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High School Mathematics Problems from Alaska

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Writing an Equation:
Altitude Range vs. Day in Barrow, Alaska
(Problem Four)

 

 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, A4.3.1, A4.4.2, A4.3.3, A4.3.4, A4.3.5, A5.4.6, 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.

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

When sighting an object’s altitude in the sky relative to an observer, a compass-like system is also used. While facing an object on the horizon, it has an altitude of 0 degrees and an object straight overhead has an altitude of 90 degrees. The altitude of a visible object has an altitude between 0 and 90 degrees.

Altitude Range also shows the TOTAL arc the sun traverses in the sky each day. On February 14 the sun rises (comes above the horizon) at an altitude of 0 degrees and reaches its zenith (its highest altitude) at an altitude of 6.7 degrees in Barrow, Alaska. This gives an Altitude Range (the difference between the sunrise and sunset altitude) of 6.7 degrees for that day.

Avaiyak knows that the sun first rises above the horizon in Barrow, Alaska on January 23. Using a Global Positioning System (GPS), he notices that it rises at an azimuth of 174.3 degrees and sets at 185.9 degrees.

He also notices that it rises through an altitude of 0.6 degrees before setting.

In March, he takes the following data on the following days:

Date

Day

Altitude Range

Date

Day

Altitude Range

March 16

75

17.9

March 22

81

20.3

March 17

76

18.3

March 23

82

20.7

March 18

77

18.7

March 24

83

21.1

March 19

78

19.1

March 25

84

21.5

March 20

79

19.5

March 26

85

21.9

March 21

80

19.9

 

Answer the following questions using complete sentences.

  1. Convert the following dates to their respective day of the year:
    1. February 2



    2. March 1



    3. March 15



    4. March 27



    5. March 28



    6. April 21.
 

 

 

  1. Given the data from above, predict the altitude range the following dates:
    1. March 27.


    2. March 28.


    3. April 21.


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

 

 

  1. What was the altitude range on:
    1. March 15?


    2. March 1?


    3. February 2?


    4. What strategy did you use to find these answers?

 

 

 

  1. Using the data from 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 altitude range with respect to the day.

 

 

 

  1. On what day is the Altitude Range:
    1. 17.1 degrees?


    2. 23.5 degrees


    3. 32.3 degrees


    4. 95.1 degrees?


    5. What methods did you use to find these answers?
 

 

 

  1. Did your answer to question 6d make sense? Why or why not?

 

 

 

 

  1. Using the information from question 6, on what date do each of these altitude ranges occur?
 

a.

 

b.

 

c.

 

d. 

 

 

 

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

 

 

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