Hy Density: Archimedes Revisited
Teacher Information Page Activity 3B Part 4
Activity Description:
Students will read the background on Archimedes and the Golden Crown.
After having done the Buoyancy and Equal Arm Balance activities, they will
apply what they learned to design an experiment based on how Archimedes helped Hiero II,
king of Syracuse.
Activity Background:
Archimedes is best known as one of the greatest mathematicians of all time; particularly in
the area of geometry. In ancient Greece he would have been known by local farmers not as a
mathematician, but as the guy who invented the “screw” so that they could easily move
water from a stream up a hill to their fields! Greek soldiers would have known Archimedes
as the inventor who helped them defend Syracuse by using mirrors to burn ships or the
Claw used to hook a ship and tip it over!
Archimedes exact time of birth and death are not known for certain. It is believed that he
lived around 287-212 BC. Archimedes lived in Syracuse of Greek Sicily. The fact that it was
considered Greek Sicily gives one an added insight. Sicily was a multicultural island, mainly
due to a variety of invaders. In Archimedes time, it happened to be the Greeks.
The story of the Golden Crown is well known among mathematicians and scientists. In
essence, Hiero II, king of Syracuse, commissioned a goldsmith to make him a golden crown
in the shape of a wreath. This was the common shape for crowns during that time. Hiero II
wanted to use the crown on a statue of a god or goddess he worshiped.
After the goldsmith had shaped the gold into the wreath crown he returned
it to Hiero II. As the story goes, this is when the rumors began about the
crown. The rumors that reached Hiero II were that the goldsmith had not
used all the gold but had replaced some of it with another metal.
Archimedes was the kind of man that would sink himself in his work; mind and body. One
day while he was sinking himself into a bath tub he solved the problem he had with the
crown. He had noticed that the farther he sank in the tub the more water would overflow.
2007 PROTOTYPE
Positively Aging®/M.O.R.E.
2007©The University of Texas Health Science Center at San Antonio
LESSON 3
ACTIVITY 3B PART 4
Corpulosity
Hiero II asked Archimedes to help him determine if the crown was indeed
made of pure gold or not. The problem was that the crown was considered holy because it
belonged to a god or goddess. Archimedes could not do anything to the crown that would
change it in anyway.
1
When Archimedes realized he had figured out a way to answer King Hiero’s question,
he literally jumped out of the tub and took off running to find the king. As he
ran he was yelling “Eureka! Eureka!” which means “I have found it! I have
found it!” The end of the story is that while Archimedes had found the
answer of how to test the crown, he had forgotten his towel and clothes.
Yes, he ran through Syracuse naked!
It is believed that Archimedes did not just dunk the crown in water and measure
the amount of water that overflowed. You see, Archimedes had already written two laws
that helped him find the solution: the Law of Buoyancy and the Law of Levers. Some experts
believe that Archimedes would have used a lever with the crown on one end and the same
mass of gold as was originally given to the goldsmith.
Archimedes would have lowered both objects into
water at the same time. If the crown was not pure
gold then the gold would make the lever (balance)
uneven. Since gold has a greater density, and thus
displaces more water, the end of the balance with
gold on it would sink more than another common
metal of the time: silver.
Archimedes determined the mass of the wreath and found that it was the same mass as the
original lump of gold. The equal arm balance was level. This was fine but Archimedes knew
that if there was anything in the crown other than gold that that metal would not have the
same buoyant nature as gold.
When Archimedes lowered both the wreath
crown and the gold he would have seen the equal
arm balance tilt down on one end—the end with
the gold, see Figure 1. Archimedes proved that the
goldsmith had cheated Hiero II. It is believed that
Hiero II had the goldsmith killed.
Activity Materials
N
Figure 1 Was It Pure Gold?
1 Bin of materials provided by your teacher (per group)
N
1 copy of the Student Information Page (from class set)
N 1 copy of the Student Data Page (per student)
Activity Management Suggestions:
Students need to work in groups of 3-4; try to make sure that you have at least 1 person in
the group who excels at recording information; a person who is kinesthetic; a person good
at helping others stay on task
Extensions:
Have students write another scenario in which they apply the same equipment
and techniques to determine density of other materials.
