High School Mathematics Problems from Alaska

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Extensions of Data:
(Problem Six)

James H. Grey
jgrey@northstar.k12.ak.us

Standards: Geometry, Estimation and Computation, Functions and Relationships, Statistics/Probability, Problem-Solving, Communication, Reasoning.

Performance Standards: A5.4.1, A5.3.3, A5.4.3, A5.3.5, A5.4.5, A5.3.6, A5.4.6, A5.4.7, A3.4.1, A4.3.2, A4.3.4, A6.3.2, A6.3.4, A6.4.5, B1.4.1, B1.3.3, C1.3.3, D1.4.1, D1.4.2, D1.4.3

Concepts: Using given data to extrapolate new information, using a linear equation to predict later behavior, and using previous knowledge to synthesize new conjectures

Carnegie Chapter: No corollary, perhaps after doing work on linear equations.

Overview: Focusing on synthesis and extrapolations from a given set of data and previous knowledge.

Teacher Notes: This does not have a specific slot in the existing Carnegie hierarchy, but could be included with a culminating lesson in linear equations.

This activity might be easier if you have a globe available for your students to use. You may also want your students to access the following websites in order to get some data for comparison:

http://www-das.uwyo.edu/cgi-bin/sun?ID=PABR&DATE=cyear

http://aa.usno.navy.mil/

Be aware of multiple ways to calculate slope in this problem.

Extensions of Data from Barrow, Alaska Sunrise/Sunset Information (Problem Six)

Avaiyak has collected the following sunrise information for Barrow, Alaska:

 Date Day Azimuth (Rise/Set) Azimuth Range Altitude Range Jan 23 23 174.3/185.9 11.6 0.6 Jan 24 24 169.5/190.8 21.3 0.8 Jan 25 25 165.9/194.0 28.1 1.0 Jan 26 26 163.2/196.8 33.6 1.3 Jan 27 27 160.8/199.4 38.6 1.5 Jan 28 28 158.6/201.5 42.9 1.7 Jan 29 29 156.6/203.6 47.0 2.0 Jan 30 30 154.7/205.5 50.8 2.2 Jan 31 31 152.7/207.4 54.7 2.5 Feb 1 32 151.0/209.3 58.3 2.7

Answer the following questions using complete sentences.

1. How might this data appear in Hawaii? Why?

1. How about farther north, such as a polar research station? Why?

1. How could this data be used?

1. What are some practical applications?

2. What other data might you need to make this information more relevant?

1. How could you "sell" this information to a borough?

1. How might a borough use it?

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Handbook for Culturally Responsive Science Curriculum by Sidney Stephens
Excerpt: "The information and insights contained in this document will be of interest to anyone involved in bringing local knowledge to bear in school curriculum. Drawing upon the efforts of many people over a period of several years, Sidney Stephens has managed to distill and synthesize the critical ingredients for making the teaching of science relevant and meaningful in culturally adaptable ways."

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