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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.

Reading a Graph:
Azimuth Range vs. Day in Barrow, Alaska
(Problem Three)

 

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

MS Word Download

 

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

Performance Standards: A4.3.1, A4.4.2, A4.3.4, A5.3.5, A5.4.3, A5.4.6, A6.3.4

Concepts: Interpreting graphical information, slope, x and y intercepts, writing a linear equation from graphical information, predictions based upon trends.

Carnegie Chapter: Finding an Equation from Its Graph.

Overview: Focusing on reading and interpreting information from a graph.

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

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

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

 

 

Azimuth Range shows the TOTAL arc the sun traverses in the sky each day. On February 14, the sun rises (comes above the horizon) at an azimuth of 131.4 degrees and sets (goes below the horizon) at an azimuth of 229.3 degrees in Barrow, Alaska. This gives an Azimuth Range (the difference between the sunrise and sunset azimuth) of 97.9 degrees for that day.

The graph below shows the Azimuth Range, in degrees, the sun traverses in the sky each day in Barrow, Alaska.

Azimuth Range vs. Day

Use the information above to answer the following questions in complete sentences.

 

  1. According to the graph, what is the sun doing in the first, horizontal part (A)?

 

 

  1. What does the second, inclined part (B), of the graph signify?




  2. What is happening in the third, horizontal part (C), of the graph?

 

 

 

  1. Describe each lettered part of the graph in terms of its slope. (Remember, slope equals rate of change.)

    A.

    B.

    C. 

     

 

  1. Extend the curve of part B so that it intersects both the x and y-axis.
    1. What is the x-intercept of B and what is its meaning?



    2. What is the y-intercept of B and what is its meaning?

     

 

 

  1. a) What is the equation of line A?

 

b) What is the equation of line C?

 

 

 

  1. Name two ordered pairs on curve B.
    1. Using the ordered pairs, write the equation of the line that fits B.

 

 

 

  1. Predict what the graph will do next, after part C. 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