SCIENCE AND ENGINEERING OF THE 2014 OLYMPIC WINTER GAMES: Shaun White & Engineering the Half Pipe - Integration Guide (Grades 7-12)
Objective:
Students synthesize science, technology, engineering design, and math concepts involved in designing the Olympic venue called the halfpipe and apply their understanding to other curricular areas.
Introduction Notes:
SCIENCE AND ENGINEERING OF THE 2014 OLYMPIC WINTER GAMES
Shaun White & Engineering the Halfpipe
INTEGRATION GUIDE
Middle School Focus / Adaptable for Grades 7–12
Lesson plans produced by the National Science Teachers Association.
Video produced by NBC Learn in collaboration with the National Science Foundation.
Background and Planning Information............................................................ 2
About the Video........................................................................................................................... 2
Video Timeline ............................................................................................................................ 2
Promote STEM with Video............................................................................. 2
Connect to Science...................................................................................................................... 2
Connect to Technology................................................................................................................ 3
Connect to Engineering............................................................................................................... 4
Connect to Math.......................................................................................................................... 4
Incorporate Video into Your Lesson Plan........................................................ 6
Integrate Video in Instruction...................................................................................................... 6
Make Predictions............................................................................................................. 6
Evaluate........................................................................................................................... 6
Compare and Contrast.................................................................................................... 6
Explain............................................................................................................................. 6
Homework....................................................................................................................... 6
As Part of a 5E Lesson Plan.............................................................................................. 6
Connect to … Trigonometry......................................................................................................... 7
Connect to … Geometry............................................................................................................... 7
Connect to … History................................................................................................................... 7
Connect to … Language Arts........................................................................................................ 7
Connect to … Geography............................................................................................................. 8
Use Video as a Writing Prompt................................................................................................... 8
Connect Video to Common Core ELA.............................................................. 8
Common Core State Standards for ELA/Literacy........................................................................ 8
Facilitate Inquiry through Media Research................................................................................. 9
Make a Claim Backed by Evidence............................................................................................. 9
Present and Compare Findings.................................................................................................... 9
Reflect on Learning................................................................................................................... 10
Inquiry Assessment.................................................................................................................... 10
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Background and Planning
About the Video
Shaun White & Engineering the Halfpipe discusses the challenges of designing and engineering the halfpipe, a snowboarding venue, which is roughly the bottom half of a sloping cylinder. Featured are Shaun White, a 2006 and 2010 Winter Olympics gold medalist in the halfpipe event, and Brianno Coller, a professor of Mechanical Engineering at Northern Illinois University. In the halfpipe event, athletes gain kinetic energy and therefore speed as they lose gravitational potential energy while going downhill. They then slide up the sides of the cylinder, vaulting into the air to do various twists and flips.
Video Timeline
0:00 0:14 Series opening
0:15 1:20 Introducing White
1:21 1:37 Discussing the importance of height
1:38 2:27 Introducing Coller who discusses why height is so important
2:28 2:50 Explaining the relationship of velocity and centripetal acceleration
2:51 3:28 Describing the impact of centripetal acceleration on White
3:29: 3:56 Describing how White could get twice as much air
3:57 4:47 Explaining how engineers lessen the force of centripetal acceleration
4:48 5:11 Summary
5:12 5:23 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.
Promote STEM with Video
Connect to Science
Science concepts described in this video include velocity (including both a speed and a direction), centripetal acceleration, and centripetal force. Also implied but not specifically described is the concept of conservation of mechanical energy, in this case conversion of gravitational potential energy to kinetic energy, and back again. This is hinted at when Brianno Coller says (at 1:17) ”Height is all speed; if you can get that speed, you can get the height,” and the narrator’s comments at 3:07–3:14 are derived from this conservation principle. Finally, momentum is also mentioned by Coller, at 2:04–2:09, with the implication that force changes momentum (essentially Newton’s Second Law of Motion).
