This is part of the ANKN Logo This is part of the ANKN Banner
This is part of the ANKN Logo This is part of the ANKN Banner Home Page About ANKN Publications Academic Programs Curriculum Resources Calendar of Events Announcements Site Index This is part of the ANKN Banner
This is part of the ANKN Logo This is part of the ANKN Banner This is part of the ANKN Banner
This is part of the ANKN Logo This is part of the ANKN Banner This is part of the ANKN Banner
Native Pathways to Education
Alaska Native Cultural Resources
Indigenous Knowledge Systems
Indigenous Education Worldwide
 

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.

Azimuth and Arc Length
(Problem Two)

 

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

 

MS Word Download

Standards: Measurement, Estimation and Computation, Functions and Relationships, Geometry, Statistics/Probability. 

Performance Standards: A2.4.3, A3.4.1, A4.3.1, A5.4.1, A5.4.2, A5.4.7, A6.3.1, A6.4.1

Concepts: Angle Measure, Azimuth, and Arc Length.

Carnegie Chapter: No corresponding problem.

Overview: Focusing on making visual representations of geometric data.

Teacher Notes: Before doing this activity, I suggest having an anticipatory-set discussion with your students regarding where the sun rises and sets at different times of the year. Some leading questions and discovery-based dialogue will help with this set of problems.


Azimuth and Arc Length

Problem Two

The directions on a compass correspond to numbers from 0-360 as shown below, where North corresponds to 0 degrees, East is 90 degrees, South is 180 degrees, and West is 270 degrees. This is known as azimuth. If an object is at an azimuth of 45 degrees, it is in the Northeast direction relative to an observer.

 

directions on a compass

 

The sun rises for the first time of the year in Barrow, Alaska on January 23. It rises (comes above the horizon) at an azimuth of 174.3 degrees and sets (goes below the horizon) at an azimuth of 185.9 degrees.

Write your answers to the following questions in the form of complete sentences.

1a. In what part of the sky, or in what direction does the sun first rise?

 

 

b. Where does it set?

 

 

 

2a. What is the mean of the sunrise and sunset azimuth?

 

 

b. What direction is it?

 

 

c. Explain why these answers might be surprising to some people.

 

 

 


Activity:

  1. Find the wall of your classroom that most closely faces south. Put a sign on it labeling it 180 degrees. Label the other three walls accordingly.

  2. Holding a protractor in a fixed position away from all four walls, run string lines from it every ten degrees toward the wall and label the wall accordingly. (Teacher note: It’s suggested that students make signs for every ten degrees that are large enough to be seen from any part of the room. Each sign should also have a mark to denote the position of the angle.) Viewed from above, your classroom will look something like this:
Holding a protractor

South Wall

 

  1. Using a piece of colored yarn, tape the arc that the sun travels from its sunrise to sunset on January 23.

  2. Using additional pieces of yarn and the table below, attach a piece to the wall for every-other day’s arc being sure to attach each end at the appropriate azimuth. (Teacher note: Labeling every day makes the wall look too "busy" and this may lead to confusion.) Label the day’s arc.

 

Date
Day
Azimuth (Rise/Set)
Date
Day
Azimuth (Rise/Set)
Jan 23
23
174.3-185.9
Jan 28
28
158.6-201.5
Jan 24
24
169.5-190.8
Jan 29
29
156.6-203.6
Jan 25
25
165.9-194.0
Jan 30
30
154.7-205.5
Jan 26
26
163.2-196.8
Jan 31
31
152.7-207.4
Jan 27
27
160.8-199.4
Feb 1
32
151.0-209.3

 

 

  1. Describe the impression you have of the arc that the sun covers each day.

 

 

 

 

4a. Using the attached polar coordinate graph paper and colored pencils, draw the arc for every-other day in the table below. Begin with the shortest arc closest to the center of the circle.

 

Date
Day
Azimuth (Rise/Set)
Date
Day
Azimuth (Rise/Set)
March 16
75
93.2-267.5
March 22
81
85.7-274.9
March 17
76
91.9-268.7
March 23
82
84.5-276.3
March 18
77
90.7-270.1
March 24
83
83.2-277.4
March 19
78
89.4-271.2
March 25
84
82.0-278.6
March 20
79
88.2-272.4
March 26
85
80.8-279.9
March 21
80
87.0-273.7

 

 

 

  1. Explain the difference between the information on the graph and the information on the wall, from part three.

 

 

 

 

  1. Why do you think that it is different?

 

graph
Click on image for a larger view

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.

 


Alaska Native Knowledge Network
University of Alaska Fairbanks
PO Box 756730
Fairbanks  AK 99775-6730
Phone (907) 474.1902
Fax (907) 474.1957
Questions or comments?
Contact
ANKN
Last modified August 18, 2006