Advanced Geometry
Mrs. Hart
Unit 1 Project
page 1 of 12
Advanced Geometry
Unit 1 Project
Geometry Advanced – Unit 1 project
Approx duration of the contract: 4 weeks
General Learning Goals – As a result of the contract, students should
KNOW:
How to use the distance formula in another setting (Degree distance)
How to do research on the web for desired data collection.
Use data to do a scatter plot, find line of best fit, and make inferences related to the data
UNDERSTAND:
How to interpret data
Use of distance formula
Use of coordinate graphs
Use of conjectures
BE ABLE TO:
Use websites to collect data on US cities.
Make scatter plots using coordinate graphing techniques.
Compare data using plots, differences, and data collections.
Make conjectures using the data comparisons.
Mrs. Hart
page 2 of 12
Advanced Geometry
Unit 1 Project
Working Guidelines for Learning Contracts
1. You will have approximately 4 weeks to complete the given project. You may work on
designated contract days as seen in the weekly assignment sheet, or in class at appropriate
times as directed by the teacher. You should plan to work outside the classroom as well.
2. Stay on task at all times with the activities you have chosen. There is a multitude of
resources to help you, use them wisely. Do not plagiarize.
3. Work on the chosen activities only after the required lesson for the day has been completed.
4. Work quietly so that you do not disturb others.
5. When you need help and the teacher is busy, quietly ask someone else who is working on
the same activity.
6. If a classmate cannot answer your question, write down your question to ask later and begin
working on another part of the activity.
7. You may sit anywhere in the room you’d like on assigned project days, as long as you are
working hard and making good progress. If you have difficulty working well in the place you
select, I will help you find a place and a plan that work better for you.
8. If the teacher is conferencing with another student, do not interrupt unless you have an
emergency.
9. Final project is due on December 18, 2007. Read through the package for information to
help you in meeting this deadline!
I agree to the above conditions. I understand that if I do not follow them, I may lose the opportunity
to continue with this independent contract and receive the appropriate grade.
Student’s signature _________________________
Date __________
Period __________
Student copy
Mrs. Hart
page 3 of 12
Advanced Geometry
Unit 1 Project
When is Weather Normal?
Introduction
USA TODAY, October 8, 2000
Climate normals are a useful way to describe the average weather of a location. Several
statistical measures are computed as part of the normals, including measures of central tendency,
such as the mean or median, of dispersion or how spread out the values are, such as the standard
deviation or inter-quartile range, and of frequency or probability of occurrence.
Over the decades the term “normal”, to the lay person, has come to be most closely associated
with the mean or average. In this context, a “climatic normal” is simply the arithmetic average of
the values over a 30-year period. This period is generally, three consecutive decades. Someone who
is unfamiliar with climate and climate normals may perceive the normal to be the weather that one
should expect to happen.
It’s important to note that the normal may, or may not, be what one would “expect” to happen.
This is especially true with precipitation in dry climates, such as the U.S. Desert Southwest, and with
temperatures at continental locations, which frequently experience large swings from cold air
masses to warm air masses.
Two discussions, with links below, will examine two examples that illustrate this misconception.
The National Weather Service station at the Yuma, Ariz. airport serves as a typical example of the
case of precipitation in dry climates. The Crosby, N.D., station serves as a typical example of the
temperature swings at continental locations. The discussions, by Richard Heim of the National
Climatic Data Center, go into statistical detail about normals.
The point about normals is illustrated by snowfall in the Northeast so far during the 1990s. Since
the winter of 1990-91, snow has been either well above or well below the seasonable average, or
“normal.”
