SCIENCE OF GOLF Volume and Displacement STEM Lesson Plan adaptable for Grades 7–12 Lesson plans produced by the National Science Teachers Association. Video produced by NBC Learn in partnership with the USGA and Chevron. Background and Planning Information .............................................................2 About the Video .......................................................................................................................... 2 Video Timeline ........................................................................................................................... 2 Next Generation Science Standards ........................................................................................... 2 Promote STEM with Video ...............................................................................3 Connect to Science...................................................................................................................... 3 Connect to Technology ............................................................................................................... 4 Connect to Engineering............................................................................................................... 4 Connect to Math ......................................................................................................................... 4 Facilitate ENGINEERING Inquiry .......................................................................5 Explore Understanding ............................................................................................................... 5 Ask Beginning Questions............................................................................................................. 6 Design Investigations .................................................................................................................. 6 Possible Materials ........................................................................................................... 6 Open Choice Approach ................................................................................................... 6 Focused Approach .......................................................................................................... 7 Media Research Option .................................................................................................. 7 Make a Claim Backed by Evidence .............................................................................................. 8 Compare Findings ....................................................................................................................... 8 Reflect on Learning ..................................................................................................................... 8 Inquiry Assessment ..................................................................................................................... 8 Incorporate Video into Your Lesson Plan .........................................................9 Integrate Video in Instruction ..................................................................................................... 9 Bellringer ......................................................................................................................... 9 Homework....................................................................................................................... 9 Using the 5E Approach? .................................................................................................. 9 Connect to … History .................................................................................................................. 9 Use Video as a Writing Prompt ................................................................................................... 9 Copy Masters ................................................................................................ 10 Open Choice Inquiry Guide for Students .................................................................................. 10 Focused Inquiry Guide for Students ......................................................................................... 11 Assessment Rubric for Inquiry Investigations........................................................................... 13 SOG: Volume and Displacement (Grades 7–12) 1 Background and Planning Information About the Video This video discusses how an ancient principle, discovered by the Greek scientist Archimedes over two millennia ago, is used to find and regulate the volume of golf club heads. It features Carter Rich, Manager of Equipment Standards for the United States Golf Association (USGA) and John Spitzer, Assistant Technical Director of the USGA’s Test Center. The video describes Archimedes’ principle and how it is applied to the problem of finding the volume of irregularly shaped club heads via the buoyancy force on them when submerged in water. The video also explains why the volume matters; a larger volume could have a higher rotational inertia, causing less club head twist on bad shots and giving the user an unfair advantage over players using club heads with less volume. Video Timeline 0:00 0:15 Series opening 0:16 0:28 Introduces how clubs can vary in size and shape 0:29 0:56 Introduces Carter Rich who explains the history of volume regulations 0:57 1:29 Introduces John Spitzer who outlines how Archimedes’ ideas apply to volume 1:30 2:02 Discusses the story of Archimedes and his solution to the gold crown problem 2:03 2:52 Describes Archimedes’ principle and the d = m/v formula 2:53 3:14 Defines buoyancy and details how it is used to find the volume of a club head 3:15 3:24 Shows the experimental method of determining volume 3:25 3:43 Discusses moment of inertia as the reason for regulating club head volume 3:44 4:32 Describes the influence of the moment of inertia on the swing 4:33 4:56 Summary 4:57 5:12 Closing credits Language Support: To aid those with limited English proficiency or others who need help focusing on the video, click the Transcript tab on the side of the video window, then copy and paste the text into a document for student reference. Next Generation Science Standards Consider the investigation described in Facilitate ENGINEERING Inquiry section as part of a summative assessment for the following performance expectations. Refer to a NGSS document for connected Common Core State Standards for ELA/Literacy and Mathematics. The investigation also supports Practices for K–12 Science Classrooms. Engineering Design MS-ETS1-2. Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. MS-ETS1-3. Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success. Science and Engineering Practices Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence, and in the design: decide on types, how much, and accuracy of SOG: Volume and Displacement (Grades 7–12) 2 data needed to produce reliable measurements and consider limitations on the precision of the data (e.g., number of trials, cost, risk, time), and refine the design accordingly. Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. Use mathematical representations of phenomena to describe explanations. Apply scientific ideas to solve a design problem, taking into account possible unanticipated effects. Promote STEM with Video Connect to Science Displacement is related to buoyancy, and is the physical principle used to find the volume of golf club heads. Archimedes discovered the science principle applied here over two thousand years ago, showing that some very ancient ideas remain valuable even in our modern world. A greater volume allows for a wider range of locations for a club head’s moment of inertia, which is what the USGA is really trying to control, indirectly, by setting limits on volume. Related Science Concepts volume mass displacement weight density Take Action with Students Have students describe the process of determining the volume of irregularly shaped objects by water displacement in a graduated cylinder. If students haven’t carried out this procedure, supply them with graduated cylinders, water, and irregularly shaped objects to allow them to discover this approach. Have students research how weighing a person underwater can be used to find body density and body fat percentage. Ask them to explain how this uses the concepts discussed in the video and the definition of density. One application of the principle of buoyancy is constructing boats that float. While the idea of the buoyant force being equal to the weight of the displaced water is simple, it is much more complicated to determine what shape of a hull will maximize the load a boat can carry without sinking, given a certain amount of material from which to make the boat. While this is a rather complex mathematical problem, a simple look at the shapes of boats might suggest that near optimal shapes have been arrived at empirically (by trial and error). However, a “V” shaped hull, for instance, might have other purposes, such as reducing drag in the water. Have students research this issue, to find what shapes are best for boats, and suggest how this might have been determined. As an inquiry, students might be given a fixed amount of aluminum foil from which to make a boat, and experiment to see what design can support the most weight (such as the number of pennies or counting cubes that can be loaded into the boat before it sinks). SOG: Volume and Displacement (Grades 7–12) 3 Connect to Technology While the volume-measuring process described in the video is not particularly complex, it does rely on the technology of measuring force (i.e., weight, though note that mass is not being directly measured here, as one might infer from the video at 3:00). An electronic, digital scale is being used in the video, while the cartoon of Archimedes at 2:34 shows him using a sort of balance. Take Action with Students Have students brainstorm methods that exist (or new ones they might think of) for weighing objects or for measuring force in general. After this, have them research existing methods. They might start with a resource such as http://www.perryscale.com/evolution-ofweighing-scales.htm. Students might try to make a scale from simple materials using a method they have found or devised themselves. Ask students to define the terms mass and weight to ensure they understand the difference. Weight is often measured as a surrogate for mass, which works because this is almost always done at Earth’s surface, where the acceleration due to gravity is dependably 9.8 m/s/s. Have students do research or brainstorm to find methods of measuring mass that do not involve measuring weight, and which would therefore work in weightless or free-fall (i.e., in orbit) conditions. Connect to Engineering The engineering design process involves identifying problems and finding solutions, usually as part of an ongoing cycle of innovation. The method for finding club head volume discussed in the video has its origins in the distant past, and yet has been engineered to work with modern materials and methods. Archimedes had different background and materials to work with and engineered his own solution at the time. Also, Archimedes is credited with a number of other inventions, which presented their own engineering challenges. Take Action with Students Have students do research to determine a likely way Archimedes might have actually done his experiment. Note that some debate exists about how he may have done this, as it is not detailed in any surviving works of his. Have them replicate the experiment using available materials, as applied to irregularly shaped objects of unknown materials. Have students research and present reports on other inventions by Archimedes, and describe the engineering challenges these presented. Challenge students to create an apparatus