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Lesson plan · Grade 11 · 50 minutes

Ferris Wheel

I can model a Ferris wheel ride with a sinusoid, read amplitude, midline and period from it, and explain radians as arc length on the unit circle.

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Standard
F-TF.A CCSS-Math
F-TF.B CCSS-Math
F-TF.C CCSS-Math
Shape
Explore first
Grouping
Pairs on devices, with whole-class pauses.
You need
The tool on the projector and on student devices. Graph paper. A string and a round lid for the radian demo.
Tool
curioclass.org/tools/ferris-wheel/
  1. Hook5 min
  2. Explore15 min
  3. Make sense12 min
  4. Apply13 min
  5. Exit check5 min

Before class

  • Open Ride with the defaults: radius 15 m, hub 18 m, one turn in 40 s, boarding at the bottom.
  • Note the equation for the defaults: h(t) = 18 + 15 sin(2πt / 40 − π/2).

Hook 5 min

  1. Press Play and let the graph grow for one full turn. "What shape is this graph? Have you seen it anywhere else?"
  2. "Anything that repeats can be modeled this way: tides, sound, daylight. Today, a Ferris wheel."

Explore 15 min

  1. Pairs press Pause and drag the car a quarter turn. The graph dot jumps to t = 10 s, h = 18 m. Then they drag the dot to t = 30 s.
  2. Pairs change one slider at a time and ride again, recording which part of the graph changed: radius, hub height or time for one turn.
  3. Pairs try Board at each position and both Turn directions, and use Keep this graph to compare up to 3 curves.
  4. "Why do Bottom-counterclockwise and Bottom-clockwise give the same graph, but Right side does not?"

Make sense 12 min

  1. On the board, connect each slider to the equation: hub height is the midline, radius is the amplitude, time for one turn is the period.
  2. Switch to Unit Circle. Press One radian: a radius-length rod bends onto the rim. Wrap the string around the lid to show the same thing.
  3. Press Unroll the arc. "The height is sin θ. Why does about 6.28 of these fit around?"
  4. Turn on Show cosine. The identity line always reads 1.000. "Why must sin² θ + cos² θ = 1?"

Apply 13 min

  1. Pairs open Match and work through the target graphs. Check accepts any wheel within 0.5 m, so equivalent wheels count.
  2. Pairs who finish open Real Wheels and compare the London Eye with Chicago 1893. "The London Eye moves at about 0.21 m/s. Why can you barely feel it move?"

Exit check 5 min

On a card: "A wheel has radius 20 m, a hub 25 m high, turns once in 60 s, and you board at the bottom. Write h(t) and give the highest and lowest heights." Then: "Why is 18 + 15 sin(2πt / 40 − π/2) the same as 18 − 15 cos(2πt / 40)?"

Support and stretch

  • Support: change only one slider at a time and write the equation after each change.
  • Support: use Step π/6 and Step π/4 to read exact values.
  • Stretch: turn on Show sideways distance and explain the live check x² + (h − D)² = r².
  • Stretch: "A radian is about 57.3 degrees. Where does that number come from?"

Short on time

  • Ride with one slider at a time (10 min).
  • One radian in Unit Circle (5 min), then the exit card (5 min).

How each button works is in the teacher notes. From Curio Class, free under CC BY 4.0: change it, print it, share it.