High School Mathematics Problems from Alaska
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cultural region and grade level. More units will be available soon.
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Problem
Setup and Pattern Recognition:
Sunrise in Barrow, Alaska
(Problem Five)
James H. Grey
jgrey@northstar.k12.ak.us
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Standards:
Numeration,
Geometry, Functions and Relationships, Statistics/Probability.
Performance
Standards: A1.3.2,
A1.3.4, A5.4.6, A4.3.1, A4.4.2, A4.3.3, A4.3.4, A4.3.5, 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.
Be aware of
multiple ways to calculate slope in this problem.
Question eight may
take quite a bit of development. It may be easiest to refer back to
Problem Two and re-ask students what "noon" means or what the mean is
for the azimuth range for any day. Given a mean of 180 degrees and an
azimuth range, students should be able to compute where the sun will
rise and set.
I first introduced
question eight by giving students an azimuth range of 100 degrees and
drawing an arc on the board. After some discussion, my students
recalled that midday is at an azimuth of 180 degrees. They then
deduced that the sun rose at an azimuth of 130 degrees and set at 230
degrees.
Problem Setup
and Pattern Recognition - Sunrise in Barrow, Alaska
(Problem Five)
Avaiyak
collected the following sunrise information in Barrow, Alaska:
Date |
Day |
Azimuth
(Rise/Set) |
Azimuth
Range |
Mar
16 |
75 |
93.2-267.5 |
174.3 |
17 |
76 |
91.9-268.7 |
176.8 |
18 |
77 |
90.7-270.1 |
179.4 |
19 |
78 |
89.4-271.2 |
181.8 |
20 |
79 |
88.2-272.4 |
184.2 |
21 |
80 |
87.0-273.7 |
186.7 |
22 |
81 |
85.7-274.9 |
189.2 |
23 |
82 |
84.5-276.3 |
191.8 |
24 |
83 |
83.2-277.4 |
194.2 |
25 |
84 |
82.0-278.6 |
196.6 |
26 |
85 |
80.8-279.9 |
199.1 |
Answer the
following questions using complete sentences.
- Predict the Azimuth Range
for:
- March 27.
- March 28.
- April 15.
- What strategies did you
use to find these answers?
- Predict the Azimuth Range
on:
- March 15.
- February 1.
- What methods did you
use to solve these problems?
- Using the data in 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 azimuth
range with respect to the day. What is the equation?
- On what day is the
Azimuth Range:
- 201.7 degrees?
- 126.7 degrees?
- 266.7 degrees?
- 426.7 degrees?
- How did you solve these
problems?
- Did your answer to question
5d make sense? Why or why not?
- Using the information from
question 4, on what date do each of these azimuth ranges occur?
a.
b.
c.
d.
e. How did you solve these
problems?
- What are the logical limits
to this equation? Why?
- Knowing the azimuth ranges
for the following dates, predict WHERE the sun will rise and set on:
- March 27.
- March 28.
- April 15.
- How did you solve these
problems?
- Where did the sun rise and
set on:
- March 15?
- February 1?
- When is your birthday?
- Using all of the information
that you have, where does the sun rise and set on your birthday?
- Does your answer make
logical sense? Why or why not?
- What is the sun’s Altitude Range on your birthday?
- Sketch and label the sun’s
path through the sky on your birthday.
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." |