Related Science Concepts
• velocity
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• centripetal acceleration
• force
• gravitational potential energy
• kinetic energy
• friction
• momentum
Take Action with Students
• Use the comment at 1:17, about the relationship between speed and height, as a springboard to prompt students for situations in which speed is used to produce height, and vice versa. Depending on students’ prior knowledge, you might also discuss gravitational potential energy (proportional to height) and kinetic energy (proportional to the square of the speed). Ask students how much higher a ball will go if thrown upwards with twice the speed. The answer is four times higher, which may surprise students. This can be explained in terms of energy, but can also be explained by pointing out that the ball thrown upwards twice as fast also spends twice as much time going up before stopping, and doubling both the time and the speed quadruples the height.
• Velocity is defined in the video as speed along with direction, and acceleration as a rate of change of velocity. Using this definition of acceleration, ask students to give examples of different ways to accelerate (e.g., speed up, slow down, or change direction). Ask students what is required to cause an object to accelerate (an outside, unbalanced force on the object). Have students discuss how forces cause acceleration.
Connect to Technology
Olympic events, including snowboarding, have traditionally been scored by judges simply watching the actions of the athletes. However, the subjective nature of this approach raises the issue of not only human error but also of personal biases and even political pressure affecting the outcome. Technology has the potential to reduce or eliminate many of these problems. High-speed video replays of the event are one way to make the scoring more objective. There are also devices that can be attached to the athlete to record his or her motions. There may also of course be drawbacks associated with these ideas.
Take Action with Students
• Have students brainstorm to come up with possible ways in which technology could be applied to scoring an event like snowboarding. Have students share these ideas, and then present arguments, possibly in the form of a debate, for and against the use of these technologies in scoring Olympic events. Finally, have students do research to find what, if any, technological aids will be allowed in scoring the halfpipe or any other events at the 2014 Winter Olympics in Sochi.
• Have students use the Internet to search for ways in which technology might be used to assess snowboarding performances. An excellent example can be found at https://www120.secure.griffith.edu.au/rch/file/b43c2c75-70f0-bcf3-0798-8d1424fc1f40/1/Harding_2010_02Thesis.pdf. Show students this (or a similar) document and ask them to find the answers to questions such as: What technological tools might be
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used to help assess snowboarding performances? What are the pros and cons of applying
these technology tools to judging? Also, use this doctoral thesis (or something similar) to
show how scientific information is presented in the real world. Explore the format of the thesis and discuss the usefulness of the abstract.
Connect to Engineering
The engineering design process uses human ingenuity to draw from science, math, and technology to solve a problem. In this case, the problem is how to design and construct a halfpipe that lessens the force of centripetal acceleration.
Take Action with Students
• Have students work in groups to discuss some of the challenges involved in designing a halfpipe. This may include not only the centripetal acceleration issues featured in the video, but also problems like the need for the sides to be nearly vertical (so the athlete won’t vault completely out of the pipe), the fact that there is actually a fairly flat section joining two quarter-pipes (as evidenced by the 65 foot width being more than twice the 22 foot height, which is approximately the radius), the need for an initial downhill section to gain speed, and the issue of keeping snow stable on a nearly vertical face. After students have brainstormed and come up with their own problems and solutions, have them do research on the Internet to find what the real problems are and how they are addressed.
• A physiological connection to science might interest students. The video discusses the need to reduce the g-force on the athletes, thereby requiring changes to the design of the halfpipe. Students may want to research what the effect of additional gravitational force is on humans, and how many g’s a typical person can tolerate and maintain consciousness or ability to perform adequately in the halfpipe. Students could share their discoveries in writing or via Keynote or PowerPoint.
Connect to Math
The video does not explicitly show the mathematical relationships among height, speed, centripetal acceleration, and radius. However, statements made by Coller and the narrator are based on such relationships. For example, at 3:07, the narrator states, “If Shaun White wanted to get twice as much air, he would have to increase the speed by almost half." From 3:23–3:31, Coller implies that this change in speed would double (from about 2.5 to 5 g’s) the centripetal acceleration. Then, from 4:17–4:31, Coller explains that doubling the radius will cut the force (and thereby the centripetal acceleration) in half. The specific relationships involved here are that height is proportional to the square of the speed, centripetal acceleration is proportional to the square of the speed, and that centripetal acceleration is inversely proportional to the radius.