for measuring mass without measuring weight. For example, students might test how an object vibrates back and forth on a spring or some other elastic holder and determine the mass based on the period of oscillation. Connect to Math Math, in the form of elementary algebra, is involved in the use of the equation d = m/v (density equals mass divided by volume). This simple equation can be rearranged to solve for one of the three variables. Middle school students without an algebra background might have learned SOG: Volume and Displacement (Grades 7–12) 4 some non-algebraic ways to “get a letter by itself” (one of these involves a triangle divided into the sections, each containing one of the three variables). SOG: Volume and Displacement (Grades 7–12) 5 Also, there are various mathematical formulae for finding volumes of particular shapes, such as cubes, spheres, and cones. None of these is likely to be a good model for an irregularly shaped object such as a golf club head, but it can be an interesting exercise to try to approximate an irregular object with a regular one for which a formula is known. Take Action with Students If students have had algebra, have them rearrange d = m/v to arrive at m = dv and v = m/d. Have students without an algebra background brainstorm to list ways to determine how to solve for one of the variables. Examples might include trying different size numbers for the variables to see if the answer varies in a reasonable way, or perhaps the “triangle” method mentioned above. Have them discuss the pros and cons of non-algebraic methods. Have students brainstorm to think of other relationships among three variables that are of the form x = y/z. Examples might include speed = distance/time or unit price = total cost/amount of item. In each case, discuss the importance of properly rearranging to solve for the variable we want to calculate. Have students examine a club head and estimate the dimensions of a cube, parallelepiped, cone, or some other standard object that might have the same volume. Students should work in separate groups to arrive at their estimates using volume formulae for their chosen figures. Have them compare the results, and record them for use in the Engineering Inquiry. Students might use the concepts from the video to do various calculations. For example, show the segment of the video from 0:48 to 1:00, where 460 cubic centimeters is equated to 28.1 cubic inches. Have students confirm this, given the number of centimeters in an inch (2.54), or alternatively, have them determine the number of centimeters in an inch from the data. Have students calculate the volume in cubic inches of a second example, shown at 3:16 to 3:23. Facilitate ENGINEERING Inquiry Encourage inquiry using a strategy modeled on the research-based science writing heuristic. Student work will vary in complexity and depth depending on grade level, prior knowledge, and creativity. Use the prompts liberally to encourage thought and discussion. Student Copy Masters begin on page 10. Explore Understanding Students will certainly be familiar with the phenomenon of floating, but might not have thought about the fact that a buoyant force must exist to hold an object up against the force of gravity, and that this force is supplied by the surrounding fluid and is equal to the weight of the displaced fluid. If needed, look at sites such as the following for more background: http://www.seaperch.org/article?article_id=313 http://www.pbs.org/wgbh/nova/lasalle/buoybasics.html The method shown in the video for measuring club head volume cleverly but simply exploits the concept, and understanding this method helps students understand Archimedes’ principle itself. Use prompts such as the following to explore what students already know. We know a buoyant force must exist on a floating object because…. This buoyant force is actually exerted by…. SOG: Volume and Displacement (Grades 7–12) 6 The strength of this buoyant force is equal to…. SOG: Volume and Displacement (Grades 7–12) 7 Show the video “Science of Golf: Volume and Displacement.” Continue the discussion of Archimedes’ principle and how the method in the video employs it using prompts such as: When I watched the video, I thought about…. The equal and opposite reaction force to the water pushing up on the club head is…. In the video, the buoyant force is measured by…. In order to determine the volume, in addition to the buoyant force, we must know…. Some possible difficulties or sources of error in determining the volume are…. It is important to be able to determine club head volume because…. Ask Beginning Questions Stimulate small-group discussion with the prompt: This video makes me think about these questions…. Then have groups list questions they have about the challenges that must be surmounted in order to develop a consistent way to measure club head volume. Ask groups to choose one question and phrase it in such a way as to be researchable and/or testable. The following are some examples. Why is water displacement used rather than other methods of determining volume? How can we determine the weight of the water that is displaced by the club head? What is the density of water, what does “density” mean, and could other fluids be used to determine the club head’s volume? How is mass related to weight? How do we calculate the volume of the club head from actually measured data? Are there different methods that would accomplish the same goals? Design Investigations Choose one of the following options based on your students’ knowledge, creativity, and ability level and your available materials. Actual materials needed would vary greatly based on these factors as well. Possible Materials: Allow time for students to examine and manipulate the materials you have available. Doing so often aids students in refining their questions, or prompts new ones that should be recorded for future investigation. In