FERRIS WHEEL NUMBERS
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1 FERRIS WHEEL NUMBERS GRADE LEVEL(S) 2-12 LESSON OBJECTIVE Students will use and understand comparison in terms of quantity and measurement: greatest, capacity, maximum, fractional amounts, rate of speed and circumference. BACKGROUND/PRIOR KNOWLEDGE NEEDED Estimation and number sense, rate, and circumference California Math Council (cmc.org) and National Council of Teachers of Mathematics (nctm.org) online resources Statistics from Santa Monica Pier A Century on the Last Great Pleasure Pier by James Harris EDUCATION STANDARDS CA 2 nd Grade: Number Sense 4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole. CA 3 rd Grade: Number Sense 2.1 Solve simple problems involving a functional relationship between two quantities (e.g. find the total cost of multiple items given the cost per unit). CA 4 th Grade: Mathematical Reasoning 2.2 Apply strategies and results from simpler problems to more complex problems. CA 5 th Grade: Number Sense 1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers. CA 6 th Grade: All of the above Standards and Measurement and Geometry 1.1 Understand the concept of a constant such as Π; know the formula for the circumference of a circle. CA 7 th Grade: Measurement and Geometry 1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. CA Algebra I: 5.0 Students solve multistep problems, including word problems involving linear equations and linear inequalities in one variable and provide justification for each step. CA Geometry: 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
2 MATERIALS NEEDED Lesson is tailored by working backwards from the Data Collection and Analysis Questions sheets. The analysis questions sheet needs to be tailored to the grade level and standard addressed and thereby made age/grade appropriate. MOTIVATION Students visit the pier and collect the pertinent numbers related to the Ferris Wheel. DIRECT INSTRUCTION Students will be put in teams of 2 to 3 students. The class will visit the pier to collect the data needed for their class s follow up analysis/problem solving. Frontloading of lessons depends on grade level and standard as do the analysis questions.
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4 Answer Key Data Collection 1. How much does it cost to ride the Ferris wheel? $5 if paying with tickets. (There is an all day pass option but we'll ignore that.) 2. Time how many seconds it takes the Ferris wheel to make one revolution. (How long does it take the wheel to go around once?) 32 seconds 3. Time the duration of the Ferris wheel ride in seconds. It normally goes around six times so around 192 seconds. 4. Time how many seconds there are between rides. In other words, how long does it take passengers to get off and new ones to board? Answers will vary. 5 minutes? 5. Estimate the height of the Ferris wheel in feet. Correct answer is 90 feet. 6. How many cars (also known as gondolas) does the Ferris wheel have? 20 cars 7. What is the maximum number of people allowed to ride in a car? 6 people 8. Estimate how many lights are used to light up the Ferris wheel at night. Correct answer is 160,000 energy efficient LEDs (light emitting diodes) FYI - old wheel had 5392 ordinary bulbs.
5 Ferris Wheel Analysis Questions 1. What is the greatest number of people that can ride the Ferris wheel at once? 2. What is the greatest amount of money the Ferris wheel can generate for one ride? 3. If one-quarter of the seats are empty, how many seats are occupied? 4. If forty percent of the seats are empty, how many seats are occupied? 5. If half the seats are empty, and the others are two-thirds filled, how many people are riding on the Ferris wheel? 6. What is the diameter of the Ferris wheel? What is its circumference? 7. How fast do the passengers on the Ferris wheel travel? Express your answer in feet per second. 8. How fast do the passengers travel in miles per hour? (1 mile = 5280 feet) 9. What is the maximum number of times the Ferris wheel can run in one hour? 10. The new Ferris wheel was purchased for $1.5 million. If it ran at full capacity five times per hour for ten hours each day, how long would it take the Ferris wheel to pay for itself? (Ignore operating costs in arriving at your answer.)
6 Answer Key Ferris Wheel Analysis Questions 1. What is the greatest number of people that can ride the Ferris wheel at once? 20 x 6 = 120 people 2. What is the greatest amount of money the Ferris wheel can generate for one ride? 120 x $5 = $ If one-quarter of the seats are empty, how many seats are occupied? ¼ x 20 = 5 empty seats, 20 5 = 15 seats (or ¾ x 20 = 15) 4. If forty percent of the seats are empty, how many seats are occupied?.4 x 20 = 8 empty seats, 20 8 = 12 seats (or.6 x 20 = 18) 5. If half the seats are empty, and the others are two-thirds filled, how many people are riding on the Ferris wheel? 10 seats x 6 people = 60 people, 2/3 (60) = 40 people 6. What is the diameter of the Ferris wheel? What is its circumference? Diameter = height of wheel = 90 ft C = πd (or 2πr) = 90 x 3.14 = 283 ft 7. How fast do the passengers on the Ferris wheel travel? Express your answer in feet per second. Speed = distance / time = 283 ft/ 32 s = 8.8 ft/s 8. How fast do the passengers travel in miles per hour? (1 mile = 5280 feet) 283 ft /5280 ft = mi, 32 s /3600 s =.0089 hr, speed =.056 /.0089 = 6.3 mph 9. What is the maximum number of times the Ferris wheel can run in one hour? Total time = ride duration + loading time = 3 min + 5 min = 8 min 60 min / 8 min = 7.5 times
7 10. The new Ferris wheel was purchased for $1.5 million. If it ran at full capacity five times per hour for ten hours each day, how long would it take the Ferris wheel to pay for itself? (Ignore operating costs in arriving at your answer.) $600 per ride x 5 rides per hour x 10 hours = $30,000 per day $1,500,000 / $30,000 = 50 days
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