Take Action with Students
• Show the portion of the video from 3:07 to 3:31. The information that the narrator and Coller give—about “increasing the speed by almost half” resulting in a doubling of both height and centripetal acceleration—is derived from the fact that the latter two variables are proportional to the square of the speed. This is a frequently encountered but often
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poorly understood type of relationship in many fields of study. Have students brainstorm
and discuss such relationships. Most middle or even high school students would be hard pressed to come up with many examples. A good alternative, then, is the following:
o Have students use a compass to draw a circle of arbitrary radius (though an exact number of squares might be a good choice) on a piece of graph paper ruled with a few lines per inch. This circle should be about one-third to one-fourth the width of the paper and roughly centered in it. Have students count the number of squares in the circle, as a whole number, following the rule that a square should be counted if at least half of it is within the circle. (Do not yet mention that this is a measure of the area of a circle—pi times the radius squared.)
o Have students draw a second circle with exactly twice the radius. Before counting the squares in this one, have students predict the number of squares this circle contains.
o Repeat for a circle three times the original radius. Have students predict the radius of a circle which will have twice as many squares in it as the first one they drew, and follow this up with trial and error circles until they achieve almost exactly the desired number of squares. Have students explain how they made their predictions and describe the relationship.
o Mention the formula for the area of a circle, if students have not brought this up already. Have students plot (on graph paper) the number of squares versus the radius, and draw a smooth curve through the points.
• Show the portion of the video, 4:17 to 4:31, that discusses the inverse proportional relationship between centripetal force and radius. Have students work in groups to come up with pairs of variables which are inversely proportional to each other and then bring these forward for class discussion. Basically, these are of the form, the more A, the less B, so that the product of A and B is constant. Examples might include the number of slices you can get from a given loaf of bread and the thickness of each slice, or the time it takes to do a certain job and the number of people working together on the job. Each of these has the property that doubling one variable cuts the other in half. Be careful, though, to test each such relationship to see if it is truly of this type. For example, the relationship between the number of boys and the number of girls in a given size class is inverse, but is not an inverse proportion since the sum of A and B is a constant.
• Show the portion of the video from 3:07 to 3:31. In a roundabout way, the narrator and Coller state that without changes to the halfpipe itself, to double the height (the air), Shaun White will have to suffer double the acceleration (g’s). This relationship is called a direct proportion, in which increasing one variable increases another by the same factor. Have students work in groups to find pairs of variables that are directly proportional to each other that can be shared with the class. Basically, these are of the form, the more A, the more B. Examples might include the amount you pay to fill up your car with gas and the number of gallons the tank will hold, or the distance travelled in a certain time and the speed you’re travelling at.
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Incorporate Video into Your Lesson Plan
Integrate Video in Instruction
As Part of the Day
• Make Predictions Ask students to imagine that the approach to the halfpipe in Sochi (see video 4:52–4:58) was made four times as long, so that the athletes descend four times as far vertically before doing their tricks. Then, ask them to predict what would happen to the athletes’ speed and to the height (amount of air) they could reach (answers: speed is doubled and height is quadrupled, based on conservation of mechanical energy). Next, ask them to predict the centripetal acceleration they would have to endure, assuming the radius remained the original value (answer: four time greater, or about 10 gs). Finally, ask what would have to be done to the radius to bring the acceleration back down to the normal 2.5 gs. (Answer: The radius would have to be quadrupled.)
• Evaluate Students work in groups to list and discuss the pros and cons of further enlargement of Olympic halfpipe events. Discussions should include types of tricks that can be done, safety issues, and construction constraints.
• Compare and Contrast Replay the video segment from 4:08 to 4:28 and then ask students to compare and contrast the halfpipe at the 1998 Olympics with the one in 2014 at Sochi.
• Explain Show the video from 1:40–1:50, pausing on the part showing the dimensions of Sochi’s halfpipe. Then, show the segment from 4:08–4:24, pausing at 4:17, 4:20, and 4:23 so students can get a good look at the cross-sectional shapes of these supposed halfpipes. Ask students what geometrical shape the term halfpipe suggests (half a cylinder), and then ask them if the Sochi halfpipe is actually a half a cylinder (no, because 22 is not half of 65). Discuss reasons with students why the halfpipe has a flat bottom and nearly vertical sides, such as to provide a respite from the action or ensure the athlete doesn’t land outside the pipe.
