Activity pubs.acs.org/jchemeduc
JCE Classroom Activity #112: Guessing the Number of Candies in the JarWho Needs Guessing? Stephanie Ryan*,† and Donald J. Wink‡ †
Learning Sciences Research Institute and ‡Department of Chemistry, University of Illinois at Chicago, Chicago, Illinois 60607, United States S Supporting Information *
ABSTRACT: Converting among different units, for example between grams and moles or among the different number of moles of substances in chemical reactions, is an important technique throughout general chemistry in high school and college. Such conversions rely on the simple idea of proportional reasoning, which students probably first encounter in grade school. However, providing a conceptual basis for proportional reasoning in chemistry can be difficult, because units such as moles and atoms are abstract and unobservable. Introducing proportional reasoning to students using a visible and engaging activity provides the opportunity to make the concept clear to students prior to using proportional reasoning in more abstract work. This Classroom Activity uses a popular giveaway game, guessing the number of candy pieces in a jar, to accomplish this goal. At the same time, it introduces students to the idea that different units and types of measurement, such as counting and mass, can be used on the same sample. The activity also includes exercises that link these concepts and skills to counting with atoms and molecules. KEYWORDS: High School/Introductory Chemistry, Curriculum, Hands-On Learning/Manipulatives, Inquiry-Based/Discovery Learning, Nutrition FEATURE: JCE Classroom Activity
I
n this activity, students are introduced to proportional reasoning and unit conversions through an estimation activity. This is done by extending a popular game of estimating the number of candy pieces in a container. Because the activity often rewards the person who makes the most accurate estimate with a prize, perhaps the candy itself, it is also highly engaging. The activity also extends into an initial experience that links mass and counting, a precursor to learning about molar mass and other units.
■
BACKGROUND Guessing the number of candies in a jar or other container is a popular giveaway challenge. In the classroom, this can become a way to introduce and practice proportional reasoning and associated methods, such as unit conversions, measurement, and accuracy and precision. In this activity, students make an initial guess of how many candies (e.g., milk chocolate M&M-type candies, a kind of small, round candy with a colored shell) are in a large container, preferably one with volume markings on the side, as shown in Figure1. Students then carry out measurements on the volume occupied by smaller samples of the candy. They use these measurements and proportional reasoning to improve their guesses about the total number of candy pieces. In the process, students need to develop their own conversion factors between volume and number. These skills are then applied to other conversions between counting, mass, and nutrition units for the candies. Finally, this is linked to the skills of counting and determining the mass of chemical substances. © 2012 American Chemical Society and Division of Chemical Education, Inc.
Figure 1. Candies in a 600 mL beaker with 50 mL gradations.
The use of mathematics is an essential part of learning chemistry, especially in introductory courses in high school and college. This is supported by research that demonstrates a strong Published: May 22, 2012 1171
dx.doi.org/10.1021/ed1009943 | J. Chem. Educ. 2012, 89, 1171−1173
Journal of Chemical Education
Activity
low. Here, the activity is conducted with M&M-type candies. Other similarly sized candies, including jellybeans and round fruit flavored candies, can be used, so long as they are of uniform size. We recommend using milk chocolate M&M-type candies because of their bulk availability and the possibility of comparison using peanut or almond varieties of M&M-type candies. It is a good idea to have fun-size (small individual) packages of candy for the students to consume outside of class after the activity. Larger bags may be given to students who made an informed estimate that was closest to the actual amount of candy pieces. Each group will need two zip-seal plastic bags, labeled Bag 1 and Bag 2 with 20 candies and 40 candies, respectively. Each student group will need a 100 mL graduated cylinder. The teacher will need two identical large 400−600 mL beakers with measurements on the side to hold the candies for the “guessing” competition. One of the beakers is for use just in case students want to weigh an empty beaker as part of their informed estimate. The class should also have access to at least one of the following: a 25 mL graduated cylinder, a 100 mL beaker, and a 250 mL beaker. The additional graduated cylinders can be used by students if they need a visual cue to answer question 10 in the Student Activity (see the online Supporting Information). If peanut M&M-type candies are used, the students will note that there are fewer pieces in a given volume and, because peanuts are variable in size, there may be a larger spread in the data. This permits the introduction of the importance of relative size on density of particles. The activity has four parts. In the first part, the students are asked to make an initial estimate of the number of candy pieces in the container. They are then directed to count, weigh, and determine the volume occupied by two samples of candies. This concludes with direction to create number/mass, number/ volume, and mass/volume ratios for both samples. The ratios calculated for the two samples are then compared to one another. They should see that, although the number of candies in each sample is different, the ratios are very similar. This illustrates the fundamental concept of proportion as it occurs in proportional reasoning. The second part invites students to reconsider their estimate. They are prompted with an initial question: to predict the volume and mass of a sample that has twice as many candies as their largest sample. Students then turn to the question of the number of candies in the container. At this point, the question is posed in an open-ended fashion. Depending on the level of their understanding of proportional reasoning, the students may need some additional guidance from the instructor. Specifically, they will need to use the proportions they determined in part 1 and the information on the volume of the candies in the container to calculate the number and mass of the candies in the container. Students are asked to consider the nutrition of the candies using proportional reasoning in part 3. Finally, part 4 acts as a bridge between the activity and chemistry by connecting the candies to chemistry concepts, such as atomic mass units.