Mrs. Hart
page 4 of 12
Advanced Geometry
Unit 1 Project
The Task
You are working as an assistant to a meteorologist for a local television station. The meteorologist
wants to provide viewers with some interesting information about weather. She has asked you to
research the relationship between latitude, longitude, and average monthly temperature. You need
to prepare a portfolio of the data that you collect including any relationships shown by the data. If
you prefer, you can prepare a Web page with this information that the TV viewers could access. Be
sure that your portfolio or Web page contains the following information:





the latitude and longitude for five pairs of U.S. cities, rounded to the nearest degree (pairs
of cities must be located in different states);
the average high or low temperature for each city for a month of your choice (the month
must be the same for all cities);
a scatter plot comparing the difference in latitude and the difference in monthly
temperatures for each pair of cities;
a scatter plot comparing the difference in longitude and the difference in monthly
temperatures for each pair of cities;
a scatter plot comparing the degree distance and difference in the monthly temperatures for
each pair of cities (you will learn about degree distance in Lesson 1–3).
Mrs. Hart
page 5 of 12
Advanced Geometry
Unit 1 Project
The Process
To successfully complete this project, you will need to complete the following items:



Do all of the first 8 (eight) items.
Choose one of the 6 (six) additional questions.
Complete the project in one of the 4 (four) ways listed in the completion section or by a
method approved by your teacher.
Task 1:
You must complete all of the following 8 (eight) items.
_____1. Complete lessons 1-3 in this packet.
_____2. Select five pairs of cities in the U.S. that are not included in lesson 1-3. For each pair of
cities, the distance between the cities should be greater than 100 miles. Search the Internet
for the latitude, longitude, and average monthly temperature data for each city. For help, try
these Web sites.
www.usatoday.com/weather/wnormals.htm
www.infoplease.com
www.cpc.ncep.noaa.gov/products/predictions/new_climates/
www.statistics.com
_____3. Make a table similar to lesson 1-3, to record the latitude, longitude, degree distance, and
temperature for each pair of cities. For more information on degree distance, see the
exercise in Lesson 1–3 or try this Web site. http://www.indo.com/distance/
_____4. Make scatter plots of your data. You must have at least three scatter plots as described
below. (See the Exercise in Lesson 1–3 for more detail on these scatter plots.)
a. difference in latitude versus difference in temperature for the five pairs of cities
b. difference in longitude versus difference in temperature for the five pairs of cities
c. degree distance versus difference in temperature for the five pairs of cities
_____5. Complete lesson 2-3 in this packet.
_____6. Make conjectures about the relationship between latitude, longitude, degree distance, and
temperature for your chosen cities. For information on distance between cities, try this Web
site.
www.infoplease.com
_____7. Complete lesson 3-5 in this packet.
_____8. Be creative. Add some additional data, information, or even pictures to your portfolio or Web
page.
Mrs. Hart
page 6 of 12
Advanced Geometry
Unit 1 Project
Task 2
Choose one of the following questions to include in your project.
1. Compare the difference in latitude, longitude, or degree distance for pairs of cities to the
difference in the low or high record temperatures.
2. Make scatter plots for locations in the Southern Hemisphere.
3. Compare cities and locations in the Northern Hemisphere with locations in the Southern
Hemisphere.
4. Compare the difference between the lowest and highest temperatures for the year of cities
to the latitude and/or longitude.
5. Investigate the effect on the climate of a city located on an ocean or large lake.
6. Investigate the effect of altitude on climate.
Task 3
Conclusion: Choose one of these ideas for concluding your project.
1. Present your project to your class or at a family night.
2. Present the information on a Web page. Have other students critique your project and help
you to make improvements to your project.
3. Write a one–page summary of your project, including what you have learned from
researching this topic.
4. Interview a meteorologist. Find out what education is needed to pursue this career.
Research the opportunities for employment in this field.
Mrs. Hart
page 7 of 12
Advanced Geometry
Unit 1 Project
Questions
Lesson 1–3
Bonnie has decided to use the five pairs of cities shown in the table below for her research. She
chose to use the average high temperature for July to make her comparisons. The latitude and
longitude have been rounded to the nearest degree.
