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.

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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.

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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

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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.

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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. Think and write like a mathematician and use the tools, language, and examples that you discovered during your investigation.

3. You have been asked to speak at Career Day at a local high school. Connect the correlations you have found between coaster design features to concepts you have learned about in science class. Conduct additional research as needed to analyze how forces, friction, and energy influence design and construction. Prepare a speech to explain the mathematical and scientific concepts you are required to know and understand as an engineer designing amusement park rides.

4. Design a scale drawing and/or model of a new attraction. Attend to precision and keep a log of the mathematics and reasoning used in your design to present to your team. Include your problems, solutions, work-arounds, and challenges as well as your successes.

5. Conduct research to gather additional data about the g-force of the attractions. Create your own real world situation and mathematical problem to be solved using this additional data. Apply concepts related to scatter plots and the line of best fit to the situation you create.

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Glossary

Drop height - the distance between the Inversions - upside down sections of a ride. highest and lowest point when a roller coaster makes one drop.

Engineer - a person who designs, builds, or maintains engines, machines, or public works (see also Job Background section).

ANSWER KEY LEVEL 1 1. Cedar Point Drop Height vs Max Speed 700 600 500 400 300 200

Drop Height (feet) 100 0 0 20 40 60 80 100 Max Speed (mph)

2. a. The drop height tends to increase. b. They have a positive correlation. c. Magnum XL-200 has a large drop height with a slower speed than expected. 3. Cedar Point Duraon vs Length 02:53

02:10

01:26

Duraon (mins) 00:43

00:00 0 1000 2000 3000 4000 5000 6000 7000 Length (feet)

4. a. The duration tends to increase as the track length increases. b. This also has a positive correlation. c. Disaster Transport has a longer duration than expected for the track length.

Updated July 2014 © NextLesson 2014 Cedar Point ANSWER KEY LEVEL 2 5. Cedar Point Drop Height vs Max Speed 800 600 400 200 0 Drop Height (feet) 0 20 40 60 80 100 Max Speed (mph)

a. y=5.56x+-81.49 b. For every 5.56 feet of drop height, the max speed increases by 1 mph. c. 23.65 d. 474.51 6. Cedar Point Duraon vs Length 02:53

02:10

01:26

00:43 Duraon (mins) 00:00 0 1000 2000 3000 4000 5000 6000 7000 Length (feet)

a. Yes. b. y=0.01x+77.4 For every 0.01 seconds, the ride length increases by 1 foot. b. Answers will vary. It could make sense as you might expect a longer track to have a longer ride length, but the ride could also go much more quickly and take less time.

7. Answers will vary. Students should expect a correlation of higher speeds with more inversions, as well as longer track lengths and ride durations.

1. Red = Busch Gardens Tampa Bay Cedar Point and Busch Gardens Tampa Bay Drop Height vs Max Speed 700 600 500 400 300 200

Drop Height (feet) 100 0 0 20 40 60 80 100 Max Speed (mph)

Cedar Point and Busch Gardens Tampa Bay Duraon vs Length 04:19 03:36 02:53 02:10 01:26

Duraon (mins) 00:43 00:00 0 1000 2000 3000 4000 5000 6000 7000 Length (feet)

Answers will vary. Students could compare the data from each park, & note how Busch Gardens Tampa Bay has an exponential curve for max speed vs drop height.

2. a. Height vs Max Speed: y=6.49x+-191.27 Length vs Duration: y=0.02x+86.39

Answers will vary based on the equations students came up with. They should compare slopes (greater, lesser, approximately the same) and y-intercepts, and recognize that the calculator’s method might provide a more precise line of fit as it takes into account all of the data points. b. 0.668. There is a moderate linear relationship. 0.583. There is a moderate linear relationship.

3. It might be easier to fit a line with fewer data points (you only need 2 points to make a line), but the line of best fit with more data points will give a more reliable prediction as it tends to average out more random error.

4. Answers may vary. Students might conclude that slower rides have longer durations, rides with larger drop heights will have larger max speeds due to gravity, longer rides might last longer, rides with inversions might be longer to have room for the inversions, and go faster to get through the inversion, etc.

Cedar Point

Job Background

Quick Facts: Mechanical Engineers $80,580 per year 2012 Median Pay $38.74 per hour Entry-Level Education Bachelor’s degree Work Experience in a Related Occupation None On-the-job Training None Number of Jobs, 2012 258,100 Job Outlook, 2012-22 5% (Slower than average) Employment Change, 2012-22 11,600

What Mechanical Engineers Do Mechanical engineering is one of the broadest engineering disciplines. Mechanical engineers design, develop, build, and test mechanical and thermal devices, including tools, engines, and machines.

Work Environment Mechanical engineers generally work in professional office settings. They may occasionally visit worksites where a problem or piece of equipment needs their personal attention. Mechanical engineers work mostly in engineering services, research and development, manufacturing industries, and the federal government.

How to Become a Mechanical Engineer Mechanical engineers need a bachelor’s degree. A graduate degree is typically needed for promotion into managerial positions. Mechanical engineers who sell services publicly must be licensed in all states and the District of Columbia.

Pay The median annual wage for mechanical engineers was $80,580 in May 2012.

Job Outlook Employment of mechanical engineers is projected to grow 5 percent from 2012 to 2022, slower than the average for all occupations. Job prospects may be best for those who stay abreast of the most recent advances in technology.