Unit 1 Cross-Curricular Project

How’s the Weather?

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
Did you know that the record temperatures in Texas have a range of 143 °F? In 1899, the lowest temperature ever recorded in Texas was –23°F. In 1936, the highest temperature ever recorded was 120°F. The table below shows some temperature records in Texas.

     In this project, you will explore how latitude, longitude, and degree distance relate to differences in temperature for pairs of U.S. cities.

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 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 temperature for each pair of cities;
• a scatter plot comparing the difference in longitude and the difference in monthly temperature for each pair of cities;
• a scatter plot comparing the degree distance and difference in the monthly temperature for each pair of cities (You will learn about degree distance in Lesson 1–3.).

• Select five pairs of cities in the U.S. 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
• Make a table to record the latitude, longitude, degree distance, and temperature for each pair of cities. For more information on degree distance, see the Math Online exercise in Lesson 1–3. For distances between cities, try this Web site.
  http://www.indo.com/distance/
• Make scatter plots of your data. You must have at least three scatter plots as described below. (See the Math Online Exercise in Lesson 1–3 for more detail on these scatter plots.)
  1. difference in latitude versus difference in temperature for the five pairs of cities
  2. difference in longitude versus difference in temperature for the five pairs of cities
  3. degree distance versus difference in temperature for the five pairs of cities
• Conjectures about the relationship between latitude, longitude, degree distance, and temperature. For information on distance between cities, try this Web site.
  www.infoplease.com
• Be creative. Add some additional data, information, or even pictures to your portfolio or Web page.

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 for cities to the latitude and/or longitude.
5. Investigate the effect on the climate for cities located on an ocean or large lake.
6. Investigate the effect of altitude on climate.
7. Consider the dates for record temperatures in the U.S. Were there any years that were unusually hot or cold?

• Present your project to your class or at a family night.
• Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.
• Write a one–page summary of your project, including what you have learned from researching this topic.
• Interview a meteorologist. Find out what education is needed to pursue this career. Research the opportunities for employment in this field.

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 monthly normal temperatures for July to make her comparisons. The latitude and longitude have been rounded to the nearest degree.

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. (Each 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.
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.
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.

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.

1. The ordered pair (latitude, longitude) for Dalhart, TX, is (36, 103) and for Beaumont, TX, is (30, 94). 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. The air distance between Dalhart and Beaumont is about 656 miles. 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?

Teacher Notes and Answers

How’s the Weather?

TEACHER NOTES

In this project, students compare the difference in temperatures for pairs of cities with the difference in latitude (parallel rings on a globe), difference in longitude (intersecting rings on a globe), and a measure called degree distance. In general, they will find that the difference in latitude between two cities shows the most distinct relationship to the temperature difference since latitude compares how far north or south a location is from the equator.

The Guidance section of the Cross Curricular Project contains questions that would be good for a whole-class discussion and for providing interdisciplinary connections. If you prefer, have each student research one of the questions and add the information they find to the final presentation of their project.

Several Web sites are included in the project to help students in completing this project. Encourage students to find additional sites and to share those sites with other students.

Students will work on this project in Unit 1.

Lesson	1–3	2–1	3–5
Page	23	81	175

ANSWERS
Lesson 1–3

1.	City Latitude Longitude Degree Distance July High Temperature Anchorage , AK 61 N 150 W  38.4 58 Fresno , CA 37 N 120 W   82           Washington , DC 39 N 77 W  35.1 76 Salt Lake City , UT 41 N 112 W   78           Tampa , FL 28 N 82 W  19.2 82 Minneapolis , MN 45 N 93 W   74           Oklahoma City , OK 35 N 98 W  12.4 82 Bismarck , ND 47 N 101 W   71           Spokane , WA 48 N 117 W  26.9 69 San Antonio , TX 29 N 98 W   85
2.	City Degree Distance (x) Absolute Difference in Temperature (y) Anchorage, AK  38.4  24 Fresno, CA           Washington, DC  35.1 2 Salt Lake City, UT           Tampa, FL  19.2  8 Minneapolis, MN           Oklahoma City, OK  12.4  11 Bismarck, ND           Spokane, WA  26.9  16 San Antonio, TX
3.	City Absolute Difference in Latitude (x) Absolute Difference in Temperature (y) Anchorage, AK  14  24 Fresno, CA           Washington, DC  2 2 Salt Lake City, UT           Tampa, FL  17  8 Minneapolis, MN           Oklahoma City, OK  12  11 Bismarck, ND           Spokane, WA  19  16 San Antonio, TX
4.	City Absolute Difference in Longitude (x) Absolute Difference in Temperature (y) Anchorage, AK  30  24 Fresno, CA           Washington, DC  35 2 Salt Lake City, UT           Tampa, FL  11  8 Minneapolis, MN           Oklahoma City, OK  3  11 Bismarck, ND           Spokane, WA  19  16 San Antonio, TX

Lesson 2–1

1. Sample answer: Of the three scatter plots, difference in latitude versus difference in temperature appears to have the best positive correlation. The greater the difference in latitude, the greater the difference in temperature.
2. See students’ work.
3. See students’ work. In general, difference in latitude and difference in temperature should be positively correlated since latitude is the distance north or south of the equator, which affects climate.

Lesson 3–5

1. 10.8 degrees
2. 745.2 miles
3. The difference is about 89 miles. The degree distance is greater than the actual distance.
4. The degree distance is greater than the actual since the Earth is spherical and the distance between the degrees of longitude is 69 miles only at the equator and is less as the lines move towards the poles.