2007 PROTOTYPE
Positively Aging®/M.O.R.E.
2007©The University of Texas Health Science Center at San Antonio
LESSON 3
ACTIVITY 3B PART 4
Corpulosity
Modifications:
2
Hy Density: Archimedes Revisited
Student Information Page Activity 3B Part 4
Activity Introduction:
The story of Archie, Deuces and Goldie was a fictionalized version of the story
of Archimedes and the Golden Crown. In this activity you will read a more
accurate version of what is believed to be the story of how Archimedes (aka Archie)
helped Hiero II (aka: Deuces), king of Syracuse of Greek Sicily. After reading the Activity
Background you will design the experiment Archimedes would have done to find out if the
crown was as buoyant as the lump of gold. You will re-test your “crown” and “lump of gold”
from Part 1 The Golden Crown activity.
Activity Background:
Archimedes is best known as one of the greatest mathematicians of all time; particularly in
the area of geometry. In ancient Greece he would have been known by local farmers not as a
mathematician, but as the guy who invented the “screw” so that they could easily move
water from a stream up a hill to their fields! Greek soldiers would have known Archimedes
as the inventor who helped them defend Syracuse by using mirrors to burn ships or the
Claw used to hook a ship and tip it over!
Archimedes exact time of birth and death are not known for certain. It is believed that he
lived around 287-212 BC. Archimedes lived in Syracuse of Greek Sicily. The fact that it was
considered Greek Sicily gives one an added insight. Sicily was a multicultural island, mainly
due to a variety of invaders. In Archimedes time, it happened to be the Greeks.
The story of the Golden Crown is well known among mathematicians and scientists. In
essence, Hiero II, king of Syracuse, commissioned a goldsmith to make him a golden crown
in the shape of a wreath. This was the common shape for crowns during that time. Hiero II
wanted to use the crown on a statue of a god or goddess he worshiped.
Hiero II asked Archimedes to help him determine if the crown was indeed
made of pure gold or not. The problem was that the crown was considered holy because it
belonged to a god or goddess. Archimedes could not do anything to the crown that would
change it in anyway.
Archimedes was the kind of man that would sink himself in his work; mind and
body. One day while he was sinking himself into a bath tub he solved the problem
he had with the crown. He had noticed that the farther he sank in the tub the
more water would overflow.
LESSON 3
A
CTIVITY 3B PART 4
2007 PROTOTYPE
®
Positively Aging /M.O.R.E.
2007©The University of Texas Health Science Center at San Antonio
Corpulosity
After the goldsmith had shaped the gold into the wreath crown he returned
it to Hiero II. As the story goes, this is when the rumors began about the
crown. The rumors that reached Hiero II were that the goldsmith had not
used all the gold but had replaced some of it with another metal.
3
When Archimedes realized he had figured out a way to answer King Hiero’s question,
he literally jumped out of the tub and took off running to find the king. As he
ran he was yelling “Eureka! Eureka!” which means “I have found it! I have
found it!” The end of the story is that while Archimedes had found the
answer of how to test the crown, he had forgotten his towel and clothes.
Yes, he ran through Syracuse naked!
It is believed that Archimedes did not just dunk the crown in water and measure
the amount of water that overflowed. You see, Archimedes had already written two laws
that helped him find the solution: the Law of Buoyancy and the Law of Levers. Some experts
believe that Archimedes would have used a lever with the crown on one end and the same
mass of gold as was originally given to the goldsmith.
Archimedes would have lowered both objects into
water at the same time. If the crown was not pure
gold then the gold would make the lever (balance)
uneven. Since gold has a greater density, and thus
displaces more water, the end of the balance with
gold on it would sink more than another common
metal of the time: silver.
