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 Coasters 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 September 2014 © NextLesson 2014 Rates & Proportions

Teacher Guide

Sound bite for Students: “In the real world, we use unit rates to make comparisons and we display data in charts and graphs to make it easier to read.”

Skills Practiced: Principal Activity (Level 1): - Compute unit rates Step Up Activity (Level 2): - Graph a proportional relationship from a ratio table - Make multi-step measurement conversions - Find the percent of increase

Common Core Math Standards Addressed: Principal Compute unit rates associated with ratios of fractions, including ratios of 7.RP.A.1 Activity: lengths, areas and other quantities measured in like or different units. 7.RP.A.2 Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by 7.RP.A.2.a testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Step Up Identify the constant of proportionality (unit rate) in tables, graphs, 7.RP.A.2.b Activity: equations, diagrams, and verbal descriptions of proportional relationships. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, 7.RP.A.3 gratuities and commissions, fees, percent increase and decrease, percent error.

Differentiation Tips: You can edit any of the activity sheets to: - change the numbers or tasks given (e.g. eliminate some attractions or give the durations in seconds in L1) - add or remove hints for differentiation purposes (e.g. include more specific directions for graphing in L2) - Remove or add examples remove/add questions (e.g. add questions about the slope of the line in L2 or graph additional attractions) - allow students to use calculators and/or online conversion 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 September 2014. Please come back for the most recent updates.

Updated September 2014 © NextLesson 2014 Kings Island

Name: ______

You are a marketing manager working for Kings Island. You are preparing a new advertising campaign focused on the speed of the park’s rides.

Your Challenge: Which attraction best fulfills a rider’s need for speed?

LEVEL 1

The park’s manager has given you the data below. You have the length and duration (distance and time) of each ride. You need to calculate the feet per second, or unit rate, to determine the average speed of each attraction.

1. Calculate each unit rate. Round to the nearest tenth.

Length Duration in Average Speed Attraction Duration (feet) Seconds (feet per second) King Cobra 2219 2:00 Firehawk 3340 2:10 Backlot Stunt Coaster 1960 1:04 Banshee 4124 2:40 Son of Beast 7032 2:20 Flying ACE Aerial Chase 1122 1:30 Diamondback 5282 3:00 Vortex 3800 2:30 Great Pumpkin Coaster 199 0:52

2. Make observations about speed.

a. Compare the lengths to the durations. What do you notice?

b. What predictions can you make about the average speed of a ride based on the length and duration of the ride?

c. Suppose the length and duration of the ride with the greatest average speed is doubled. Estimate how the average speed will be affected.

1 Updated September 2014 © NextLesson 2014 Kings Island

LEVEL 2

When you pitch your ideas to the managers, you want to use a graph to visually display which attraction has the greatest average speed.

3. Construct a ratio table to represent a proportional relationship between time and distance for the two attractions with the greatest average speeds.

Attraction #1: Attraction #2: Time (seconds) Distance (feet) Distance (feet) 0 5 10 15 20

4. Graph the ordered pairs (time, distance) from the tables.

5. Do the plots create straight lines that intersect with the origin? Interpret what this means in regards to proportions.

6. Identify the constant of proportionality for each of the attractions.

7. Compare the steepness of the graphs. What does this mean in the context of your task as a marketing associate?

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Challenge

You realize that thrill-seeking riders are often drawn to the maximum speed of a ride, so you decide to collect additional data for the three attractions with the greatest maximum speed.

Maximum Speed Attraction (miles per hour)

Banshee 68.0 Son of Beast 78.5 Diamondback 80.0

1. Revise your ranking for which attraction best fulfills a rider’s need for speed. How does this additional data change the order? Explain how the maximum speed impacts the average speed. Apply mathematical concepts you have learned and cite evidence from the data to support your response.

2. To go deeper with your analysis and comparison of the attractions’ speeds, you need the quantities to be measured in like units.

a. Convert each maximum speed to feet per second.

b. How much faster is the maximum speed compared to the average speed? Find the percent of increase.

3. Synthesize your findings. Which attraction will be the focus of your campaign? Cite evidence to justify your reasoning.

3 Updated September 2014 © NextLesson 2014 Kings Island

Finale

You could give students one of the following ideas or have them choose themselves.

1. Create a PowerPoint presentation to give to the marketing executives to share your findings on which attraction at Kings Island best fulfills a rider’s need for speed. Be sure to use the data and graph to cite evidence as support and to make recommendations for ideas that can be used in the new advertisements.

