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Real World Performance Tasks Cedar Point Real World Performance Tasks Real World Real Life, Real Data, Real-Time - These activities put students into real life scenarios where they use real-time, real data to solve proBlems. In the Relationship Status series, we use data from theme parks and update our data regularly. Note - some data has been rounded or simplified in order to adjust the math to the appropriate level. Engaging Relevant – Students today are familiar with and enjoy amusement park rides, making these activities very relevant to children’s everyday lives. To pique their interest further, try asking the Your Challenge question to the class first. Authentic Tasks - Through these activity sheets students learn how the amusement park industry works and are prompted to form opinions and ideas about how they would solve real life proBlems. A glossary is included to help them with the unfamiliar terms used. Student Choice - Each set of activity sheets is available in multiple versions where students will do the same activities using data for different amusement parks (e.g., Busch Gardens, Hershey Park, Six Flags, etc.) You or your students can pick the location that most interests them. Modular Principal Activity - The activity sheets always start with repeated practice of a core skill matched to a common core standard, as set out in the Teacher Guide. This principal activity (or Level 1 as it is labeled to students) can Be used in isolation. This should generally take around 10-15 minutes. Step Up Activity - For the Level 2 questions, students are required to integrate a different skill or set of skills with increasing complexity. The additional skills used to answer these questions are set out in the Teacher Guide. This should generally take around 20-30 minutes. Challenge - This is designed to require critical thinking skills and stretch students to reason with math and data to come to conclusions. They are matched up with one of the Common Core Standards for Mathematical Practice. These activities work well with students in pairs or small groups where they can discuss the math. Cross-Curricular Activity - Every activity sheet also includes a finale that you can use to extend the math lesson into another suBject (usually ELA). These could Be assigned in a second lesson or for homework. Customizable All of the activity sheets are provided in Word so that they can Be differentiated to add remove or edit questions or even add space for students to show their work. Suggested customizations for each activity sheet are given in the Teacher Guide. Community We would love you and your students to tell us about your experience. Join the conversation on Twitter starting your tweet with @nextlesson and using #Coasters. Updated July 2014 © NextLesson 2014 Scatter Plots Teacher Guide Sound bite for Students: “In the real world, we use graphs to model relationships between quantities so that it is easier to investigate patterns and interpret the data.” Skills Practiced: Principal Activity (Level 1): - Construct and interpret scatter plots Step Up Activity (Level 2): - Draw and interpret a line of Best fit Common Core Math Standards Addressed: Construct and interpret scatter plots for Bivariate measurement data to Principal investigate patterns of association Between two quantities. DescriBe patterns 8.SP.A.1 Activity: such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Know that straight lines are widely used to model relationships Between two quantitative variables. For scatter plots that suggest a linear association, 8.SP.A.2 Step Up informally fit a straight line, and informally assess the model fit By judging the Activity: closeness of the data points to the line. Use the equation of a linear model to solve proBlems in the context of 8.SP.A.3 Bivariate measurement data, interpreting the slope and intercept. Differentiation Tips: You can edit any of the activity sheets to: - change the numbers or tasks given (e.g. construct one scatter plot in L1 for the students and ask them to simply interpret it) - add or remove hints for differentiation purposes (e.g. provide a scale for the plots in L1, include terminology for students to use when describing the associations in L1) - remove/add questions (e.g. eliminate the data in L2 relating to inversions) - encourage students to create scatter plots in Excel or use graphing calculators Due to school paper restriction, the spacing provided is only for answers. However, you could modify the spacing to add room for work if desired. Updates: At NextLesson we strive to engage students with data that is real and real-time. This lesson uses data as of July 2014. Please come Back for the most