correlation between success in college general chemistry with how much mathematics students took in high school. Interestingly, the effect of prior mathematics completed in high school is an even stronger predictor of students’ success in college chemistry than prior performance on any particular topic (including stoichiometry) from high school.1,2 Similarly, student performance on a custom-written mathematics pretest in secondsemester general chemistry was a strong predictor of student success.3 Proportional reasoning is an essential component of math used in basic chemistry;4 it is based on the concept that the ratio between two extensive measurements is often a fixed proportion. Thus, proportional reasoning is the conceptual basis for a variety of unit conversion strategies, sometimes referred to as dimensional analysis, the factor-label method, or the unit-factor method, among other terms. The ratio used in these methods can be a property of a substance (molar mass or density at a fixed temperature) or is defined as part of a measurement system (conversions among metric units such as km and cm). In other cases, the ratio relates numbers of atoms or substances (molar ratios for chemical reactions or for the atoms in a substance). Finally, in many situations, a ratio is variable from sample to sample, but still fixed for a specific homogeneous sample (molarity). It is surprising that students have difficulty remembering and applying basic mathematics skills in beginning chemistry. The algebra and simple proportional reasoning skills used in these introductory courses are usually taught well before they are needed in chemistry, sometimes as early as middle school. However, ample evidence indicates that people learn best if instruction specifically links prior knowledge with current learning goals.5 As a result, students can treat the calculations of chemistry as separate from other kinds of calculations, and even from the concepts of chemistry themselves.6 Recent research on student understanding of number in chemistry also indicates the difficulty in transferring strong proportional reasoning skills to chemistry settings.7 One way of addressing this is to provide students with a clear and visible basis for the conceptual basis of calculations themselves. And, connecting to students’ personal perspectives is a likely source of engagement for their learning, as suggested by the “social and personal perspectives” of the National Science Education Standards8 and many of this Journal’s Classroom Activities.
■
ABOUT THE ACTIVITY This activity addresses the need for students to understand how unit conversion strategies use proportional reasoning. To avoid the problems inherent in reasoning about invisible quantities (such as atoms) or conceptual entities (such as the mole), this activity works with macroscopic things: pieces of candy. The activity is presented in the form of an engaging and often familiar challenge: estimating the number of pieces of candy in a container, which also improves student engagement. The activity is focused on making measurements that can be directly seen by students, especially through counting and weighing. Thus, students work with ratios that relate the volume and number of candies (analogous to molarity or volume percentage) and the mass and number of candies (formula weight or molar mass). In the follow-up parts of the activity, they also consider the more abstract ratio of nutritional content to the mass of candies (analogous to percent composition and enthalpy of reaction). This activity is simple to perform with minimal setup. The same materials can be reused year to year, so cost over time is
■
INTEGRATING THE ACTIVITY INTO THE CURRICULUM This activity is intended for high school or introductory college chemistry students and also works well with middle school students. With older students, the activity can be a good “icebreaker” activity, especially in the process of activating prior knowledge on proportional reasoning. Student background for the activity can be minimal. Familiarity with simple measurement (mass, count, and volume) is helpful, as is some familiarity with 1172
dx.doi.org/10.1021/ed1009943 | J. Chem. Educ. 2012, 89, 1171−1173
Journal of Chemical Education
■
