Assessment
IMPORTANT 
READ FIRST:
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 stadia = 185.4 meters
 5,000 stadia x 185.4 meters = 927,000 meters
 927,000 m = 927 km
 360° / 7.2° = 50 'slices'
 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
 Sun Angle: 40.5º
 Central Angle: 1.6º
40.5º (Eastlake sun angle)  38.9º (Manasquan sun angle) = 1.6º
 Number of 'earth slices': 225 'earth slices'
360º / 1.6º (central angle btwn. Manasquan & Eastlake)
= 225
 v: 111 km
4,541 km (distance from Eastlake to Equator)  4,430 km (Manasquan to
Equator) = 111 km
 Circumference (estimate): 24,975 km
111 km * 225 'earth slices' = 24,975 km
 Percentage Error: 37.6%
24,975 km / 40,000 km = 62.4%
100%  62.4% = 37.6%

____/6 
2. Offenburg, Germany
 Sun Angle: 49.5º
 Central Angle: 10.6º
49.5º (Offenburg sun angle)  38.9º (Manasquan sun angle) = 10.6º
 Number of 'earth slices': 34.0 'earth slices'
360º / 10.6º (central angle btwn. Manasquan & Offenburg)
= 34.0
 North/south distance (arc length): 888 km
5,318 km (distance from Offenburg to Equator)  4,430 km = 888 km
 Circumference (estimate): 30,192 km
888 km * 34.0 'earth slices' = 30,192 km
 Percentage Error: 24.5%
30,192 km / 40,000 km = 75.5%
100%  75.5% = 24.5%

____/6 
3. Balgowan, South Africa
 Sun Angle: 28.0º
 Central Angle: 66.9º
38.9º (Manasquan sun angle) + 28.0º (Balgowan sun angle) = 66.9º
 Number of 'earth slices': 5.4 'earth slices'
360º / 66.9º (central angle btwn. Manasquan & Balgowan)
= 5.4
 North/south distance (arc length): 7,639 km
3,209 km (distance from Balgowan to Equator) + 4,430 km = 7,639 km
 Circumference (estimate): 41,251 km
7,639 km * 5.4 'earth slices' = 41,251 km
 Percentage Error: 3.0%
40,000 km / 41,251 km = 97.0%
100%  97.0% = 3.0%

____/6 
4. Adelaide, Australia
 Sun Angle: 36.5º
 Central Angle: 75.4º
38.9º (Manasquan sun angle) + 36.5º (Adelaide sun angle) = 75.4º
 Number of 'earth slices': 4.8 'earth slices'
360º / 75.4º (central angle btwn. Manasquan & Adelaide)
= 4.8
 North/south distance (arc length): 8,305 km
3,875 km (distance from Adelaide to Equator) + 4,430 km = 8,305 km
 Circumference (estimate): 39,864 km
8,305 km * 4.8 'earth slices' = 39,864km
 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)
