Categories
Class Openers Statistics

Class Opener – Day 42 – A Sampler of Sampling Methods

2014-11-05_0001After a day off for election day, it’s back to the world of random sampling, margin of error and plausible intervals.  These tend to be tricky ideas for students, as we move from the “absolute” world of algebra and into the slightly more wishy-washy world of sampling and plausability.  My board scribblings were intended to remind students that we draw samples to represent populations, and that random sampling is king!

But random sampling is messy business, and there are other sampling techniques I want students to consider, and think about their effectiveness.  Rather than lecture each type (caution – excessive vocabulary lectures may cause drowsiness), I gave students a list of words I expected them to research and find suitable resources.

  • Cluster Sampling
  • Stratified Sampling
  • Systematic Sampling
  • Convenience Sampling

After a few rounds of walking around the room to discourage random copying of definitions which they didn’t understand anyway, many groups began to ask the “right” questions, relating the ideas to hypothetical surveys we could do of high school students.  Towards the end of our time, each group was assigned one term to “explain” on a poster through a visual representation. And now, we have a great crowd-sourced wall of survey vocabulary to refer to during discussions!

posters

Categories
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!

Categories
Uncategorized

Class Opener – Day 40 – Candy Corn Samples

It’s Halloween – it’s also close to election day – let’s combine these events into one big super-terrific class opener!

candyI spent last night at Wegman’s assembling my candy corn population, which consists of lots of “regular” candy corn, and some apple-flavored candy.  Walking through the aisles as students got out their calculators and homework, of course they all wanted to know if the candy was destined for their bellies, or just another statistical tease.  But we can do both!  As the class worked through their entrance ticket, the bucket passed through the room, with instructions to pour 20 candies from the spout – without looking or choosing deliberately.  Our task: to estimate the proportion of candy corns which are apple.

After our warm-up, students then approached our class dotplot and contributed their result. A discussion of how this drawing on candies is similar / different that what happens in polling scnearios followed, and I have planted lots of seeds for margin of error, which we will study formally next week.

dotplot