Category: Class Openers

How I start my class each day

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Class Openers

Class Opener – Day 41 – All Hail Martin Gardner

Sometimes class openers have nothing at all to do what is happening in class, and are meant to generate positive math vibes, or think about ideas beyond the confines of curriculum. Today my classes celebrated the 100th birthday of Martin Gardner, the long-time master of the math challenge. His birthday would have actually been last month, but better late than never to enjoy some math puzzlers, these from a 2011 edition of Scientific American, where his problems were often published.  Many similar problems appear online, and can be easily found through searches.

Gardner

The “crazy cut” problem proved difficult for students, though eventually a few students found the answer, which was shared under the document camera.  Click the Scientific American link above for the solution.

2014-11-03_0003The Martini Glass problem was solved quickly, and modeled on the board by a number of students using strips of paper and magnets.  I’m hoping that enough students were intrigued by the puzzles to look up more great Garnder puzzles on their own!

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Class Openers Statistics

Class Opener – Day 39 – It’s a Heat (Map) Wave!

Finishing up discussions with scatterplots – today’s visual when students entered presented a new idea in scatterplots (from the awesome Plot.ly site) – a scatterplot representing the score of every NFL game ever played!

superbowl

What’s the story here? So many great features of this plot to discuss including:

  • It’s apparent symmetry
  • The vertical and horizontal avoidance lines
  • The colors – many students have never seen a heat map before
  • The clustering in the center of the graph

This was a quick warm up as I wanted to get to the main event – scatterplot stations!  Students worked in teams to complete activities (in 15-minute intervals) designed to strengthen their understanding of many ideas surrounding scatterplots.

Station 1 – using graphing calculators to assess data sets, and writing clear summaries of the trends.

Station 2 – estimating best-fit lines given a scatterplot, and using their algebra skills to make good estimates.

Station 3 – netbooks! Play with the Rossman-Chance “Guess the Correlation Applet” and develop and understanding of “least squares” with this Geogebra applet.

Fun day today…..moving on to sampling tomorrow!

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Algebra Class Openers Statistics

Class Opener – Day 38 – Are Any of My Students Compatible?

Today’s opener was inspired by a movie correlations activity I have used in AP Statistics, and Cathy Yenca’s awesome activity which brings this idea down to the Algebra level.

For my freshman class, I wanted to students to “discover” the role of the correlation coefficient r – how it acts as a measure of the strength of the relationship between two quantitative variables.  To begin, 10 potential vacation / off-day activities were listed on the board:

  • Ski
  • Go to Beach
  • Amusement Park
  • Baseball Game
  • Broadway Show
  • Camping
  • Washington DC Tour
  • Shopping Day
  • Big Concert
  • Cruise

Students were each asked to rank these activities from 1 to 10 (10 being most desirable) and using each number only once. The class then moved into partnerships with my suggestion that they work with someone they maybe did not know so well in class, and compared results.  With an odd number of students, I worked with a student to share interests.  Results for each activity were plotted as ordered pairs, with each partner contributing their number score.  Students plotted their points on graph paper, while my student partner and I used Desmos – and quickly discovered that we have little in common.

Colin

galleryFrom there, students learned how to use graphing calculators to analyze the data – making the scatterplot and finding the best-fit line.  The partnerships also wrote this mysterious new statistic – r – on the bottom of the graph and shared their graph in the board.  Through a gallery walk, the class examined the graphs and tried to conjecture the meaning of r.

This worked better than planned, as the class quickly made some key observations:

  • Pairs with stronger relationships have “higher” r values.
  • There are no r-values greater than 1.
  • r can be negative if people answer opposite each other.

Definitely will add this activity to my arsenal every year!

If you are interested in the activity for AP Stats, you can check out the Google Form we use, then some instructions for processing the data in this video: