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
compasslike 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.
 Convert the following dates
to their respective day of the year:
 February 2
 March 1
 March 15
 March 27
 March 28
 April 21.
 Given the data from above,
predict the altitude range the following dates:
 March 27.
 March 28.
 April 21.
 What strategies did you
use to find these answers?
 What was the altitude range
on:
 March 15?
 March 1?
 February 2?
 What strategy did you
use to find these answers?
 Using the data from numbers
2 and 3, which is the independent and dependent variable? Why?
 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.
 On what day is the
Altitude Range:
 17.1 degrees?
 23.5 degrees
 32.3 degrees
 95.1 degrees?
 What methods did you
use to find these answers?
 Did your answer to question
6d make sense? Why or why not?
 Using the information from
question 6, on what date do each of these altitude ranges occur?
a.
b.
c.
d.
 What are the logical limits
to this equation? Why?
Table of
Contents
For the Teacher's Guides, please email Alaska
Native Knowledge Network
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." 