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Native Pathways to Education
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High School Mathematics Problems from Alaska

A database of lessons and units searchable by content and cultural standards, cultural region and grade level. More units will be available soon. You can use Acrobat Reader to look at the PDF version of the Cover Sheet for the Units and Self-Assessment for Cultural Standards in Practice.

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

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

MS Word Download

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.
Table of Contents

 

AL-CAN Highway Problem

Cigarette Smoking

Commercial Salmon Fishing

Cutting Cordwood

Dog Lot Math

Firefighting Crew

Firewood Problem

Investigation of Herring Statistics

Jesse Thomas Moose Hide Problem

Predicting Plant Coverage

Problem 1 - Converting the Date to the Day of the Year

Problem 2 - Azimuth and Arc Length

Problem 3 - Reading a Graph: Azimuth Range vs. Day in Barrow, Alaska

Problem 4 - Writing an Equation: Altitude Range vs. Day in Barrow, Alaska

Problem 5 - Problem Setup and Pattern Recognition: Sunrise in Barrow, Alaska

Problem 6 - Extensions of Data: Barrow, AK Sunrise/Sunset Information

Problem 7 - Writing an Equation: Fundraiser

Problem 8 - Writing an Equation: Fundraiser Choosing a Distributor

Stanley Jonas Travel Problem

Subsistence Fishing on the Kenai

Tourist and Traveler Information

 

 

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

Whouy Sze Kuinalth
"Teaching Our Many Grandchildren"
Tauhna Cauyalitahtug
(To Make a Drum)
Math Story Problems
St. Lawrence Island Rain Parka Winds and Weather Willow
Driftwood Snowshoes Moose
Plants of the Tundra Animal Classification for Yup'ik Region Rabbit Snaring
The Right Tool for the Job
Fishing Tools and Technology
Blackfish Family Tree
Medicinal Plants of the Kodiak Alutiiq Archipelago Beaver in Interior Alaska Digging and Preparing Spruce Roots
Moose in Interior Alaska Birds Around the Village  

 

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."

 

 

Go to University of AlaskaThe University of Alaska Fairbanks is an affirmative action/equal opportunity employer and educational institution and is a part of the University of Alaska system.

 


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Last modified August 18, 2006