Latitude
Longitude
Anchorage, AK
Fresno, CA
61 N
37 N
150 W
120 W
July High
Temperature
58
82
Washington, DC
Salt Lake City, UT
39 N
41 N
77 W
112 W
76
78
Tampa, FL
Minneapolis, MN
28 N
45 N
82 W
93 W
82
74
Oklahoma City, OK
Bismarck, ND
35 N
47 N
98 W
101 W
82
71
Spokane, WA
San Antonio, TX
48 N
29 N
117 W
98 W
69
85
City
Degree
Distance
(Source: World Almanac)
1. Fill in the Degree Distance column using the following directions. For each pair of cities,
write an ordered pair (x, y) for each city such that x is the latitude and y is the longitude.
Use the Distance Formula to find the degree distance for each pair of cities using the
ordered pairs. (A pair of cities has only one degree distance.) The resulting value will be the
distance between cities relative to the degrees of latitude and longitude.
2. Make a scatter plot comparing degree distance and temperature. For each pair of cities write
the ordered pair (degree distance, |difference in temperature|). Plot the five ordered pairs
and look for a relationship. Describe the relationship found.
3. Make a second scatter plot comparing latitude and temperature. For each pair of cities write
the ordered pair (|difference in latitude|, |difference in temperature|). Plot the five ordered
pairs and look for a relationship. Describe the relationship found.
4. Make a third scatter plot comparing longitude and temperature. For each pair of cities write
the ordered pair (|difference in longitude|, |difference in temperature|). Plot the five ordered
pairs and look for a relationship. Describe the relationship found.
Lesson 2–1
Refer to the three scatter plots you made in Lesson 1-3.
1. Make a conjecture about the relationship shown by each scatter plot.
2. Find the five pairs of cities you will use for your project. Make a table and three scatter plots
for your chosen cities. Compare your scatter plots to those you made in Lesson 1–3.
3. Do the conjectures you made in Exercise 1 hold for the scatter plots you made in Exercise 2?
Explain.
Mrs. Hart
page 8 of 12
Advanced Geometry
Unit 1 Project
Lesson 3–5
A degree of latitude or longitude measures about 69 miles at the equator. The land distance
between degrees of longitude gradually reduces until it is 0 at the poles. The distance between
degrees of latitude varies slightly as you move away from the equator but is still about 69 miles at
the poles. (Source: World Almanac)
1. The ordered pair (latitude, longitude) for Washington, D.C., is (39, 77) and for Los Angeles,
California, is (34,118). Find the degree distance for the two cities to the nearest tenth of a
degree.
2. Find the distance to the nearest tenth of a mile between the two cities using the degree
distance. Since these cities are not located at the pole, assume that a degree of latitude or
longitude measures 69 miles.
3. Find the actual air distance between the two cities. Compare it to the distance you found in
Exercise 1.
4. Compare the distance between other pairs of cities using the degree distance measure and
the actual distance. What seems to be the relationship?
Mrs. Hart
page 9 of 12
Advanced Geometry
Rubric for grading Unit 1 project
Unit 1 Project
Points possible: 400
40 Complete lesson 1-3 in this packet. (due 11/22)
_____1.
20 Select five pairs of cities in the U.S. that are not included in lesson 1-3. (due 11/22) For
_____2.
each pair of cities, the distance between the cities should be greater than 100 miles. Search
the Internet for the latitude, longitude, and average monthly temperature data for each city.
For help, try these Web sites.
www.usatoday.com/weather/wnormals.htm
www.infoplease.com
www.cpc.ncep.noaa.gov/products/predictions/new_climates/
www.statistics.com
_____3.
Make a table similar to lesson 1-3, to record the latitude, longitude, degree distance, and
10
temperature for each pair of cities. For more information on degree distance, see the
exercise in Lesson 1–3 or try this Web site. http://www.indo.com/distance/
30
_____4.
Make scatter plots of your data. You must have at least three scatter plots as described
below. (See the Exercise in Lesson 1–3 for more detail on these scatter plots.)
a.
b.
c.
difference in latitude versus difference in temperature for the five pairs of cities
difference in longitude versus difference in temperature for the five pairs of cities
degree distance versus difference in temperature for the five pairs of cities
30 Complete lesson 2-1 in this packet.
_____5.
40 Make conjectures about the relationship between latitude, longitude, degree distance, and
_____6.
temperature for your chosen cities. For information on distance between cities, try this Web
site.
