Math Activity Mountain Climbing Name ________________________ The students of Falcon High School have gone mountain climbing. The main peak of Mount Moraine stands 4700 feet above sea level. The countryside surrounding the mountain is 850 feet above sea level. There are two secondary peaks along the main ridge, one rising 2400 feet above the base of the mountain, the other 3050 feet lower than the main peak. Falcon High School is located 150 feet above sea level. The bus left Falcon High at 6:00 AM and arrived at the mountain at 9:15 AM. After a 15 minute preparation and orientation period, they began the climb. The group ate lunch at the top and started back down at 1:00 PM. The bus left the base of the mountain at 4:30 PM, stopped to eat for 45 minutes and returned to the school at 8:15 PM. The students took temperature readings as they climbed. At the base of the mountain, the temperature was 68 degrees Fahrenheit. At 1000 feet, the reading was 64 degrees; at the first peak, 55 degrees; at 1470 feet (first valley), 57 degrees; at 2000 feet, 52 degrees; at 2500 feet, 46 degrees; at the second peak, 39 degrees; at 2950 feet (second valley), 41 degrees; at 3500 feet, 37 degrees; at 4000 feet, 34 degrees; at 4500 feet, 30 degrees; and at the top, the temperature was 28 degrees. Going back down the mountain, the readings were as follows: 32 degrees at the main peak, 34 degrees at 4500 feet, 37 degrees at 4000 feet, 40 degrees at 3500 feet, 43 degrees in the higher valley, 49 degrees at the second peak, 48 degrees at 2500 feet, 55 degrees at 2000 feet, 59 degrees in the lower valley, 55 degrees at the lowest peak, 63 degrees at 1000 feet and 66 degrees at the base. The times the students arrived at the top and back at the base were recorded. Some of the arrival times at the top were: Sam, 12:15 PM; Maria, 12:18 PM; Sue, 12:14 PM; John, 12:31 PM; Tom, 11:43 AM; Alicia and Kirsten, 12:22 PM; Bob, 12:00 PM; Mike and Mary, 12:40 PM; and James, 12:47 PM. Some of the arrival times at the base were: Tom, 2:55 PM; Sam, Sue and Maria, 3:35 PM; Fred, 3:25 PM; John, 3:17 PM; Alicia and Bob, 3:46 PM; Kirsten and James, 3:31 PM; and Mike and Mary, 3:50 PM. The biology class listed the wildlife they observed. 13 students saw chipmunks, 18 saw crows, one saw a ground squirrel and two saw deer. Five students found the footprints of a fox and eight discovered a nest of wild honeybees. 15 of the students also reported seeing butterflies. Two students did not report seeing any wildlife. (One was not very observant; the other was too noisy and scared away the wildlife.) One-third of the earth-science class of 24 students observed a massive granite formation. 25% of the class noted sedimentary intrusions of chalcedony and silica. Half that many recorded igneous intrusions of dolomite and basalt. Four students saw a metamorphic layer of quartzite. The rest reported seeing glacial erratics composed of pegmatite. The social-studies class made a diagram of the trail from a road map. The data they used made up the following table: Distance (mi): 0 120 121.1 121.9 123.7 124.2 125.6 Landmark: school base 1st 1st 2nd 2nd main peak valley peak valley peak 1 MOUNTAIN 1) How high above the base is the main peak of the mountain? ______________ 2) How high above the base is the lowest peak? ____________________________ 3) What is the altitude of the middle peak above sea level? _______________ 4) What is the altitude of the lowest peak above sea level? _______________ 5) What is the difference in altitude between the main peak and the middle peak? Between the middle peak and the lowest peak? __________ __________ 6) Make a graph of the distance of the bus from school for the time of day. Assume that the bus travels at a constant rate when it is moving. 7) How long did it take the bus to travel to the mountain? ________________ Back to school (only while it was moving)? _____________________________ 8) Which time interval was shorter? __________ How much shorter? __________ 9) What might account for the difference in travel times? _________________ ___________________________________________________________________________ 10) What information would you need to make this graph more accurate? ___________________________________________________________________________ 11) What was the average speed of the bus while it was moving: Going to the mountain? _______ Returning? _______ Round trip? _______ 12) Make a graph of the altitude of the students above sea level for the time of day. Assume that the students are hiking at a constant rate. 13) Make a line graph of the temperature readings at each altitude. 14) What conclusions can be made from this graph? _________________________ ___________________________________________________________________________ 15) What might account for the differences in temperature between the ascent and descent? ___________________________________________________ 16) Estimate the temperatures which might have existed during that day at: 2250 ft 5000 ft 8000 ft 10000 ft sea level _____ _____ _____ _____ ____ 17) Which tend to be more accurate, predictions made between data points or predictions made beyond the available data points? ____________________ 18) Why? __________________________________________________________________ 2 MOUNTAIN 19) Make a table showing how long it took each student to ascend the mountain. Arrange the time intervals from fastest to slowest. 20) Make a similar table for descent intervals. 21) Make a back-to-back stem-and-leaf plot comparing the time intervals for ascent and descent. 22) Make a back-to-back stem-and-leaf plot comparing ascent-time intervals for boys and girls. Make another plot for descent time intervals. 23) What might invalidate the comparison of of the boys' and girls' times? ___________________________________________________________________________ 24) Whose time was not recorded at the end of the ascent? _________________ 25) Find the mean, median, mode and range for each of the following: Mean Median Mode Range .---------.---------.---------.---------. a) Altitudes of mountain peaks | | | | | `---------'---------'---------'---------' b) Temperature readings .---------.---------.---------.---------. 1) Ascending | | | | | |---------|---------|---------|---------| 2) Descending | | | | | |---------|---------|---------|---------| 3) Both | | | | | `---------'---------'---------'---------' c) Climbing time intervals .---------.---------.---------.---------. 1) Ascending | | | | | |---------|---------|---------|---------| 2) Descending | | | | | |---------|---------|---------|---------| 3) Both | | | | | `---------'---------'---------'---------' 26) In general, were the ascent or descent times faster? __________________ 27) On the average, how much faster? ______________________________________ 28) The students took the same trail ascending and descending, but the times were different. Based on this observation, what is the difference between slope and steepness? _______________________________ ___________________________________________________________________________ 29) Where were the students descending while climbing the mountain or ascending while leaving the mountain? _________________________________ 3 MOUNTAIN 30) Make a bar graph showing the number of biology students who reported each kind of wildlife. Include a category for the students who saw nothing. 31) Could some of the students listed have reported more than one kind of wildlife? Explain. _____ ______________________________________________ 32) What was the maximum number of biology students in the group? _________ 33) What was the minimum number of biology students in the group? _________ 34) A circle graph of the biology data would have to be based on the total number of instead of the number of students. ________________________ 35) Make a circle graph representing the earth-science students who observed each type of geological formation. 36) How many more students observed the massive granite formation than saw the sedimentary intrusions? ___________________________________________ 37) The same number of earth-science students saw igneous intrusions and glacial erratics. Does this number represent a mode? _________________ Explain. ______________________________________________________________ 38) What were the average slopes between each of the landmarks list in the social-studies table? School to base of mountain ______ Base of mountain to 1st peak ______ 1st peak to 1st valley __________ 1st valley to 2nd peak ____________ 2nd peak to 2nd valley __________ 2nd valley to main peak ___________ 39) Draw a side-view diagram of the mountain based on the data. Note that for readablity, the vertical scale will have to be different from the horizontal scale. Label each landmark. Show the distance between each landmark. Mark all temperature readings at corresponding altitudes. 40) Write at least one math question from the data given on page 1. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 4