2. Design a billboard and a one-page advertisement to run in the local newspaper to persuade people to visit the theme park. Focus on the attraction that best fulfills a rider’s need for speed. Include your own catchy slogan and use the data in a way that will grab a viewer’s attention.

3. Create an infographic flow chart that teaches how to compare rates for the marketing executives to help them understand your interpretation of the data. Think and write like a mathematician and use the tools, language, and examples that worked well for you.

4. You have been asked to speak at Career Day at a local high school. Connect what you have learned about speed to concepts you have learned about in science class. Conduct additional research as needed to analyze how drop heights, forces, and friction also impact speed. Prepare a speech to explain the mathematical and scientific concepts that are helpful to know and understand as a marketing associate working for an amusement park.

5. Conduct research to gather additional data about the amusement park attractions. Create your own real world situation and mathematical problem to be solved using this additional data. Apply concepts related to ratios and proportions to the situation you create.

4 Updated September 2014 © NextLesson 2014 Kings Island

ANSWER KEY LEVEL 1

1. Length Duration in Average Speed Attraction Duration (feet) Seconds (feet per second) King Cobra 2219 2:00 120 18.5 Firehawk 3340 2:10 130 25.7 Backlot Stunt Coaster 1960 1:04 64 30.6 Banshee 4124 2:40 160 25.8 Son of Beast 7032 2:20 140 50.2 Flying ACE Aerial Chase 1122 1:30 90 12.5 Diamondback 5282 3:00 180 29.3 Vortex 3800 2:30 150 25.3 Great Pumpkin Coaster 199 0:52 52 3.8

2. a. Longer rides tend to have a longer duration while shorter rides tend to have a shorter duration.

b. Longer rides tend to have a higher average speed.

c. The average speed will not change at all as you are multiplying the numerator and denominator by the same number.

Updated September 2014 © NextLesson 2014 Kings Island

ANSWER KEY LEVEL 2

3. Attraction #2: Backlot Stunt Attraction #1: Son of Beast Coaster Time (seconds) Distance (feet) Distance (feet) 0 0 0 5 251.1 153.1 10 502.3 306.3 15 753.4 459.4 20 1004.6 612.5

1200

1000

800

600 Son of Beast Backlot Stunt Coaster 400

200

0 0 5 10 15 20

5. Yes; the rides start at zero time and zero distance and then increase a set distance for every five second interval, or proportionally over time.

6. Son of Beast: 50.2 Backlot Stunt Coaster: 30.6

7. Son of Beast is steeper, so it has the greatest average speed. Students should recognize that this would be a good way to advertise high speed rides to thrill seekers.

ANSWER KEY Challenge

Maximum Speed Attraction (miles per hour)

Banshee 68.0 Son of Beast 78.5 Diamondback 80.0

1. Diamondback would be a good candidate as it reaches the highest maximum speed. A higher maximum speed will increase the average speed on a ride, as it will be gaining speed until the max speed and also will drag the average up with its higher velocity.

2. a. Banshee: 99.73 ft/s Son of Beast: 115.13 ft/s Diamondback: 117.33 ft/s

b. Banshee: 287% Son of Beast: 129% Diamondback: 300%

3. Answers will vary. Students could select the ride with the highest percent increase as it would have the most drastic acceleration, or the overall highest average speed or maximum speed.

Job Background

Quick Facts: Advertising, Promotions, and Marketing Managers $115,750 per year

2012 Median Pay $55.65 per hour

Entry-Level Education Bachelor’s degree

Work Experience in a Related Occupation See How to Become One

On-the-job Training None

Number of Jobs, 2012 216,000

Job Outlook, 2012-22 12% (As fast as average)

Employment Change, 2012-22 25,400

What Advertising, Promotions, and Marketing Managers Do Advertising, promotions, and marketing managers plan programs to generate interest in a product or service. They work with art directors, sales agents, and financial staff members.

Work Environment About 24 percent of advertising and promotions managers worked for advertising agencies in 2012. About 16 percent of marketing managers worked in the management of companies and enterprises industry.

How to Become an Advertising, Promotions, or Marketing Manager A bachelor’s degree is required for most advertising, promotions, and marketing management positions. These managers typically have work experience in advertising, marketing, promotions, or sales.

Pay In May 2012, the median annual wage for advertising and promotions managers was $88,590. The median annual wage for marketing managers was $119,480 in May 2012.

Job Outlook Employment of advertising, promotions, and marketing managers is projected to grow 12 percent from 2012 to 2022, about as fast as the average for all occupations. Advertising, promotions, and marketing will continue to be essential for organizations as they seek to maintain and expand their share of the market.