MCTP
Maryland Collaborative
for Teacher Preparation
Counting by Weighing:
Bead Jewelery Construction as a Metaphor for Chemical Stoichiometry
Thomas C. O'Haver
Department of Chemistry and Biochemistry
University of Maryland
College Park, MD 20742
(301) 4051831
to2@umail.umd.edu
NSF Cooperative Agreement No. DUE 9255745
Topic
Precursor to understanding of law of definite proportion; mass
relationships in a chemical reaction.
Primary Expected Outcomes
Students will be able to describe in their own words how the bead jewelry
activity serves as a metaphor for atoms and molecules, for the weight
relationships in a chemical reaction (the law of definite proportion),
and for the microscopic/macroscopic dilemma of physical science.
Scientific and/or Math Concepts
Conservation of mass; microscopic interpretation of chemical reactions as
a rearrangement of atoms; law of definite proportion; atomic and
molecular weight; stoichiometry (mass relationships in a chemical
reaction); the mole concept; "limiting reagent" problems; problem
solving, estimation, proportional reasoning, ratio.
Disciplines integrated
Chemistry, mathematics
Prerequisite knowledge
AAAS Benchmarks for middle school: Structure of matter (Everything made
of atoms; Limited number of kinds of atoms; All atoms of one kind are
identical; Size of atoms; Atoms form molecules)
Student's Preconceptions
From the AAAS Benchmarks: "Middle-school and high-school students are
deeply committed to a theory of continuous matter. Although some
students may think that substances can be divided up into a small
particles, they do not recognize the particles as building blocks, but as
formed of basically continuous substances under certain
conditions....Students of all ages show a wide range of beliefs about the
nature and behavior of particles. They lack an appreciation of the very
small size of particles; attribute macroscopic properties to particles;
believe there must be something in the space between particles....many
students do not view chemical changes as interactions. They do not
understand that substances can be formed by the recombination of atoms in
the original substances."
Multicultural aspects
Bead jewelery and decorations occur in several diverse cultures.
Activities and Experiences
Required supplies and equipment: A selection of various sizes and types
of small beads, sequins, and other light-weight jewelry parts that are
small enough to be sold by weight rather than by count, cotton thread, a
needle; small glass bottles or beakers; a scale or balance with a
sensitivity of 0.1 - 1.0 gram (but not sufficiently sensitive to weigh a
single bead).
1. Students, divided into groups of 2-3, are given a plastic bag of
small colored glass beads of uniform small size (the ones that are sold
in small 70 gram plastic bags in the craft shops). They are asked to
estimate the number of beads and write down their estimate. Then they
are asked to devise a method to determine the number of beads more
accurately by any means they wish, as long as their method can be carried
out in 15 minutes or less. Each group has access to a top-loading
digital scale that reads to the nearest gram. (Instructor's note: there
are approximately 7,000 beads in the bag, so that direct counting, while
theoretically a possibility, is not likely to be discovered by the
students to be a practical method. Moreover, the students' scale is not
sufficiently sensitive to weigh a single bead, so one obvious method -
weigh one bead and divide into weight of all the beads - is not
practical. This should force the student to the notion of the weight of
a predetermined number of beads.) Each group writes down a description
of their method, carry it out, write down their measurement of the number
of beads, and to estimate the accuracy of their method and justify that
estimate. Selected groups describes their method to the rest of the
class.
2. Student groups are then given a selection of various sizes and types
of small beads. Each group is asked to design a necklace or bracelet
that uses two or more types of beads and multiples of some beads. Using
a coding scheme designed by the class that represents each type of bead
by a 2-letter code (e.g. Br = red bead; Sg = gold sequin, etc), the
groups are asked to write down a "formula" for their design, using
subscripts to represent the number of beads of each type in the design
(e.g. Br2Sg5). Discussion question: does this formula uniquely specify
the design; that is, is there only one possible design with a given
formula?
3. Scale-up. The groups are now given the task of specifying the
materials needed to mass produce one kilogram (1000 g) of their design.
Assume that the raw materials are sold by weight, e.g. by the gram. How
many grams of each type of bead would have to be purchased? Given one 70
gram bag of each of the required beads, how may complete products could
you produce, which beads would run out first and what would be left over?
(Chemists call this a "limiting reagent" problem; it is generally
considered to a "tough" problem for many students).
4. Extension. Devise a general method for calculating the weight of each
type of bead need to product any weight of a product, given its "formula"
and combining the bead-weight data from the other groups. Some groups may
come up with a method based on single bead weights, others may devise a
method based on weights of an arbitrarily chosen large number of beads.
Discuss which approach would be most convenient if the weight of the
beads were very much smaller (e.g. 10-12 rather than 10-2 grams). Help
student to realize that to work these sorts of problems, one need to know
the relative weights of the beads. Have the students prepare a "Table of
the Beads" that lists the relative weights of all bead types.
