Math Lesson: European Debt Crisis

My latest contribution to the New York Times Learning Network is a Math Lesson designed around exploring loan repayment and risk assessment in the context of the European Debt Crisis.

In this lesson, students interact with some cool infographics, collect debt data, run the numbers on possible loan repayment schedules, and explore an elementary notion of “risk” in finance.

Math Lesson: Fantasy Football

My latest contribution to the New York Times Learning Network is a Math Lesson designed around a simple Fantasy Football-style game.

In this lesson, students use data, statistics, and a novel matchup metric to evaluate players and choose their teams.

As the results come in every week, students can refine their strategies and try to make more accurate projections!

The Perils of Teacher Blogging

hands typingI find my blog to be a very useful teaching tool.  It’s full of resources for students to explore, and after doing so they often follow up in class with interesting questions and comments.  The blog helps extend our mathematical conversations beyond the classroom.  Sometimes, it works too well.

In a recent discussion on probability, we considered the following question:

Suppose you randomly choose a positive integer.  What is the probability that the number you choose is divisible by five?

The students thought about the question and discussed their ideas.  I asked for their thoughts.  The usual good answers came out (0, \frac{1}{5}, \frac{1}{2}, 1) as well as at least one bad one (infinity!?).  I asked students to explain their reasoning, and an eloquent student sitting in the back volunteered to defend his answer.

“The answer is zero,” he said.  “Although there are infinitely many multiples of five and infinitely many total integers, the probability is zero because a small infinity divided by a big infinity is zero.”

“A small infinity divided by a big infinity is zero?” I responded, trying to appear as perplexed as possible.  “That sounds kind of crazy to me.  What does that even mean?”  I tried to stir up the anti-zero sentiment in the room.

The student persisted.  “According to you, a small infinity divided by a big infinity is zero.”

“That doesn’t sound like something I’d say,”  I said, which is what I say when students remember something I wish they hadn’t.  I usually get away with it.  Not this time.

“You didn’t say it,” replied the student.  “You wrote it on your blog.”

In a rare moment, I had no response.  What could I say?  I did write it on my blog.  I had nowhere to hide.

The class celebrated this clear and decisive victory.

Math Lesson: Charting Population Growth

My latest contribution to the New York Times Learning Network is a math lesson designed to get students thinking quantitatively about the increase in population growth around the world.  Here is an excerpt.

A typical feature of population growth is that the rate of increase itself increases over time. Visually, this means that the line segments get steeper from left to right. When the slopes of each line segment are computed for each 10-year interval, students can look for a pattern in how the slopes, i.e. the rates of population growth, change. For example, students might notice that, every ten years, the slope of the line segments increase by 0.5 million people per year: this means that the rate of change of population increases by 0.5 million people per year.

Once a pattern is identified, students can then extend their graph beyond 2010 by drawing a line segment from the 2010 data point whose slope fits this pattern. By extending this new line segment so that it covers 10 years on the horizontal axis, this will create a population projection for the year 2020. By repeating the process, students can create population projections for 2030, 2040 and beyond.

Using a recent revision on world population growth by the United Nations population bureau as a starting point, students choose a country to profile.  By using available population data, students create piece-wise linear graphs to model that countries population growth, and look for trends in order to make population projections.

You can find the full article here.

Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

This question is based on the rise in popularity of “internet sweepstakes cafes” in Florida.  How much revenue are these casinos generating every year?


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