recent updates. Updated July 2014 © NextLesson 2014 Cedar Point Name: ________________________________ You are an engineer working for a company that designs rides for amusement parks. You are investigating the construction of various attractions at Cedar Point. Your Challenge: How do the thrill features of a ride’s construction influence the design process? LEVEL 1 You decide to begin your investigation with two of the features that thrill riders often seek. 1. Construct a scatter plot that shows the relationship between the maximum speed and the drop height. Max. Drop Attraction Speed Height (mph) (feet) Millennium Force 93 299 Maverick 70 328 Wicked Twister 72 206 Magnum XL-200 72 639 Disaster Transport 40 50 2. Interpret the scatter plot. a. What tends to happen as the maximum speed increases? b. Describe the association between the two quantities. c. Identify any outliers, gaps, or clusters. 1 Updated June 2014 © NextLesson 2014 Cedar Point Next, you examine two of the features that are considered at the start of any design project: length and duration of the ride. 3. Construct a scatter plot that shows the relationship between the track length and the duration of the ride. Length Attraction Duration (feet) Millennium Force 6,595 02:20 Maverick 4,450 02:30 Wicked Twister 675 00:40 Magnum XL-200 5,106 02:00 Disaster Transport 1,932 02:32 4. Interpret the scatter plot. a. Describe the association between the two quantities. b. How does this relationship compare to the relationship between speed and height? c. Identify any outliers, gaps, or clusters. 2 Updated July 2014 © NextLesson 2014 Cedar Point LEVEL 2 Now that you have found relationships between some of the design features, you want to make predictions to help the design team make decisions about new construction. You know a line of best fit can be used to estimate and predict and you decide to draw one on a graph and write an equation to calculate the best fit. 5. Draw a line of best fit in the scatter plot that shows the relationship between the maximum speed and the drop height. a. Write an equation of the line of best fit. b. Interpret the slope of the line of best fit. c. Predict the maximum speed with a drop height of 50 feet. d. Estimate the drop height needed for a maximum speed of 100 miles per hour. 6. Draw a line of best fit in the scatter plot that shows the relationship between the track length and the duration of the ride. a. Is it possible to draw a line of fit for the data? If so, write an equation of the line of fit and interpret the slope. b. Is it reasonable to use the scatter plot to predict the duration of a ride based on the length of the track? Explain. 7. You have also gathered data on the number of inversions each ride has. Relate this data to the other variables. Do you expect to find any correlations? Attraction Inversions Millennium Force 0 Maverick 2 Wicked Twister 0 Magnum XL-200 0 Disaster Transport 0 3 Updated July 2014 © NextLesson 2014 Cedar Point Challenge Before presenting your findings to the park’s management team, you decide to expand your investigation to include attractions from another park, Busch Gardens Tampa Bay. Max Speed Drop Height Length Attraction Duration Inversions (mph) (feet) (feet) Cheetah Hunt 60 130 4,429 3:30 1 Gwazi 51 92 3,508 2:30 0 Kumba 60 135 3,978 2:54 7 Montu 60 128 3,983 3:00 7 Sand Serpent 28 46 1,214 1:50 0 Scorpion 41 45 1,818 1:30 1 1. Revise your scatter plots to include the data from the attractions at both theme parks. Use another color to represent the Busch Gardens Tampa Bay. What do you notice? 2. Use a graphing calculator to find the line of best fit for each scatter plot. a. Differentiate between your equation of the line of fit and the calculator’s line of best fit. b. Identify and interpret the correlation coefficient. 3. Explain the difference between estimating the line of best fit with more data points rather than with fewer data points. 4. Synthesize your findings to explain how different features of a ride’s construction may influence the design process. Think about their relationships with each other and how they influence each other. 4 Updated July 2014 © NextLesson 2014 Cedar Point Finale You could give students one of the following ideas or have them choose themselves. 1. Create a presentation to give to your design team to share your findings on how different features of a ride’s construction may influence the design process. Be sure to use the data trends to cite evidence as support. 2. Safety is a major concern for the engineering design team. Create an infographic to suggest appropriate maximum speeds to consider in relation to other features for a new ride you are designing.
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