Archimedes determined the mass of the wreath and found that it was the same mass as the
original lump of gold. The equal arm balance was level. This was fine but Archimedes knew
that if there was anything in the crown other than gold that that metal would not have the
same buoyant nature as gold.
When Archimedes lowered both the wreath
crown and the gold he would have seen the equal
arm balance tilt down on one end—the end with
the gold, see Figure 1. Archimedes proved that the
goldsmith had cheated Hiero II. It is believed that
Hiero II had the goldsmith killed.
Activity Materials:
Figure 1 Was It Pure Gold?
N
Activity Instructions:
Ë
Ë
1. As a group you will devise a procedure to find out if the “crown” you used in Part 1
is truly gold.
2. On the Student Data Page you will find a guide and a rubric to help you
plan your investigation.
2007 PROTOTYPE
Positively Aging®/M.O.R.E.
2007©The University of Texas Health Science Center at San Antonio
LESSON 3
ACTIVITY 3B PART 4
Corpulosity
1 Bin of materials provided by your teacher (per group)
N 1 copy of the Student Information Page (from class set)
N 1 copy of the Student Data Page (per student)
4
Hy Density: Archimedes Revisited
Student Data Page Activity 3B Part 4
Problem Statement
(this should be a sentence
that states what this activity
is about):
____________________________________
____________________________________
____________________________________
____________________________________
Activity Materials ____________________________________ Activity Background
(list only the materials that are
(information that helps others
needed for the activity and
understand what has been
describe them fully):
done in the past related to
____________________________________
this investigation):
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
Title:
____________________________________
____________________________________
____________________________________
Results:
(Draw a data table in which to
collect your results):
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
Procedures
(write instructions in numbered
steps so that anyone could repeat
them; you will need to write
how to set-up and equal arm
balance as well as how to attach
the “crown” and “lump of gold”
and how to read the results):
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
2007 PROTOTYPE
Positively Aging®/M.O.R.E.
2007©The University of Texas Health Science Center at San Antonio
LESSON 3
ACTIVITY 3B PART 4
Corpulosity
Conclusion:
(After analyzing your results,
describe the final outcome
of your investigation):
____________________________________
____________________________________
____________________________________
____________________________________
5
Hy Density: Archimedes Revisited Rubric
Exemplary
4
Accomplished
3
Developing
2
Beginning
1
No Attempt
Made
Presents a
Gives too much
concise
Problem
information—
sentence
more like
Statement that states
a summary.
the problem.
Does not
give any
Gives very
Did not write
information
little
a problem
about what to
information.
statement.
expect in
the lab.
Presents a
concise backGives too much
Activity
ground for
information—
Background the activity
rambles.
with relevant
information.
Background
Gives only
lacking in
Did not write
one or two
relevant
a background.
relevant facts.
information.
List format,
includes all
List format and
the materials includes all the
Materials needed and
exact quanti- materials needed
ties needed to to complete lab.
complete lab.
List format, but List format,
does not include
but
all the materials incomplete
needed to
complete lab or and poorly
described.
materials not
well described.
Score
Did not list
materials.
Some of the
Presents
Most of the
Not
steps are
easy-to-follow steps are undersequential,
understandDid not write
steps which
most steps
Procedure are logical and standable; some
able; most are
a procedure.
lack detail or
are missing or
adequately
confusing and
are confusing.
are confusing.
detailed.
lack detail.
Presents
Conclusion is Conclusion
logical
Conclusion based
written, but
incomplete
conclusion upon analysis of
Did not write
not based
and does not
Conclusion
based upon
a conclusion.
results, but is
clearly explain upon analysis
analysis of
not complete.
the results.
of results.
results.
Grammar All grammar
and spelling
and Spelling are correct.
Only one or
two errors.
More than
two errors.
Very frequent
grammar
and/or
spelling
errors.
No attempt
made to
write the
assignment.
Total
2007 PROTOTYPE
Positively Aging®/M.O.R.E.
2007©The University of Texas Health Science Center at San Antonio
LESSON 3 ACTIVITY 3B PART 4
6