Estimate the Circumference of the Earth
using Eratosthenes' Method

Assessment

Since students will measure the shadow length on paper using a ruler, the sun angles might vary by as much as 1º as compared to the answers provided for questions 1 - 4 under Part B (see below). This will affect all of the other calculations for each question with the exception of the "North/south distance (arc length)" and therefore the students' answers should be evaluated based on the subsequent calculations made with the computed sun angle. If the sun angle is off by more than 1º, then the answer is wrong but the other questions should be evaluated based on the calculations using the computed angle.

Student Worksheet Questions Score (points)
A: Estimate the circumference of the Earth using Eratosthenes' calculations
1. Circumference of the earth in kilometers: 46,350 km
(see calculations below)
 6 4 2 Answer is correct and student writes all calculations Answer is correct and student writes some of the calculations Answer is correct w/o calculations OR answer may be incorrect but simple error made in calculations
• Calculations:
1. 1 stadia = 185.4 meters
2. 5,000 stadia x 185.4 meters = 927,000 meters
3. 927,000 m = 927 km
4. 360° / 7.2° = 50 'slices'
5. 50 'slices' x 927 km = 46,350 km
____/6
2. The answer should provide a thorough explanation in the students' words and include at least one proposed method to repeat Eratosthenes' experiment today .

 6 4 2 Provides clear & organized explanation using supportive facts. Provides explanation using supportive facts. Provides explanation.
____/6
B: Estimate the circumference of the Earth using Eratosthenes' method
1. Eastlake, OH, USA
1. Sun Angle: 40.5º
2. Central Angle: 1.6º
40.5º (Eastlake sun angle) - 38.9º (Manasquan sun angle) = 1.6º
3. Number of 'earth slices': 225 'earth slices'
360º / 1.6º (central angle btwn. Manasquan & Eastlake)  = 225
4. v: 111 km
4,541 km (distance from Eastlake to Equator) - 4,430 km (Manasquan to Equator) = 111 km
5. Circumference (estimate): 24,975 km
111 km * 225 'earth slices' = 24,975 km
6. Percentage Error: 37.6%
24,975 km / 40,000 km = 62.4%
100% - 62.4% = 37.6%
____/6
2. Offenburg, Germany
1. Sun Angle: 49.5º
2. Central Angle: 10.6º
49.5º (Offenburg sun angle) - 38.9º (Manasquan sun angle) = 10.6º
3. Number of 'earth slices': 34.0 'earth slices'
360º / 10.6º (central angle btwn. Manasquan & Offenburg)  = 34.0
4. North/south distance (arc length): 888 km
5,318 km (distance from Offenburg to Equator) - 4,430 km = 888 km
5. Circumference (estimate): 30,192 km
888 km * 34.0 'earth slices' = 30,192 km
6. Percentage Error: 24.5%
30,192 km / 40,000 km = 75.5%
100% - 75.5% = 24.5%
____/6
3. Balgowan, South Africa
1. Sun Angle: 28.0º
2. Central Angle: 66.9º
38.9º (Manasquan sun angle) + 28.0º (Balgowan sun angle) = 66.9º
3. Number of 'earth slices': 5.4 'earth slices'
360º / 66.9º (central angle btwn. Manasquan & Balgowan)  = 5.4
4. North/south distance (arc length): 7,639 km
3,209 km (distance from Balgowan to Equator) + 4,430 km = 7,639 km
5. Circumference (estimate): 41,251 km
7,639 km * 5.4 'earth slices' = 41,251 km
6. Percentage Error: 3.0%
40,000 km / 41,251 km = 97.0%
100% - 97.0% = 3.0%
____/6
1. Sun Angle: 36.5º
2. Central Angle: 75.4º
38.9º (Manasquan sun angle) + 36.5º (Adelaide sun angle) = 75.4º
3. Number of 'earth slices': 4.8 'earth slices'
360º / 75.4º (central angle btwn. Manasquan & Adelaide)  = 4.8
4. North/south distance (arc length): 8,305 km
3,875 km (distance from Adelaide to Equator) + 4,430 km = 8,305 km
5. Circumference (estimate): 39,864 km
8,305 km * 4.8 'earth slices' = 39,864km
6. Percentage Error: 0.3%
39,864 km / 40,000 km = 99.7%
100% - 99.7% = 0.3%
____/6
BONUS: The answer should provide a thorough explanation in the students' words. Students should realize that the greater distance between the two cities results in a smaller percentage error because a greater central angle results in fewer 'earth slices' with more room for error in the angle measurement.

 3 2 1 Provides clear & organized explanation using supportive facts. Provides explanation using supportive facts. Provides explanation.
____/3
Total: ____/36

(NOTE: this RWLO is based on the Noon Day Project)

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