out the original problem or the first part of the solution.

So, I mentioned last time that I was rather surprised at the result of the Balancing Ruler Problem. I expected the balancing point to be further away from the center. In case you are having a hard time reading the ruler, the balancing point of the one penny-two pennies ruler was at 5 7/16″ inches. This means that the prism was moved 9/16 of an inch toward the two pennies end from the center.

One Penny – Two Pennies

So, I decided that I would see how the position of the prism changes if the proportion of the masses stays constant, but the amount of mass changes. So, I recreated the balancing act with dimes instead of pennies.

One dime – two dimes

The balancing point appeared to be at 5 9/16″. The prism was located a full eighth-inch back toward the center. In my mind, this demonstrated that the mass at the end is a variable as much as the proportion of the two masses. Also, it seemed to suggest that the prism will move away from the center if the masses are greater. So, I decided to test this hypothesis by combining the coins so that there was one penny and one dime on one end and two of each at the other.

One Dime, One Penny – Two Dimes, Two Pennies

The balancing point is located a 5 3/8″ meaning that combining the masses moved the balancing point another eighth-inch away from the center. This supported my hypothesis.

Well, what about quarters? Balancing point: 5 3/16″

one quarter – two quarter

And quarters and pennies together? Balancing point: 4 15/16″.

One quarter, one penny – two quarters, two pennies

So, it seems like there is more support for my hypothesis.

Then, a student and I decided to grow the project a bit.

One calculator – two calculators

With the number of variables that have changed, this photo doesn’t really mean a whole lot, but we had fun trying to balance calculators on a yardsticks.

The balancing point of the calculators

So, how can we explain this phenomena? What causes the balance point to move predictably even though the ratio of the masses at the end is a constant?

Ideas?