Kids, I’ll tell you why you need math…

So I was at Kroger and I was thirsty.

I went to the cooler to pick out a 20 oz. Coke. $1.69. Reasonable. About what you’ll pay most places, at least around these parts.

2014-09-28 16.47.29
But I had some more shopping to do. So, I kept walking. Gathering the items on my list.

Then I saw some 2-liter Cokes. (Remind me. Which is a bigger amount of Coke? 2 Liters? or 20 ounces?)

The 2-Liter Coke was priced at “2/$3.00”. (Which, I’m pretty sure is less than $1.69.)

(Oh! And you don’t have to buy 2 to get that price. Kroger is awesome like that.)
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I get pricing a little bit. I worked concessions at a college football stadium for a while (true story, by the way). I know the shtick. It’s upselling.

“For an extra quarter, you get almost double the pop!”

But this isn’t like that.

You have to buy 4 twenty-ouncers to fill a 2-liter. 4! You include the 10-cent bottle deposit here in the great state of Michigan, and that’s over $7.00!

2-Liter? $1.50

This isn’t even close.

Kids, THAT’S why you learn math.

NPR wants to advise your pizza order…

Quoctrung Bui from NPR says that there are at least 74476 reasons that you should always get the bigger pizza. (The article has an awesome interactive graph, too!)

If we could mix the article with a math exploration, we could provide an awesome opportunity for a math-literacy activity that can combine reasoning, reading, writing, and some number-crunching all in the same experience. That’s a nice combination. Also I suspect the content hits close to home for most students. (The leadership in our district is often looking for opportunities to increase authentic reading and writing in math classes. This seems to fit the bill quite well.)

Here’s an activity:

Although without fail, the menus from a variety of local pizza joints will probably be a bit more engaging. (Look for an update coming soon…)

Shauverino Pizziano

But the big question is why?

According to Bui: “The math of why bigger pizzas are such a good deal is simple: A pizza is a circle, and the area of a circle increases with the square of the radius.” 

Yup… that’s pretty much it.

The Hershey Bar Problem (#3Act Revised and Updated)

About a month ago, I posted The Hershey Bar Problem in which I discussed, among other things, the ways in which I rip off other teachers work. This is an example of that. This is a Dan Meyer rip-off pure and simple. I just want to cover myself in that regard.

As usual, all constructive feedback is welcome.

Here’s the rest:

Act II – Dimensions of the Hershey Bar or Dimensions of the segments after the cuts.

Act III

Sequel #1

Sequel #2

Double Stuf Oreos: Are they really double the Stuf?

Double Stuf: A factual statement or clever marketing trick?

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.

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?

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.

What math class looked like today.

Then we compiled the results.

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

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.

The Snickers Problem: The Aftermath

What math class looked like this week

What math class looked like early this week

There is nothing quite like watching the students get there hands dirty with the mathematics. This is especially true when the students are literally getting their hands dirty. In this case, it was with caramel, chocolate and nougat.

Here is some of the aftermath of the students exploring The Snickers Problem. (Check it out for a description.)

Snickers #2

To me, the value of this assignment lies in its ability to draw the students in. This problem featured 100% engagement. It featured the type of proportional reasoning that shows up in endless amounts in our unit on Similarity and Dilations. The students were analyzing the size comparison of a fun-sized Snickers and predicting the number of peanuts.

Others preferred the more antiquated utensils...

Others preferred the more antiquated utensils…

This was a fantastic activator. Formal proportional reasoning is difficult for many students, but informal proportional reasoning is intuitive. Many of the students found that their predictions were pretty close. (Although, we did find some Snickers that had remarkably low numbers of peanuts.)

Knife and fork worked for some

Knife and fork worked for some

And the fantastic questions that come up when students are thinking mathematically.

Is this prediction close enough?

What do we do about half-peanuts and peanut pieces?

Their prediction was right, but ours was wrong… but we predicted the same thing! Our snickers had different number of peanuts!

These are all evidence of students having to have an experience with the mathematics. That’s something I’d like to see more of.