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Rational Roller Coasters

Dive into the world of roller coaster design, exploring the balance between safety and excitement. Learn how engineers use math concepts to create thrilling yet safe rides, and discuss societal challenges related to amusement park safety.

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Rational Roller Coasters

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  1. Rational Roller Coasters

  2. STARTER - Day 1 How do you loop the loop? The infamous loop of a roller coaster adds both fun and entertainment to riders, but a headache for engineers.

  3. THE HOOK - Instant Challenge How high do you have to make the starting point of your roller coaster in order for the marble to "loop-the-loop"? • Design a roller coaster hill and first loop so that the marble can make it successfully through the hill in multiple attempts. • The group that can pinpoint the minimum and maximum height to allow this to work will win!

  4. MATERIALS Loop the Loop Materials in Envelope • 5 ft. foam pipe insulation • Marble • Scissors • Masking Tape • Yardstick • Table (textbooks) You have only 30 Minutes! Go!

  5. STARTER - Day 2 Yesterday we got to design our own roller coasters to loop the loop. We then represented our hills as a linear function in slope-intercept form. Discuss in yours groups WHY is it important for engineers to know the slope, y-intercept, and equation of a roller coaster?

  6. THE BIG IDEA Engineers use knowledge of functions and energy to design roller coasters that are safe and entertaining. While safety and entertainment tend to oppose each other, it is an engineer’s job to find the maximum amount of thrill and safety for each ride.

  7. SOCIETAL IMPACT Name some challenges that are present in our society today that are related to the Big Idea at the city, state and country level? • CITY • STATE • COUNTRY

  8. CITY: SON OF BEAST DEMOLITION

  9. SOCIETAL IMPACT • CityKings Island - After 6 injuries upon opening the Son of Beast, the ride had to take out its 118 foot loop. Eventually, the ride was taken down in 2012. • StateOhio Amusement Parks average almost 4,000 injuries per year related to thrill ride incidents. • CountryFrom 1990-2005, there were 52 deaths caused by thrill rides. The probability that you will get injured on a thrill ride is more likely than getting attacked by a shark.

  10. PROJECT IDEAS • Now that we have learned about functions what type of project do you want to do? • Let’s think of some questions (called essential questions) that we could explore by creating a challenge that would answer our questions. (something that we would like to learn more about) But we must make sure we involve functions and roller coasters!

  11. BRAINSTORMING RULES • No “right” or “wrong” idea • No evaluation • QUANTITY > QUALITY • Write down ALL idea!

  12. ESSENTIAL QUESTIONS Keeping the Big Idea and the math concept in mind... 1. Brainstorm 5 questions (that interest you) that we could explore using or relating roller coaster safety/thrills to algebraic functions. WhiteBoard Brainstorm Time: Individually (3 min) Team (7 min)

  13. ESSENTIAL QUESTIONS Keeping the Big Idea and the math concept in mind... 1. Brainstorm 5 questions (that interest you) that we could explore using or relating roller coaster safety/thrills to algebraic functions. 2. Choose the top idea and please submit it here: Core A: https://todaysmeet.com/MSargoA Core B: https://todaysmeet.com/MSargoB Core C: https://todaysmeet.com/MSargoC Core D: https://todaysmeet.com/MSargoD Brainstorm Time: Individually (3 min) Team (7 min)

  14. CHALLENGE IDEAS Keeping the Big Idea and the math concept in mind... 1. WHAT CHALLENGE would you like to tackle that will attempt to solve our big idea/problem? 2. As a team, come up with 2 ideas and add them to our TODAY’S MEET! Core A: https://todaysmeet.com/MSargoA Core B: https://todaysmeet.com/MSargoB Core C: https://todaysmeet.com/MSargoC Core D: https://todaysmeet.com/MSargoD

  15. TICKET OUT What is one of the ideas that your group came up with for the challenge? Be as specific as possible!

  16. HOMEWORK MRS #13 (due friday) THANKS A VETERAN!

  17. ROLES Please choose a role for each member of your group: 1. Project manager - keeps everyone up to date on what has to be done, may assign jobs if necessary. They also are in charge of making sure everyone gets along and everyone does their fair share. 2. Communicator Specialist - this person will communicate with the teacher if a question can’t be answered in the group and take pictures. 3. Materials Supervisor - this person is in charge of getting the materials and putting them away. You also need to collect all project papers and make sure they are in the folder each day (kept in room) 4. Time Manager - this person makes sure all deadlines are met and gets approval from teacher when a task is complete on the checklist.

  18. Starter - Day 3 Materials Supervisor: Grab your team folder! Project Manager: Grab a rational roller coaster EDP WS from the back circle table. Time Supervisor: Make sure all members are logged onto google classroom as class begins! Communication Manager: Grab 2 pieces of scrap paper for each team member from the back kidney bean table.

  19. THE ESSENTIAL QUESTION Based on the Results, I generated your ideas and there seemed to be common theme safety (materials, design) and thrill (loops, hills, speed) which lead us to this essential question: How can we use different materials and strategies to increase the thrill of our coaster while simultaneously increasing the safety? Great job to Core D for taking all guiding questions and brainstorming this EXACT question!