this inquiry, students might use materials such as a container of water, a weighing scale of some sort, and an irregularly shaped object (such as a golf club head) whose volume is to be determined. Safety Considerations: To augment your own safety procedures, see NSTA’s Safety Portal at http://www.nsta.org/portals/safety.aspx. Open Choice Approach (Copy Master page 10) Groups might come together to agree on one question for which they will explore an answer, or each group might explore something different. Students should brainstorm to form a plan they would have to follow in order to answer the question, which might include researching background information. Work with students to develop safe procedures that control variables and enable them to gather valid data. Encourage students with prompts such as the following: Information we need to understand before we can start our investigation is…. We might create a method for determining club head volume by…. The variables used in developing our method might be…. We might test our method by…. To conduct the investigation safely, we will…. SOG: Volume and Displacement (Grades 7–12) 8 Focused Approach (Copy Master pages 11–12) The following exemplifies how students might design a device for determining the volume of an irregularly shaped object such as a golf club head and use it to determine the volume of one or more such objects. 1. After students examine the materials you have available for making a volume-measuring device, ask them questions such as the following to help them envision their investigation. How will we decide how much water to put in the container? How will we weigh the container with water in it? How will we ensure that only the object itself is submerged, and not other parts of the object or apparatus? How will we calculate the volume from our measurements? On what objects might we use our apparatus? What are some other ways we might determine volume that would give us comparative values? 2. Students might now use the apparatus to determine the volumes of the given objects, using the inferred buoyant force, the mass implied by this, and the density of water. We will determine the buoyant force from the before and after submerging weights by…. The units we will use are _____ because…. To adjust our scale’s units, we will…. We need to determine the mass of the displaced water from its weight because…. The density of the water is _____ and it depends on room conditions such as…. Volume differs from mass and density in that…. 3. Students might make comparisons among the values they determined and values available from other methods or that they find in product documentation or specifications. Help them analyze their data using prompts such as the following. The percent error between previous volume estimates to those we determined from water displacement was…. This method is more/less accurate than using water displacement in a graduated beaker or cylinder because…. 4. More advanced students might repeat the experiment with more complex shapes or by using other fluids. They might also try objects with cavities that present challenges such as the existence of air bubbles inside, or compressible objects that change volume under the pressure of water. The objects whose volumes we are determining are more challenging because…. We will attempt to surmount these challenges by…. Our initial volume estimates are more/less accurate than before because…. We could improve our methods by…. To conduct the investigation safely, we will…. Media Research Option Groups might have questions that are best explored using print media and online resources. Students should brainstorm to form a list of key words and phrases they could use in Internet search engines that might result in resources that will help them answer the question. Review how to safely browse the Web, how to evaluate information on the Internet for accuracy, and how to correctly cite the information found. Suggest students make note of any interesting SOG: Volume and Displacement (Grades 7–12) 9 tangents they find in their research effort for future inquiry. Encourage students with prompts such as the following: Words and phrases associated with our question are…. The reliability of our sources was established by…. The science and math concepts that underpin a possible solution are…. Our research might feed into an engineering design solution such as…. To conduct the investigation safely, we will…. Make a Claim Backed by Evidence Students should analyze their data and then make one or more claims based on the evidence their data shows. Encourage students with this prompt: As evidenced by… we claim… because…. An example claim might be: As evidenced by how much closer the measurement of our volume displacement method was to the technical specifications than the geometric method we tried, we claim that our volume displacement method is superior to our geometrically-based methods, because it is likely that superior equipment and expertise on the part of the operators make the values in technical specifications more accurate and reliable than any of our methods. Compare Findings Encourage students to compare their ideas with others, such as classmates who investigated a similar (or different) question or system, or to compare their ideas with material they found on the Internet or in their textbooks or heard from an expert they chose to interview. Remind students to credit their original sources in their comparisons. Elicit comparisons from students with prompts such as: My ideas are similar to (or different from) those of the experts in the video in that…. My ideas are similar to (or different from) those of my classmates in that…. My ideas are similar to (or different from) those that I found on the Internet in that…. Students might make comparisons like the following: My ideas about what constitutes a good system for measuring club