5. Groups are asked to discuss how the above activities serve as a
metaphor for the microscopic/macroscopic problem in physical science: the
extremely small size of atoms and molecules makes it impossible to count
them directly and inconvenient to use the masses of single atoms and
molecules in routine calculations; atoms and molecules are sold by weight
(or mass) but are needed in specific small whole-number ratios, just like
the small beads.
6. Application. "Atomic weight" and "molecular weight" as conventionally
defined in chemistry are not the weights of individual atoms or
molecules, but rather the weights of a very large number, originally
chosen to be the same as the number of atoms in exactly 1 gram of the
lightest element, hydrogen.
Accessment activity
Students submit their lab notes, a sample of their jewelry design, and
the results of their calculations, explain in writing how the bead
jewelry activity serves as a metaphor for atoms and molecules, for the
weight relationships in a chemical reaction (the law of definite
proportion), and for the microscopic/macroscopic dilemma of physical
science;.
Bibliography
Students Handouts
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Chemistry 121/122 Name________________________________
Fall, 1994 Partner_____________________________
Laboratory 1
Seed Beads and Sequins:
What Do They Have to Do with Chemistry?
A. Counting by Weighing
You are to work in groups of two or three and you may discuss among your
partners and share measurements and observations. However, you are
expected to write your own personal answers to the questions in this
handout.
Each group will be given a small plastic bag of "seed beads". These are
small glass beads that are use in making jewelery and other decorative
items. You will also have access to an electronic scale that can measure
the mass (weight) of items in grams.
1. Read the label on the bag and notice that these beads are sold by
weight rather than by count. Why do you that that is so?
2. How many beads does your group estimate are in the bag? Just make a
guess, without opening the bag. The teaching assistant will write each
group's guess on the blackboard. We will have a sort of "contest" to to
see which group makes the best guess.
3. Now try to devise a more accurate method for measuring the number of
beads in the bag, assuming that you will be allowed to open the bag and
use the electronic scale if you find it useful. Before you actually try
anything, explain here the procedure that your group will try to use.
4. Now try out your method for measuring the number of beads in the bag.
What difficulties did you encounter that made your group's method more
difficult that you had anticipated?
5. Did you find that you had to modify your groups method? If so, in
what way?
6. What is your group's final measurement of the number of beads in the
bag?
7. How did your group's measurement compare to your first guess?
8. With the equipment you have, it is possible to measure the weight of
an individual bead? How or why not?
9. Would it be easier to measure the weight of a large number of beads,
say the weight of 10, or 100, or 1000 beads together?
10. Use the measurements your group made of the weight of a large number
of beads to measure the average weight of a seed bead. Discuss this in
your group and describe the method you decided upon here and give the
result (average weight of one bead, in grams).
11. Use the measurements your group made of the weight of a large
number of beads to measure the average weight of a seed bead. Discuss
this in your group and describe the method you decided upon here and
give the result (average weight of one bead, in grams).
B. Bead Jewelery Construction as a Metaphor for Chemical Composition
1. Using the selection of beads and sequins, design and construct a
necklace, bracelet, or other decorative item that uses at least two
types of beads and uses multiples of some beads.
2. Within your group, design a shorthand notation that represents each
type of bead by a 2-letter code (for example, Rs = red seed bead; Gs =
gold sequin, or something like that).
3. a. Write down a "formula" for your group's design, using subscripts
to represent the total number of beads of each type in the design (for
example, Rs5Gs10 would represent a design made of a total of five red
seed beans and ten gold sequins).
b. Does this formula uniquely specify the design; that is, is there
only one possible design with a given formula? Or could there be more
that one design with the same formula?
c. Propose a way to write a more detailed "structural formula" for
your creation that completely specifies the arrangement of beads?
4. Now suppose that your group is a jewelery manufacturer and that you
have received an order for 1 kilogram (1000 grams) of your product (at
a handsome price, I might add). So obviously you need to scale up
production. The question is: for each type of bead used in your design,
how many grams of that type of bead would you have to order so that you
will have the right amount of beads and as little as possible left
over? (Hint: measure the weight of each type of bead in your design
and put the values into the table in number 2, above)
5. Given one 70 gram bag of each of the required beads, how may
complete products could you produce and which beads would "run out"
first?
6. In this experiment, the seed beads that you used were so small they
were sold by weight, rather than by count. However, in designing bead
jewelry, you needed a specific number of each type of bead. Explain
how this situation serves as a metaphor for chemical (molecular)
composition.
7. Give some ways that bead jewelry is different than atoms and
molecules? In principle, you could have actually counted the beads in
the bag, rather than weighing them, if you had had enough time. What
about the possibility of counting atoms, rather than weighing them?