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Class Openers

Class Opener – Day 34 – Dolphin Tales

It’s Wednesday, and that means it’s Student Choice for today’s opener.  This week’s ideas comes from Katie, who loves dolphines.  An article from Discovery claims that dolphins may be math geniuses, using the subtraction of echos from their built-in sonar to determine location and depth.  There are some links here to the geometric distributions we have been studying in class.

Before sharing the article, I let the video below play, which features a pod of dolphins caught on GoPro camera. There’s a “wow” moment here, as students realize how organized and detailed the pod is with their travels.

More great student sharing next week!

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Class Openers Statistics

Class Opener – Day 33 – Mind Control with 9th Graders

argentina-road-mapA map of Argentina….a class of impressionable 9th graders…and a devious teacher….what could go wrong? I’m currently reviewing past statistical ideas with my 9th graders, with an eye towards standard deviation, the normal curve and sampling.  To generate some data, I asked each of my classes 2 questions about the country of Argentina:

MORNING CLASS:

  1. Do you believe the population of Argentina is MORE or LESS than 10 million?
  2. Estimate the population of Argentina.

AFTERNOON CLASS:

  1. Do you believe the population of Argentina is MORE or LESS than 50 million?
  2. Estimate the population of Argentina.

Both classes gave me strange looks.  But with instructions to answer as best they could, the students played along and provided data.  Did you note the subtle differences between the two question sets?  The two classes provide striking different estimates, due to the anchoring from the first question.

argentina

The inspiration for this activity comes from the book A Mathematician Reads the Newspaper by John Allen Paulos, which contains many other quick nuggets to use in your classroom.  And now we have a rich conversation regarding the wording of poll questions to enjoy in the next few days!

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Class Openers

Class Opener – Day 32 – What the Heck is an LCD, Anway?

Today’s opener was chosen for totally selfish reasons, which I will explain below. We’re starting our statistics unit today, so we’ll be a doing a lot of review of means, meadians, quatiles, and graphical displays – all with an eye towards interpretation.  But only after I have students respond to a prompt for me:

What is a least common denominator (LCD)?  Provide directions for finding an LCD to someone who may not know how to find one.

This Friday, I will be out of school for the Association of Math Teachers of New Jersey conference, where I am looking forward to participating in an Ignite session, hosted by my friends from the Drexel Math Forum. In these talks, a speaker has 5 minutes and 20 slides to share their idea – mine is on the importance of language skills in math classrooms.

So, today’s opener was entirely selfish, as I was looking for examples to share during the Ignite. The LCD problem is one I have given before during rational expressions units. – try it with your classes and watch the misconceptions fly!  Responses to this prompt can often be pigeonholed:

THE “EXPLANATION BY EXAMPLE” CROWD

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THE “NOT QUITE COMPLETE” CROWD

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THE “MINIMALISTS”

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To be fair, I gave this prompt out of context, as fractions aren’t on our radar now. But it’s fascinating to see what built-in ideas students come to the high school with regarding a task they have now done for many years.