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Elementary STEM Certification: 2 nd Annual Summer Institute

STEMifying Math; Mathifying STEM. Elementary STEM Certification: 2 nd Annual Summer Institute. Francine Winston Johnson Thursday, July 19, 2012. Outline of Session. Data Analysis and Probability Lesson Problem-Based Approach Development of STEMathematics Lesson.

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Elementary STEM Certification: 2 nd Annual Summer Institute

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  1. STEMifying Math; • Mathifying STEM Elementary STEM Certification:2nd Annual Summer Institute Francine Winston Johnson Thursday, July 19, 2012

  2. Outline of Session • Data Analysis and Probability Lesson • Problem-Based Approach • Development of STEMathematics Lesson

  3. Random Sampling and Estimation • Learning how to use results of a random sample to estimate characteristics of an entire population • Select a random sample • Describe sample-to-sample variation • Predict the accuracy of an estimate • Assess the effect of sample size on accuracy

  4. Common Core State Standards: Standards of Mathematical Practice • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

  5. Counting Penguins • Mobility of Penguins • Weather • Access • Size of Region • Expense • Time Required

  6. How many penguins are there on a particular ice floe in the Antarctic? What can I say about a whole population based on information from a random sample of that population? Simplified version of 100 aerial photos of smaller subregions

  7. Group Samples n= 1 Sample Size n=2 Sample Size n=3 Sample Size n = 10 Sample Size

  8. Sample Estimates

  9. Fair Sampling • How might you select 10 sub-regions from the 100 total sub-regions so that you would be most likely to have a “representative” sample for estimating the size of the penguin population in the entire region?

  10. Methods of Fair Sampling Pair of ten-sided dice in different colors Numbered positions  .6745331315  .5503091595  .8311198328 Ten-section spinner Calculator-generated random numbers

  11. What Would Be the Effect of Sample Size? Sample size of 20?

  12. Would your method work for the following distributions?

  13. Scientist complete the first ever emperor penguin count from space • There are twice as many emperor penguins in Antarctica as previously thought, as determined by an international research collaboration that included University of Minnesota Polar Geospatial Center scientist First Census Emperor Penguins

  14. Satellite Image of Colony at Cape Roget From space the colonies look like smudges on the ice

  15. Colony at Cape Colbeck Using a technique called pan- sharpening to increase the resolution, scientists were able to distinguish between birds, ice, shadow, and penguin poo.

  16. References • http://www.agic.umn.edu/ • http://www.learner.org/courses/learningmath/data/ • Perry, Mike and Kader, Gary (February, 1998). Counting Penguins. Mathematics Teacher, 91 (2), 110-116. • Woolley, Thomas (Autumn, 1998). A Note on Illustrating the Central Limit Theorem. Teaching Statistics, 20 (3), 89-90.

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