• Homework Ask students to hand-plot separate graphs of centripetal acceleration, as calculated from a_{c} = v^{2}/r, versus speed (v) and versus r, each using a fixed value of the other independent variable.
As Part of a 5E Lesson Plan
If you use a 5E approach to lesson plans, consider incorporating video in these Es:
• Engage Ask students to brainstorm and think of situations in which they have personally experienced or caused centripetal forces. Take this further by asking how speed and radius factored into their experiences. Examples of experiencing them might include riding in a car on an exit or entrance ramp, various amusement park rides, and skateboarding. An example of causing a centripetal force is whirling a small bucket of water in a circle vertically.
• Elaborate Students research to find the actual mathematical equations for centripetal acceleration and centripetal force, and discuss how they connect to the content of the video. Also have them find the equations for gravitational potential and kinetic energy, and explain how the idea of the sum of these being conserved yields a way to calculate speed from height change, and vice versa. Have groups of students discuss why mechanical energy (sum of potential and kinetic) might not be conserved on Sochi’s halfpipe.
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Connect to … Trigonometry
Angle Measurement Middle or early high school students may be years away from learning trigonometric functions, but the design of the halfpipe presents an excellent opportunity to challenge students with a problem that will later be seen to illustrate the need for the functions sine, cosine, or tangent. The dimensions given in the video (22 feet high, 65 feet wide, and 557 feet long) left out a crucial piece of information: the vertical drop of the pipe along its 557-foot length. This drop is what allows Shaun White to maintain or even increase speed during the event.
• Have students do research to find the slope of a halfpipe (about 18 degrees).
• Have students do a scale drawing (i.e., 557 feet could be 5.57 cm) showing a line segment tilted 18 degrees relative to the horizontal.
• Have them then measure the vertical height (by constructing a perpendicular to a horizontal line; graph paper may be a good medium for this) of the upper end of this line segment and convert back to feet to find how much vertical drop the Sochi halfpipe has.
• Have students divide the height by the length and record this value, and then find the sine of the 18-degree angle on a calculator (the calculation and the sine should be about the same).
• Next, ask them to measure the horizontal length (width) of the triangle and divide by the 557-foot side, and then find the cosine of the 18-degree angle (the calculation and the cosine should be about the same)
• Students then divide height by the width and find the tangent of the 18-degree angle (the calculation and the tangent should be about the same).
• Finally, have students square the two shorter sides, add these together, and take the square root to see if the result matches the longest side, to check the Pythagorean Theorem.
Connect to … Geometry
Puzzler To have students explore geometry in the form of a puzzle or brain-teaser, ask them why they think Shaun White’s trick is called the Double McTwist 1260 (3 ½ times 360 degrees, or three and a half full turns). If no one comes up with this answer, a prompt could be how many degrees are in a circle?
Connect to … History
Sochi’s complex past Located in the Caucasus region, Sochi and its surroundings are geographically located between Europe and Asia, between historically Christian and Muslim regions, and in the path of various invaders throughout history. Have groups of students research the history of the region over the last two millennia and make a timeline of significant events that includes the political entities that controlled the Caucasus at various times.
Connect to … Language Arts
Word roots Centripetal and the related word centrifugal are based on Latin roots. Have students do research on the Internet (a possible site being http://en.wiktionary.org/wiki/Appendix%3AEnglish_words_by_Latin_antecedents) to find the Latin root for centri- and also that for -petal and -fugal. Have students generate lists of English
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words along with their definitions—there are several—that use these roots. Students can introduce words to the class to stimulate a discussion about how each word’s meaning is similar to that of centripetal or centrifugal.
Connect to … Geography
Climate for winter sports Have students research the locations of past winter Olympics and plot them on a map. Google Earth (or something similar) could be used to find the longitude, latitude, and elevation of each site. Ask students what these locations have in common (generally high latitude, high elevation, and mountainous terrain). As further extension, students might research questions such as:
• What are the mean February temperatures at these sites?
• Why are Olympics held in February when January is generally colder?
• How much colder does it get for every 1000 feet increase in elevation?
• Have any southern hemisphere sites been chosen? Could a southern hemisphere site be suitable? What might be some problems with southern hemisphere winter Olympics?
