Monthly Archives: January 2015

Baxter Academy Shadow Day

Yesterday was a “Shadow Day” at Baxter Academy. That means that most of our students were off on a job shadow of their choosing. I’m anxious to hear about the shadows that they were able to arrange during the snowiest week of the winter, so far. I would have checked in today, but we have another snow day – the third this week.

Anyway, while our students were off doing their shadows, we had about 120 prospective students, interested in attending Baxter Academy next year, join us for a “simulated day.” The students were placed into 16 different groups, each led by a couple of current Baxter students through a day of classes that included a math class or two, a science class or two, humanities, and an elective or two.

I co-taught our modeling class with one of our science teachers. This is the introductory math & science class at Baxter. It’s technically two sections, but they are integrated and teamed up so that the two teachers are working with the same groups of students. Sometimes we meet separately, as a math class and a science class, and sometimes we meet together. I’ve written about the class before, and the kinds of modeling we have made them do.

But what do you do with a bunch of 8th graders who are are with you for only an hour? Introduce them to problem solving through with this TED talk by Randall Munroe. And then take a page from Dan Meyer’s Three Act problems – a page from your own back yard: Neptune*. A brief launch of the problem and off they went. Not every group was able to answer both parts of the question: How big is the Earth model and where is it located? But most groups were able to come up with a solution to at least one part.

The point of the day was to provide a realistic experience of what it’s like to be a Baxter student. We grouped them together with others they didn’t know before walking into the building. We asked them to collaborate to solve a problem they’d never seen before. We asked them to do math without giving them directions for a specific procedure to follow. We asked them to share their results in front of strangers. We gave them an authentic Baxter experience.

*For more information about the Maine Solar System Model, visit their website. It’s really a rather amazing trip along this remote section of US Route 1. I’ve done it – I’ve driven through the solar system.

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The Frozen Code – A Classroom Example

I could have kicked myself when I saw Dan Meyer’s post about Gelato Fiasco‘s Frozen Code. I mean, they are literally just blocks away from my school. I didn’t use Dan’s map to launch the problem (Gelato Fisaco only has two actual stores), but just dove into the main idea that he posed. Here’s the prompt.

I have a bunch of students, mostly 9th graders, in a class called Functions for Modeling. So today I gave them the challenge of finding a function rule for the Frozen Code. We started by assuming that the gelato that they purchase would cost $5.00. One class came up with three different rules:

IMG_1074The blue group originally had just the middle rule: P(T) = 0.05T + 3.40. Students in both classes were eager to point out that the rule only applies if the temperature drops below 32 degrees Fahrenheit, and they wanted to somehow make that clear in the function rule. So we started to add to the definition. Then someone pointed out that there would be a bottom limit to the discount, too. After all, Gelato Fiasco might be willing to give you gelato for free if you are that willing to venture out into the extreme cold and they are still open, but they are unlikely to pay you to come in. So we added the third bit about temperatures below -68 degrees Fahrenheit.

What I love about the above work is that before we got into all the piecewise stuff, I was able to ask them, “How do we know if these three function rules are equivalent?” They told me that they “generated the same results,” that they could “use algebra to change from one to another,” and that they “would all produce the same linear graph.” How cool is that? We were also able to discuss how one form easily told us the price (of a $5 gelato) when the temperature was 0 degree F and another form showed us all the calculations clearly.

But they weren’t satisfied. After all, every gelato purchase isn’t going to cost $5 – price is also a variable. So that’s how we got into functions that have two independent variables. I asked them to modify their rules to reflect this new information. Here’s what they did:


Once again I asked if these were equivalent and how they knew. We wondered what the graph would look like. Would it be flat or curvy?

We’ll check that out tomorrow.

[Update: Here are the graphs comparing the set price of $5 to the variable price model.]

gelato models

By the way, my students think this is a pretty good marketing strategy – you are fairly likely to get some kind of discount for buying gelato in the dead of winter, but not that big a discount, on average. Last Thursday would have been a great day, though. The temperature was -10 after the sun set.

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