  20. THE CHALLENGE Congratulations Engineer! You have been selected to design Kings Island newest roller coaster! As with any engineer you will need to consider what makes a roller coaster safe and what makes it exciting. You will use your knowledge of algebraic functions to design your coaster

  21. THE CHALLENGE EDP STEP #1 Materials: • 10 feet of ½’’ vinyl tubing • 1/4’’ ball bearing • 15 twist ties • 5 zip ties • 15 popsicle sticks • 1 foam board • 3 ft. Tape • Graph paper/Scissors • CREATIVE ITEM (approved by Ms. Argo) Model Requirements & Constraints: • Minimum Function Components (thrill) • 1 Linear Function • 2 Non-linear functions • 1 Non function • Stopping Component (safety) • Free Standing Coaster • Continuous Trip ALL ROLLER COASTERS WILL BE GRADED on a safety and thrill scale. HIGHEST AVERAGE WINS! KI is looking for fastest speed at any given point. Final Decisions made by KI REP.

  22. RESEARCH WEBQUEST Each team member will have a time limit to research their topic, take notes, and then will be in charge of reporting back to their team. Then, teams will synthesize their research and fill out EDP #2! • RESEARCHER #1: MATERIALS • RESEARCHER #2: Energy-Motion-Speed • RESEARCHER #3: THRILL • RESEARCHER #4: SAFETY EDP STEP #2

  23. TICKET OUT Do you feel prepared to start making your design tomorrow? If not, what else do you need to do as a team to prepare?

  24. HOMEWORK MRS #13 (due tomorrow)! ROLLER COASTER RESEARCH!

  25. Starter - Day 4 Friday Funny: What do you call a number that can’t keep still? Have MRS #13 on your desk and ready to grade!

  26. MRS #13 Answers 9. 15 10. 15 & 40 11. 2 12. -11/q 13. ABEGH 14. B (about 20 in more) 15. A 16. (-4,-1) (-6,-1) (-4,-7) (-4,-1) • ⅘ or 80% • 1/12 or about 8.3% • x= -7 • j+13 • B • a(b) + a(c) = ab+ac • 80 • B 3

  27. Starter - Day 4 JUST IN FROM MS.FARGO (KI REP)... After some market research, Kings Island has decided that they would like a roller coaster that is both safe, fun, and emphasizes the element of speed. Please adjust your plans accordingly.

  28. INDIVIDUAL BRAINSTORM TAKE 5 minutes to create a sketch of your own model idea that meets all requirements and constraints.

  29. TEAM BRAINSTORM Share ideas with your group and fill out Step 3 of the EDP WS. Then, continue along with the EDP Process and complete steps 4-6. EDP STEP #3-7

  30. FINAL SKETCH • Finalize your sketch of your roller coaster, remember to: • use a scale that is proportional to you foam board 20x30in • label your materials on sketch • include stability measures for safety • think marketing - do you have a name for it?

  31. INDIVIDUAL TICKET OUT What type of function does hill represents? What type of function does a loop represent? What type of function does a corkscrew represent? Are you ready to start building on Monday?

  32. HOMEWORK MRS #14 (due Friday)! ROLLER COASTER RESEARCH!

  33. Starter - Day 5 Grab your team folder and get our your team 2-D model. Where are you in the EDP PROCESS? STEP #5

  34. NEXT STEPS…. Do you have enough track? Can you build your 3-D model from your 2-D blueprint? • Finish 2-D MODEL • scale (1 block=1 inch?) • materials • precision • BUILD 3-D Model • Draw final 2-D Model • PRESENT

  35. NEXT STEPS…. • Finish 2-D MODEL • scale • materials • precision • BUILD 3-D Model • Draw final 2-D Model • PRESENT

  36. INDIVIDUAL TICKET OUT Where are you in the building process? Did you run into any setbacks today?

  37. HOMEWORK MRS #14 (due Friday) ROLLER COASTER PRESENTATIONS (due FRIDAY)

  38. Starter - Day 6 Grab your team folder, supplies, and begin building! TODAY'S GOAL: FINISH 3-D model & begin final 2-D STEPS #5-7

  39. INDIVIDUAL TICKET OUT Are you done with your model? Does it meet all requirements? continuous, safe stop, functions/nonfunctions?

  40. HOMEWORK MRS #14 (due Friday) ROLLER COASTER PRESENTATIONS (due FRIDAY)

  41. Starter - Day 7 Grab your team folder, supplies, and begin building! TODAY'S GOALS • FINISH 3-D model (see rubric) • FINISH 2-D model (see rubric) • BEGIN PITCH! STEPS #5-7

  42. 3-D Design Model Requirements & Constraints: • Minimum Function Components (thrill) • 1 Linear Function • 2 Non-linear functions • 1 Non function • Stopping Component (safety) • Free Standing Coaster • Continuous Trip

  43. 2-D Design TIME & POSITION GRAPH • labeled scale • labeled axis • COLOR CODE • labeled functions f(x), g(x), h(x), etc. • labeled non-functions • labeled non-linear functions • AVERAGE RATE OF CHANGE for each function • Explanation of Linear/Nonlinear Parts • Function Rule for 2 Functions FINAL PRODUCT ON GRAPH PAPER and CARDSTOCK!

  44. PITCH EXPLAIN HOW your roller coaster: • meets the constraints • is thrilling (speed & length of trip) • is safe (stop and trip) • can be marketed (name, claim to fame) EXPLAIN why your coaster should be chosen. 90 SECOND ELEVATOR PITCH!!!

  45. INDIVIDUAL TICKET OUT Are you done with your… 3-D model? 2-D final model? pitch? Who is working on what? Will you be able to finish by the end of class on Thursday?

  46. HOMEWORK MRS #14 (due Friday) ROLLER COASTER PRESENTATIONS (due FRIDAY)

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