head volume are similar to those discussed by presenters in the video and practiced by the USGA. However, I found sources of error not mentioned in the video, such as the dependence of the density of water on temperature. Reflect on Learning Students should reflect on their understanding, thinking about how their ideas have changed or what they know now that they didn’t know before. Encourage reflection, using prompts such as the following: The claim made by the expert in the video is…. I support or refute the expert’s claim because in my investigation…. When thinking about the expert’s claims, I am confused as to why…. Another investigation I would like to explore is…. Inquiry Assessment SOG: Volume and Displacement (Grades 7–12) 10 See the rubric included in the student Copy Masters on page 13. SOG: Volume and Displacement (Grades 7–12) 11 Incorporate Video into Your Lesson Plan Integrate Video in Instruction Bellringer: Show the video with the sound muted as students are getting settled on a day when the class will explore the relationship among mass, density, and volume. Repeat as needed. Have students respond to the following prompt: This video describes how to…. Homework: The video showcases Archimedes, who is one of the greatest, but by no means the only great scientist, mathematician, or engineer of the ancient world. Have students research and do reports on other great scientists of antiquity, with a focus on how their achievements have contributed to our world even now. Using the 5E Approach? If you use a 5E approach to lesson plans, consider incorporating video in these Es: Explain: Many slow motion views of club heads striking balls are shown in the video, for example at 1:06, 3:25, 3:34, and 3:58. These club heads behave in a variety of ways after striking the ball—some twisting right, some twisting left, and some twisting hardly at all. Have students explain what causes these different results, and also explain what the whole issue of measuring club head volume has to do with this. Advanced physics students might be able to use measurements made on the paused video segments to do some degree of quantitative analysis of these events, using the concepts of center of mass, torque, and rotational or moment of inertia. Elaborate: Use the “Eureka” story in the video to start a discussion among students about scientific discoveries made suddenly in unusual circumstances. Ask students to find information about such moments online. This may require some creativity regarding search phrases such as sudden scientific discoveries. Have students debate the extent to which these events are due to chance or luck, or whether they really have background stories involving a lot of preparation and hard work. Connect to … History Archimedes’ scientific contributions are best understood in the context of his time. Have students research historical questions related to Archimedes, his world, and how it affects ours. Some examples: Why might certain kings have been suspicious of those providing their crowns? Does the fact that people took baths mean that homes had running water piped into them? A look at Archimedes’ inventions shows that many of them were weapons—where did he live, who was his country fighting, and why? Archimedes died an untimely death—how and why, and what would have been different if he had lived? We know some things about Archimedes, but not as much as we wish—how was this information recorded, who saved it, and how was any of it lost? Why is there a city in California called “Eureka”? Use Video in as a Writing Prompt Show the part of the video around 2:36, where the cartoon figure of Archimedes is shown dipping a crown and a piece of gold into two containers of water, while these objects hang from a balance, and appear to become unbalanced in the water. Then have students write a short paragraph describing how this action led Archimedes to his revelation. SOG: Volume and Displacement (Grades 7–12) 12 COPY MASTER: Open Choice Inquiry Guide for Students Science of Golf: Volume and Displacement Use this guide to design an apparatus for determining the volume of a golf club head or another irregularly shaped object. Write your lab report in your science notebook. Ask Beginning Questions The video makes me think about these questions…. Design Investigations Choose one question. How can you answer it? Brainstorm with your teammates. Write a procedure that controls variables and makes accurate measurements. Look up information as needed. Add safety precautions. Information we need to understand before we can start our investigation is…. The principle on which our system will be based it…. We will construct any equipment needed by…. The procedure to be used with our equipment is…. We will evaluate or test our system by…. To conduct the investigation safely, we will…. Record Data and Observations Record your observations. Organize your data in tables or graphs as appropriate. Make a Claim Backed by Evidence Analyze your data and then make one or more claims based on the evidence your data show. Make sure that the claim goes beyond summarizing the relationship between the variables. My Evidence My Claim My Reason Compare Findings Review the video and then discuss your results with classmates who investigated the same or a similar question. Or do research on the Internet or talk with an expert. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons. My ideas are similar to (or different from) those of the experts in the video in that…. My ideas are similar to (or different from) those of my classmates in that…. My ideas are similar to (or different from) those that I found on the Internet in that…. Reflect on Learning Think about what you found out. How does it fit with what you already knew? How does it change what you thought you knew? The claim made by the expert in the video is…. I support or refute the expert’s claim because in my investigation…. When thinking about the expert’s claims, I am confused as to why…. Another investigation I would like to explore is…. SOG: Volume and Displacement (Grades 7–12) 13 COPY MASTER: Focused Inquiry Guide for Students Science of Golf: Volume and Displacement Use this guide to determine how to design an apparatus that determines the volume of a golf club or other irregularly-shaped object. Write your lab report in your science notebook. Ask Beginning Questions How can we design a volume-measuring device to measure irregular-shaped objects? Design Investigations Brainstorm with your teammates about how to answer the question. Write a procedure that controls variables and allows you to gather valid data. Add safety precautions as needed. Use these prompts to help you design your investigation. Factors we should take into account in developing a system for determining volume are…. Archimedes’ principle is _____, and we will use it to…. We will standardize use of the device by…. The calculations that are necessary to use the device are…. The objects whose volumes we will determine are…. Other methods for measuring, calculating, or otherwise determining volume include…. To conduct the investigation safely, I need to…. Record Data and Observations Organize your observations using a table such as the following. Determining the Volume of _____ Initial estimated volume using _____ method Volume found by water displacement Volume according to product specifications Percent “error” (initial estimate compared to water displacement) Percent “error” (initial estimate compared to product specifications) Percent “error” (water displacement compared to product specifications) SOG: Volume and Displacement (Grades 7–12) 14 Focused Inquiry Guide continued Ideas for Analyzing Data How did the initial, geometrically estimated volumes compare to the ones determined by water displacement? If you tried objects with known volume based on product specifications, how did the volumes found by geometrical and water displacement methods compare to the known ones? Which of your two methods was more accurate? What are some sources of error in our methods, and how could your accuracy be improved? Make a Claim Backed by Evidence Analyze your data and then make one or more claims based on the evidence shown by your data. Make sure that the claim goes beyond summarizing the relationship between the variables. My Evidence My Claim My Reason Compare Findings Review the video and then discuss your results with classmates who did the investigation using the same or a similar system or with those who did the investigation using a different system. Or do research on the Internet or talk with an expert. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons. My ideas are similar to (or different from) those of the experts in the video in that…. My ideas are similar to (or different from) those of my classmates in that…. My ideas are similar to (or different from) those that I found on the Internet in that…. Reflect on Learning Think about what you found out. How does it fit with what you already knew? How does it change what you thought you knew? The claim made by the expert in the video is…. I support (or refute) the expert’s claim because in my investigation…. When thinking about the expert’s claims, I am confused as to why…. Another investigation I would like to explore is…. SOG: Volume and Displacement (Grades 7–12) 15 COPY MASTER: Assessment Rubric for Inquiry Investigations Criteria Initial question Investigation design Variables Safety procedures Observations and data Claim Findings comparison Reflection 1 point Question had a yes/no answer, was off topic, or otherwise was not researchable or testable. 2 points Question was researchable or testable but too broad or not answerable by the chosen investigation. The design of the While the design investigation did not supported the initial support a response to question, the procedure the initial question. used to collect data (e.g., number of trials, control of variables) was not sufficient. Either the dependent or While the dependent independent variable and independent was not identified. variables were identified, no controls were present. Basic laboratory safety Some, but not all, of the procedures were safety equipment was followed, but practices used and only some specific to the activity safe practices needed were not identified. for this investigation were followed. Observations were not Observations were made or recorded, and made, but were not data are unreasonable in very detailed, or data nature, not recorded, or appear invalid or were do not reflect what not recorded actually took place during appropriately. the investigation. No claim was made or Claim was marginally the claim had no related to evidence relationship to the from investigation. evidence used to support it. Comparison of findings Comparison of findings was limited to a was not supported by description of the initial the data collected. question. Student reflections were limited to a description of the procedure used. SOG: Volume and Displacement (Grades 7–12) Student reflections were not related to the initial question. 3 points Question clearly stated, researchable or testable, and showed direct relationship to investigation. Variables were clearly identified and controlled as needed with steps and trials that resulted in data that could be used to answer the question. Variables identified and controlled in a way that results in data that can be analyzed and compared. Appropriate safety equipment used and safe practices adhered to. Detailed observations were made and properly recorded and data are plausible and recorded appropriately. Claim was backed by investigative or research evidence. Comparison of findings included both methodology and data collected by at least one other entity. Student reflections described at least one impact on thinking. 16