Foundations of Algebra and Geometry
Chapter 1 Answers
Working with Data
Maps and map views provide lots of information -- from longitude and latitude to mileage.
Part A, Numbers and Location
1. Longitude (the number of degrees going east or west) and latitude (the number of degrees going north or south) have been used by sailors for centuries to locate various places on the earth. Learn more about longitude and latitude at the University of Tennessee's Science bytes site.
a. Draw a view of the earth with lines of longitude shown.
b. Draw a view of the earth with lines of latitude shown.
2. Visualize your drawings in 1 from the top of the earth.
a. Which lines form concentric circles -- longitude or latitude? [latitude]
b. Which lines form the bearings -- longitude or latitude? [longitude]
3. You can use a number line instead of a circular grid to represent the locations of points. Draw a number line from -180° to +180°. Put tick marks every 20°. The number line will represent the longitude of various cities. For example, a longitude of 30° west would be plotted at -30°. So going west of 0° is a negative number of degrees and going east of 0° is a positive number of degrees. Look at the List of cities around the world, find the longitude of the cities below, and plot them on your number line.
a. San Francisco, USA [-122°]
b. Cairo, Egypt [32°]
c. Hong Kong, China [114°]
d. Sydney, Australia [151°]
e. Abidjan, Ivory Coast [-4.5°]
f. Guatemala City, Guatemala [-91°]
Part B, Coordinate Grids
4. Make a coordinate grid so that (0, 0) represents 0° longitude and 0° latitude. Look at the List of cities around the world, find the longitude and latitude of the cities below, and plot their locations on the coordinate grid. Your x-axis should go from -180 to +180. Your y-axis should go from -90 to +90.
a. Havana, Cuba [-82°, 24°]
b. Panama City, Panama [-79°, 9°]
c. London, UK [0°, 51.5°]
d. Johannesburg, South Africa [28°, -26°]
e. Ankara, Turkey [33°, 40°]
f. Bangkok, Thailand [100.5°, 13°]
g. Honolulu, USA [-158°, 21°]
h. Rio de Janeiro, Brazil [-43°, -23°]
Graphs provide information in a visually organized manner which helps people to see trends in the data. Look at different kinds of graphs and the kinds of information each is best at displaying.
Part B, Making Bar Graphs
Assume you need to plan meals for a day for an athlete who is supposed to eat 2500 calories a day.
1. At CyberDiet's daily food planner you can plan up to 13 days of meals complete with shopping lists and nutritional information. Plan your meals for a day.
a. Enter 2,500 calories and click "Go." Make sure nutritional information at the bottom of the page has an "x" in the box. After you have decided what you want to eat for each meal, click on "I'm Finished!" The computer will generate a report for you.
b. Make a list of all the food you chose for each of the four meals.
c. Make a bar graph of the total grams of fat, carbohydrates, fiber, and sugar for all meals combined.
d. Make a circle graph of the calorie distribution of the four meals -- breakfast, lunch, snack, and dinner. Include beverages in the appropriate meal.
e. Make a pictograph of the number of calories consumed in each meal.
Part D, Making Connections
1. Pick 8 River rafting trips to investigate. Choose only summer trips where you know the number of days you will be gone. Also, to ensure your safety, any trip you investigate must have a responsible guide. Pick trips you might consider doing someday if you had the time and money.
a. Make a table of all 8 trips complete with description, number of days, and the prices.
b. Calculate the mean, median, and mode of the prices.
c. Make a scatter plot of the data. Show the days on the horizontal axis and the prices on the vertical axis. Draw a trend line between the prices.
d. Make a stem and leaf plot of the data.
e. Make a box and whisker plot of the data.
f. Which method of data analysis was most helpful to you? Why?