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Haley Jackson
Math 4161 C
Spring 2004
The Highs and Lows of Backpacking
This activity deals with elevation in the United States and of Mt.Everest in China. In this activity students learn about negative elevation, sea level, and positive elevation. This lesson integrates social studies and math. Students are required to measure a distance of twenty feet, use a stopwatch, and calculate how long it would take them to walk the distance of elevation at a steady pace. Students are required to use simple formulas to calculate time into speed. Students also learn how to predict as well as make decisions on how to approach a problem from his/her own perspective in a different manner. This LAP is designed for students in 7th-8th grade on a moderate difficulty level.
Name:______
Date:______
The Highs and Lows of Backpacking
We walk everyday of our life and never even realize that we are climbing. Every piece of land you walk on has an elevation. It may be hard to believe that your sidewalk that looks flat actually has an elevation, but it does. We usually think of elevation when we talk about mountains, not our front yard. Elevation is the angle at which something is elevated or raised. We consider sea level to be an elevation of 0 (no elevation) and then everything above sea level has a positive elevation. There are many places in the World, and even in the United States, that are at sea level. Anywhere the ocean meets the land the elevation is at sea level. There are also places that are below sea level. The elevation of places below sea level is calculated as a negative number, meaning below zero.
Now that we have discussed elevation, let’s take a backpacking trip! You are backpacking the highest elevations across the United States. But, before you go backpacking you need to figure out your average walking speed in order to estimate how long it will take you to backpack different elevations.
To do this you need: a partner
tape measure
stopwatch
pencil
paper
To figure out your average walking speed, you will need to measure out twenty feet and have your partner time you while you walk at a normal, steady pace. You and your partner have to decide whether to start and stop the watch when one or two feet have crossed the line. Take the average of five trials to use for your future calculations.
Average Walking Time
Trials / Time in Seconds / Show How You Calculated Average Time and Speed Here:1
2
3
4
5
Average Time:
Once you have figured out your average walking time, you have to figure out how many feet you walk per second. This is your average speed. Use your average time and calculate how many feet you walk per second. ______feet per second. (Hint: If you walked for twenty feet, how far did you walk in one second?)
Now that you have calculated your average walking speed, look at the chart below for the highest elevations in the United States. Based on your average walking speed, calculate how long it would take you to walk this elevation distance. Remember, you calculated your average walking time in feet per second and this elevation is in feet, so there is no need for conversions. Calculate your speed in seconds, minutes and then your speed in hours.
Five Highest Points in the United States
Place
/ Elevation / Speed (Seconds) / Speed (Minutes) / Speed (Hours)Mt.McKinley (Alaska) / 20,320 ft.
Mt.Whitney (California) / 14,494 ft.
Mt.Elbert (Colorado) / 14,433 ft.
Mt.Rainier (Washington) / 14,410 ft.
Gannett Peak (Wyoming) / 13,804 ft.
Calculations:
We have looked at the highest elevations in the United States, now let’s look at the lowest!!
The lowest elevation in the United States is Death Valley in California, where the elevation is 282 feet below sea level. If your average walking speed were 4.2 feet per second, how long would it take you in seconds to walk from sea level to Death Valley, if you could walk straight from sea level to Death Valley? ______seconds.
You calculated your average walking speed when you figured out how long it would take you to backpack up the five highest elevations in the United States. Do you think your calculations of speed will be accurate if you were to really backpack up these mountains? ______The predictions will probably not be very accurate because you walk faster on land that has little elevation, rather than land that has steeper elevations. How do you think you could alter your equation to make it more accurate, taking elevation into consideration? What could you have done instead of measuring out twenty feet and taking the average speed?
______
The Highest Elevation In The World
The highest elevation in the world is Mt.Everest in China with an elevation of 29,035 feet. If you were to backpackMt. Everest with your average walking speed, how long would it take you in seconds ______
minutes ______
hours ______
The lowest elevation in China is Turpan Pendi at -154 meters (154 meters below sea level). What is the elevation of Turpan Pendi in feet? ______feet(hint: there are 3.281 feet in 1 meter). What is the difference in meters between the highest and lowest points in China? ______meters What is the difference in feet? ______feet What is the difference in feet between the highest point in the United States and the highest point in the world? ______feet
Answer Key
Average Walking Time
Calculate average time by adding the five times together and then dividing by five.
Average Walking Speed
Calculate this by dividing twenty by your average time. This will give you how many feet you walk per second.
Five Highest Points in the United States
Take your average speed and divide it into the given elevation. This will give you seconds. Then divide by 60 for minutes and 60 again for hours.
- Speed for Death Valley: 67.14 seconds
- Are the calculations accurate for real backpacking? NO
- What could you have done differently? (Answers vary)
Highest Elevation in the World – China
Divide elevation by the average walking speed. (Answers Vary)
Turpan Pendi
Elevation in feet: Multiply -154 m by 3.281 ft/m Answer: -505.27 ft.
- What is the difference in the highest and lowest points in China?
29,035 ft. divided by 3.281 ft/m = 8,849.44 meters
8,849.44 m – (- 154 m) = 9003.44 m
- What is the difference in the highest and lowest points in China?
29,035 ft – (-505.27 ft) = 29,540.27 ft
- What is the difference in feet of the highest elevation in the world and the highest elevation in the United States? 29,035 – 20,320= 8,715 feet