High School Mathematics Problems from Alaska

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Azimuth Range vs. Day in Barrow, Alaska
(Problem Three)

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

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.

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.

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?

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

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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."

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