High School Mathematics Problems from Alaska

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Problem Setup and Pattern Recognition:
Sunrise in Barrow, Alaska
(Problem Five)

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

Standards: Numeration, Geometry, Functions and Relationships, Statistics/Probability.

Performance Standards: A1.3.2, A1.3.4, A5.4.6, A4.3.1, A4.4.2, A4.3.3, A4.3.4, A4.3.5, A6.3.2, A6.3.4

Concepts: Making predictions using given data, writing a linear equation from given data, and using a linear equation to predict later behavior

Carnegie Chapter: Modeling Situations with Formulas, Tables of Values, and Graphs.

Overview: Focusing on writing and using the results of a linear equation.

Teacher Notes: It may help to do problem one first and carry over the information to this problem.

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

Question eight may take quite a bit of development. It may be easiest to refer back to Problem Two and re-ask students what "noon" means or what the mean is for the azimuth range for any day. Given a mean of 180 degrees and an azimuth range, students should be able to compute where the sun will rise and set.

I first introduced question eight by giving students an azimuth range of 100 degrees and drawing an arc on the board. After some discussion, my students recalled that midday is at an azimuth of 180 degrees. They then deduced that the sun rose at an azimuth of 130 degrees and set at 230 degrees.

Problem Setup and Pattern Recognition - Sunrise in Barrow, Alaska
(Problem Five)

Avaiyak collected the following sunrise information in Barrow, Alaska:

 Date Day Azimuth (Rise/Set) Azimuth Range Mar 16 75 93.2-267.5 174.3 17 76 91.9-268.7 176.8 18 77 90.7-270.1 179.4 19 78 89.4-271.2 181.8 20 79 88.2-272.4 184.2 21 80 87.0-273.7 186.7 22 81 85.7-274.9 189.2 23 82 84.5-276.3 191.8 24 83 83.2-277.4 194.2 25 84 82.0-278.6 196.6 26 85 80.8-279.9 199.1

Answer the following questions using complete sentences.

1. Predict the Azimuth Range for:
1. March 27.

1. March 28.

1. April 15.

1. What strategies did you use to find these answers?

1. Predict the Azimuth Range on:
1. March 15.

2. February 1.

3. What methods did you use to solve these problems?

1. Using the data in numbers 2 and 3, which is the independent and dependent variable? Why?

1. Select from the data, numbers that form two ordered pairs in order to derive the equation for the azimuth range with respect to the day. What is the equation?

1. On what day is the Azimuth Range:
1. 201.7 degrees?

2. 126.7 degrees?

3. 266.7 degrees?

4. 426.7 degrees?

5. How did you solve these problems?

1. Did your answer to question 5d make sense? Why or why not?

1. Using the information from question 4, on what date do each of these azimuth ranges occur?

a.

b.

c.

d.

e. How did you solve these problems?

1. What are the logical limits to this equation? Why?

1. Knowing the azimuth ranges for the following dates, predict WHERE the sun will rise and set on:
1. March 27.

2. March 28.

3. April 15.

4. How did you solve these problems?

1. Where did the sun rise and set on:
1. March 15?

2. February 1?

1. When is your birthday?

1. Using all of the information that you have, where does the sun rise and set on your birthday?

2. Does your answer make logical sense? Why or why not?

3. What is the sun’s Altitude Range on your birthday?

1. Sketch and label the sun’s path through the sky on your birthday.

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For the Teacher's Guides, please email Alaska Native Knowledge Network

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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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