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 ------------------------------------------------------------------------- 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?