Use Video as a Writing Prompt
• Explain to students that they will use information from the video to write a clear, complete, and concise persuasive essay from Shaun White’s perspective for why the Olympic Committee needs to build a larger radius halfpipe. Show the video segment from 2:12 to 4:47 twice, so that students can take careful notes and get a good understanding of the logical steps leading to that conclusion. Have students include this logic in their argument. Consider having students exchange papers for peer editing before sharing their work with the class.
• After showing the video, ask students to think about how the nature of halfpipe snowboarding might change as the dimensions of the halfpipe are changed. Students can write an essay about their ideas that they share with the class, perhaps using PowerPoint or Keynote to share their findings. After having heard each others’ ideas, groups of students can collaborate on what they think is most likely to occur as the dimensions change.
Connect Video to Common Core ELA
Encourage inquiry via media research. Student work will vary in complexity and depth depending on grade level, prior knowledge, and creativity. Use prompts liberally to encourage thought and discussion.
Common Core State Standards Connections: ELA/Literacy –
RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions
WHST.6-8.1 Write arguments focused on discipline-specific content.
WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.
WHST.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.
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Facilitate Inquiry through Media Research
Show Shaun White & Engineering the Halfpipe, and encourage students to jot down notes while they watch. Groups of students should generate questions from areas of interest in the video. Questions will be narrowed down through class discussion to determine which questions are best explored using print media or online resources. Divide the questions up among the groups. Make print materials available. Each group can 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 their questions. 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 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….
• Halfpipe snowboarding is similar to (or different from) halfpipe skateboarding in that…
Related Internet Resources
• http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html#cf2
• http://www.watchknowlearn.org/Category.aspx?CategoryID=1753
• http://www.math.washington.edu/~morrow/mcm/10756.pdf
• http://physik.uibk.ac.at/04-05/erde/spezial/aufgaben/snowboard+landing_force.pdf
• http://www.real-world-physics-problems.com/physics-of-snowboarding.html
Make a Claim Backed by Evidence
As students carry out their media research, ensure they record their sources and findings. Students should analyze their findings in order to state one or more claims. Encourage students with this prompt: As evidenced by… I claim… because….
Present and Compare Findings
Encourage students to prepare presentations that outline their inquiry investigations so they can compare findings with others. Students might do a Gallery Walk through the presentations and write peer reviews as would be done on published science and engineering findings. Students might also make comparisons with material they find on the Internet, the information presented in the video, or 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 findings are similar to (or different from) those of the experts in the video in that….
• My findings are similar to (or different from) those of my classmates in that….
• My findings are similar to (or different from) those that I found on the Internet in that….
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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 before. Encourage reflection, using prompts such as the following:
• I claim that my ideas have changed from the beginning of this lesson because of….
• My ideas changed in the following ways….
• When thinking about the claims made by the experts, I am confused about....
• One part of the investigation I am most proud of is… because….
• Additional questions I have are…..
Inquiry Assessment
Assessment Rubric for Inquiry Investigations
Criteria |
1 point |
2 points |
3 points |
Initial question or problem |
Question or problem had had a yes/no answer or too simple of a solution, was off topic, or otherwise was not researchable or testable. |
Question or problem was researchable or testable but too broad or not answerable by the chosen investigation. |
Question or problem was clearly stated, was researchable or testable, and showed direct relationship to investigation. |
References cited |
Group incorrectly cited all of the references used in the study. |
Group correctly cited some of the references used in the study. |
Group correctly cited all of the references used in the study. |
Claim |
No claim was made or the claim had no evidence to support it. |
Claim was marginally supported by the group’s research evidence. |
Claim was well supported by the group’s research evidence. |
Presentations |
Groups neither effectively nor cooperatively presented findings to support their stance. |
Groups effectively or cooperatively presented findings to support their stance. |
Groups effectively and cooperatively presented findings to support their stance. |
Findings comparison |
Only a few members of the group constructively argued their stance. |
Most members of the group constructively argued their stance. |
All members of the group constructively argued their stance. |
Reflection |
None of the reflections were related to the initial questions. |
Some reflections were related to the initial questions. |
All reflections were related to the initial questions. |
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