Standing on One Foot Maria stood on her bathroom scale with two feet. She read her weight on the scale. She then lifted one foot. Circle what you think happened to the reading on the scale when she stood on one foot. A It showed an increase in weight. B It showed a decrease in weight. C Her weight stayed the same. Explain your thinking. What rule or reasoning did you use to select your answer? 61
Standing On One Foot Teacher Notes Purpose The purpose of this assessment probe is to elicit students ideas about weight and pressure. The probe is designed to determine whether students think their weight changes when the force exerted per unit area (pressure) on a scale changes. Related Concepts force, gravity, pressure, weight Explanation The best answer is C: Her weight stayed the same. Weight is the force of gravity acting on an object. Regardless of whether you stand on two feet or one foot, the force of gravity acting on your body as you stand on a bathroom scale is the same. When you stand on two feet, the force is distributed over a wider area (the total area covered by the two soles of your feet). When you lift one foot, the same force is distributed over a smaller area (the area covered by the sole of one of your feet). Pressure changes as the constant weight of the body is distributed over different areas. Because pressure is described as force per unit area (P = F A), as the area covered by the body on the scale decreases by lifting one foot, the pressure increases. Although the pressure increases, the weight remains constant. Curricular and Instructional Considerations Elementary Students In the elementary grades, students use simple instruments to gather data. They learn to measure weight and mass using various types of scales and pan balances. At this stage, weight 62 N a t i o n a l S c i e n c e T e a c h e r s A s s o c i a t i o n
is an observational property that they use to describe objects and materials. Elementary students are not expected to know that weight is caused by the force of gravity. However, they should be able to observe that the weight of an object stays the same in the same location on Earth. Middle School Students At the middle school level, students should begin to distinguish between weight and mass. They develop an understanding that the force of the Earth s gravity affects the weight of an object. They often confuse pressure with weight. This is a time when their use of mathematics (area and proportionality) can be used to explain why their weight doesn t change when different amounts of their body are in contact with the scale. High School Students In high school, students develop more sophisticated notions of weight, mass, and pressure. However, they may still revert to naive ideas about weight. Administering the Probe You can demonstrate the context for this probe by bringing in a bathroom scale, standing on it with two feet, then lifting one foot. Make sure students do not see the reading on the scale as you demonstrate. Related Ideas in National Science Education Standards (NRC 1996) K 4 Abilities Necessary to Do Scientific Inquiry! Use simple equipment and tools to gather data and extend the senses. K 4 Properties of Objects and Materials! Objects have many observable properties, including size, weight, shape, color, and the ability to react with other substances. Those properties can be measured using tools, such as rulers, balances, and thermometers. 5 Abilities Necessary to Do Scientific Inquiry! Use appropriate tools and techniques to gather, analyze, and interpret data. 9 12 Motions and Forces " Gravitation is a universal force that each mass exerts on any other mass. Related Ideas in Benchmarks for Science Literacy (AAAS 1993 and 200) Note: Benchmarks revised in 200 are indicated by (R). New benchmarks added in 200 are indicated by (N). K 2 Scientific Inquiry " People can often learn about things around them by just observing those things care-! Indicates a strong match between the ideas elicited by the probe and a national standard s learning goal. 63
fully, but sometimes they can learn more by doing something to the things and noting what happens. " Tools such as thermometers, magnifiers, rulers, and balances often give more information about things than can be obtained by just observing things unaided. K 2 Structure of Matter " Objects can be described in terms of their properties. 3 5 Forces of Nature " The Earth s gravity pulls any object on or near the Earth toward it without touching it. (R) 6 Forces of Nature " Every object exerts gravitational force on every other object. 9 12 Forces of Nature " Gravitational force is an attraction between masses. The strength of the force is proportional to the masses and weakens rapidly with increasing distance between them. Related Research " The idea that the weight of an object is a force the force of gravity on that object does not appear to be a firmly held idea among secondary students (Driver et al. 1994). " There is not a lot of research on students ability to distinguish between weight and pressure in relation to the surface area of an object in contact with a weighing instrument, such as a bathroom scale. Our field tests with elementary and middle school students showed that many students believed that the weight increases when there is less surface area touching the scale because it presses down harder. Some students also believed the weight would decrease because the amount of force pushing down is less when one foot is lifted. These ideas were less prevalent with high school students, although some students still believed standing on one foot would press down harder and increase the weight. Suggestions for Instruction and Assessment " This probe lends itself to an inquiry investigation. Have students commit to a prediction, explain their reasoning that supports their prediction and then test it. When students find their observation does not match their prediction, encourage them to discuss their ideas and seek information to support a new explanation. " With younger children, have them weigh a variety of objects by placing them on their side, top, bottom, or in other configurations, observing how the weight stays the same. Be sure to place the object in the center of the weighing pan or device each time. " Challenge students with other examples illustrating the difference between weight and pressure. For example, imagine that you had two different pairs of shoes that 64 N a t i o n a l S c i e n c e T e a c h e r s A s s o c i a t i o n
weighed the same. One was a pair of high spiked heels and the other was a pair with flat soles. When you put the high spiked heels on and stood on soft ground, the heel sunk down into the ground. When you put the flat sole on, you stayed on top of the ground. What changed, your weight or the shoes? Why did this change in the shoes affect how you stood on the soft ground? " After developing an operational definition of pressure, have students compare the pressure exerted by one foot on the scale with two feet on the scale. Have students trace their feet on square grid paper and count up the number of square units covered by one versus two feet. Calculate the pressure by dividing their weight by the square units. Related NSTA Science Store Publications, NSTA Journal Articles, NSTA SciGuides, NSTA SciPacks, and NSTA Science Objects (AAAS). 2001. Atlas of science literacy. Vol. 1. (See Gravity, pp. 42 43.) Washington, DC: AAAS. Nelson, G. 2004. What is gravity? Science & Children (Sept.): 22 23. Robertson, W. 2002. Force and motion: Stop faking it! Finally understanding science so you can teach it. Arlington, VA: NSTA Press. Related Curriculum Topic Study Guides (Keeley 2005) Observation, Measurement, and Tools Gravitational Force References (AAAS). 1993. Benchmarks for science literacy. New York: Oxford University Press. (AAAS). 200. Benchmarks for science literacy online. http://www.project2061.org/ publications/bsl/online Driver, R., A. Squires, P. Rushworth, and V. Wood- Robinson. 1994. Making sense of secondary science: Research into children s ideas. London: RoutledgeFalmer. Keeley, P. 2005. Science curriculum topic study: Bridging the gap between standards and practice. Thousand Oaks, CA: Corwin Press. National Research Council (NRC). 1996. National science education standards. Washington, DC: National Academy Press. 65