30
www.infoplease.com
_____7. Complete lesson 3-5 in this packet.
40
_____8. Be creative. Add some additional data, information, or even pictures to your portfolio or Web
page.
60
Choose one of the 6 (six) additional questions.
100
Complete the project in one of the 4 (four) ways listed in the completion section or by a
method approved by your teacher. Due by Dec 18, 2007. Presentation dates must be approved
by Dec. 12, 2007.
Mrs. Hart
page 10 of 12
Advanced Geometry
Unit 1 Project
Working Guidelines for Learning Contracts
1. You will have approximately 4 weeks to complete the given project. You may work on
designated contract days as seen in the weekly assignment sheet, or in class at appropriate
times as directed by the teacher. You should plan to work outside the classroom as well.
2. Stay on task at all times with the activities you have chosen. There is a multitude of
resources to help you, use them wisely. Do not plagiarize.
3. Work on the chosen activities only after the required lesson for the day has been completed.
4. Work quietly so that you do not disturb others.
5. When you need help and the teacher is busy, quietly ask someone else who is working on
the same activity.
6. If a classmate cannot answer your question, write down your question to ask later and begin
working on another part of the activity.
7. You may sit anywhere in the room you’d like on assigned project days, as long as you are
working hard and making good progress. If you have difficulty working well in the place you
select, I will help you find a place and a plan that work better for you.
8. If the teacher is conferencing with another student, do not interrupt unless you have an
emergency.
9. Final project is due on December 18, 2007. Read through the package for information to
help you in meeting this deadline!
I agree to the above conditions. I understand that if I do not follow them, I may lose the opportunity
to continue with this independent contract and receive the appropriate grade.
Student’s signature _________________________
Date __________
Period __________
Teacher copy
Mrs. Hart
page 11 of 12
Advanced Geometry
Grade sheet
Unit 1 Project
NAME __________________________ Period ____
_____1. Complete lesson 1-3 in this packet. (due 11/22)
_____2. Select five pairs of cities in the U.S. that are not included in lesson 1-3. (due 11/22) For
each pair of cities, the distance between the cities should be greater than 100 miles. Search
the Internet for the latitude, longitude, and average monthly temperature data for each city.
For help, try these Web sites.
www.usatoday.com/weather/wnormals.htm
www.infoplease.com
www.cpc.ncep.noaa.gov/products/predictions/new_climates/
www.statistics.com
_____3. Make a table similar to lesson 1-3, to record the latitude, longitude, degree distance, and
temperature for each pair of cities. For more information on degree distance, see the
exercise in Lesson 1–3 or try this Web site. http://www.indo.com/distance/
_____4. Make scatter plots of your data. You must have at least three scatter plots as described
below. (See the Exercise in Lesson 1–3 for more detail on these scatter plots.)
a.
b.
c.
difference in latitude versus difference in temperature for the five pairs of cities
difference in longitude versus difference in temperature for the five pairs of cities
degree distance versus difference in temperature for the five pairs of cities
_____5. Complete lesson 2-1 in this packet.
_____6. Make conjectures about the relationship between latitude, longitude, degree distance, and
temperature for your chosen cities. For information on distance between cities, try this Web
site.
www.infoplease.com
_____7. Complete lesson 3-5 in this packet.
_____8. Be creative. Add some additional data, information, or even pictures to your portfolio or Web
page.
____ Additional question chosen # _________
____ Completion of project method chosen______________
Completed project due by Dec 18, 2007. Presentation dates must be approved by Dec.12, 2007.
Mrs. Hart
page 12 of 12