proportional reasoning. But as this is an introductory activity, instruction can address gaps in even those basic concepts. This activity can be used at several different points in the curriculum. For example, it can be used as an initial engagement activity before a unit on quantitative reasoning, to activate student reasoning, and to set the stage for calculations on molecules (just like counting individual candies) or moles (counting one piece of candy as a mole). Part 4 of the activity specifically links to the idea of atomic or molecular mass, in parallel to the mass of one candy piece, so the activity also works well before a unit on molar mass. It can also be used to start a unit on nutrition, given the inclusion of questions about the energy content of the candies. And, while the proportional unit that is at the heart of this activity is number per unit volume, the activity can be used as an analogy to density calculations, which use grams per unit volume. Finally, a unit on measurement can benefit from this activity because different extensive measurementsvolume and numberare used in addition to proportional reasoning. Similar activities have been developed that allow for this activity to be extended in different ways. For example, “Jellybeans in a Jar” is the title of an activity to introduce “probability, randomization, bias, average, and replication”.9 The topic of predicting the number of candies in a jar was also discussed as a simple conversion exercise in a National Public Radio Science Friday report.10 Other examples of the use of candies in the classroom include studying sampling techniques11,12 and the determination of the volume of a mole of candies.13
Activity
REFERENCES
(1) Tai, R. H.; Sadler, P. M.; Loehr, J. F. J. Res. Sci. Teach. 2005, 42, 987−1002. (2) Sadler, P. M.; Tai, R. H. J. Chem. Educ. 2005, 84, 1040−1046. (3) Leopold, D. G.; Edgar, B. J. Chem. Educ. 2008, 85, 724−731. (4) Wink, D. J.; Gislason, S. F.; McNicholas, S. M.; Zusman, B. J.; Mebane, R. C. J. Chem. Educ. 2000, 77, 999−1000. (5) Commission on Behavioral and Social Sciences and Education. How People Learn: Brain, Mind, Experience, and School; National Research Council: Washington, DC, 2000. (6) Nahkleh, M. B. J. Chem. Educ. 1993, 70, 190−192. (7) Ryan, S. A. C. Ph.D. Dissertation, University of Illinois at Chicago, 2011. (8) Wink, D. J.; Daubenmire, P. D.; Brennan, S. K.; Cunningham, S. A. Chemistry and the National Science Education Standards, 2nd ed., Bretz, S. L., Ed.; American Chemical Society: Washington, DC, 2008. (9) Phillipoff, J. An Introduction to Sampling: Jellybeans in a Jar. http://www.hawaii.edu/gk-12/opihi/classroom/jellybeans.pdf (accessed May 2012). (10) Chadwick, A.; Flatow, I. Unique Shape of M&Ms Interests Scientists. National Public Radio, February 26, 2004. http://www.npr. org/templates/story/story.php?storyId=1703595 (accessed May 2012). (11) Ross, M. R. J. Chem. Educ. 2000, 77, 1015−1017. (12) Canaes, L. S.; Brancalion, M. L.; Rossi, A. V.; Rath, S. J. Chem. Educ. 2008, 85, 1083−1086. (13) Merlo, M.; Turner, K. J. Chem. Educ. 1993, 70, 453.
■
SAFETY Although this activity uses only substances that are regularly consumed, proper safety procedure requires that the students not consume any of the substances used in the activity. Reminding students that the candies have been repeatedly handled by others will deter this. If this is a significant problem in practice, switching to a nonfood item, such as marbles, is a reasonable alternative. Various dried beans could be used as an inexpensive, safe option to discourage participants from eating the supplies. However, size variability may be an issue that would need to be addressed. Also, instructors should determine whether allergies to any of the foods might affect students, especially if peanut-containing candies are used.
■
ASSOCIATED CONTENT
* Supporting Information S
Student activity worksheet; answers to questions for students. This material is available via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
■
ACKNOWLEDGMENTS This work was supported in its initial development in middle and high school settings in the Chicago Public Schools by an NSF Graduate Fellows in K−12 Education Project grant and further refined in Chicago’s After School Matters science37 program. We acknowledge the assistance of Steve Rooney, LaToyla Jones, Sara Marchlewicz, Michelle Frack, and Linda Marton in initial implementations and the suggestions of reviewers in several aspects of the paper, including useful Web sites. 1173
dx.doi.org/10.1021/ed1009943 | J. Chem. Educ. 2012, 89, 1171−1173
