Carl's Teaching Blog

A place to talk about teaching and learning

Category: Math Resources

MSRI 2015 – A national math education conference focusing on developmental ed

This year there was a pretty spectacular conference in the hills of Berkeley California that brought a number of people who are involved in Developmental Math including Deborah Ball, Bill McCallum, Hyman Bass, but mixed among them were some lesser known names including Gregory Larnell, and a scene stealing group of high school math teachers from NYC.

The Mathematical Sciences Research Institute (MSRI) is a magical place in the hills above the University of Berkeley near the Lawrence Hall of Science.  It’s home to a group of academic researchers who work on their research from the inside of a beautiful complex, largely funded by MFA creator Jim Simons, which plays hosts to a number of national conferences with various focus on a yearly basis.  The annual Critical Issues in Math Education meeting was held in March and had the focus of “developmental mathematics at two- and four-year colleges and universities and the broader dynamic of mathematics remediation that occurs at all levels.”

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Grocery Store Takedown

In my last class I focused a lot on proportional reasoning, and at the end of March I wanted to give the kids a project that would be rich with a lot of different examples of the topic.  My original idea was to do a theme based on turning a beat into a song, but it seemed contrived.  Frustrated, I headed down the street to the only empty grocery store, and thought about how all the prices there were really high.  Suddenly a flash of insight hit.

The students can take down their expensive local grocery store!

Kids can imagine a product that they like to sell, and then look up how much cheaper it would be at a warehouse store, and compare the difference in prices.  Then students can use evidence from their local store to estimate how much money they would make from a day of selling the products, and then scale what the products would make over a month.  I went back home and scribbled a bunch of notes about the idea with a Doc-Brown-Esque level of enthusiasm, but I didn’t really put together a polished task until last week.

Download (PDF, 939KB)

Here is what I gave kids, although I really wish I could have made it better.

What I like about it:

  • It is a pretty straightforward task whose end goal makes enough students that all students can really understand what their end product should mean.
  • Students need to use proportional reasoning in so many different places that there are countless numbers of places to discuss it.
  • Since all students can do different products at different stores, the entire class can come up with different project results so there is no copying fear.

What I wonder about:

  • As a project to help kids express their proportional reasoning, should I have asked them to explicitly demonstrate two or three different ways of finding a number that would proportional to some other set of numbers?  If so, which ways should they all HAVE to know how to do?
  • How could this be better?

IF you can give me any feedback about the project, I’d appreciate it if you mentioned it by commenting on the google doc of this here.

3/30

The Road Trip Project: Made to Support A Linear Equations Unit

If you received this application it means you may be selected to appear on “Illest Road Trip of All-Time.” IRT is a new show where groups of people get $10,000 for a road trip that will be a “unique, life-changing, and eminently watchable experience”.  The money you spend will mainly go towards two things your vehicle (rental and gas), and your daily expenses (Hotel and Food).  Plan carefully, groups who do not plan to spend at least $9500 of the money will not be considered.

These are the first four lines of a Road Trip project that I have been using with kids for the past few years.  This project is a good companion to a linear equations unit that could provide a rich context to help students think about using these equations to solve a real world problem, instead of just a “problem”.  I have taught it for a bunch of years and it has been kind of popular among choices for students portfolios so I thought it might be good to have it online somewhere in case someone wants to try it out.  That said it is still a work in progress and I would appreciate it if any readers could give any kind of feedback that would be good.  Here is a link to the full project, but I’ll walk through it below.  Let me know what you think!

Download (DOC, 658KB)

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The Piggy Bank or The Safe

“The Piggy Bank or The Safe” is a lesson I made as a way to introduce the contrasts between exponential growth or compound interest with linear growth or simple interest. This context asks students to compare a magic safe, which magically adds $100 to its contents reach day, against a piggybank which magically doubles the value of its contents each day. As the safe starts with $100 on Day 0, and the piggy bank starts with $.01, the question to ask students is: “Which would you rather have for the next 20 days?” Of course many other interesting questions could be posed, and students should also be pushed to make predictions along the way.

This Google slide presentation shows the amount of money, day-by-day, in US currency, in order to help people visualize the change over time.

After three days the presentation pauses to see if anyone would change their prediction. It might be a good time to ask kids to make a table with the first the days, and see if they can find some evidence for their prediction, it even an equation.

After 20 days it shied that the piggy bank has more value in it by a huge margin. It might be a good time to ask how big the piggy bank would be in 30 days, or how long it would take until it has over one million dollars.

After the 20 days I began making an extension, with a “Super safe” and a “Mini-piggy” which grow at different rates. The “Super safe” grows by $2000 each day, while the “Mini-piggy” grows by a multiplier of 1.5 each day, and they each begin with $1000 and $10 respectively. I didn’t make slides for the extension, but if you carry it out for 20 days you’ll find that the “Super-safe” ends up ahead by a slim margin, so that begs the question: “If you let any exponential function grow towards infinity, will it eventually pass a linear function?”

The Piggy Bank or The Safe

Edit:  A good follow up question that was suggested by @jlanier:  What would grow faster, a piggybank placed in a safe, or a safe placed inside of a piggybank?

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