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Knex 78890 - Education Amusement Park Experience Teachers Guide Manual

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LESSON 7
7: E
7: E
XAMINING
XAMINING
S
S
LOPE
LOPE
AS
AS
A
A
R
R
ATE
ATE
OF
OF
C
C
HANGE
HANGE
www.knexeducation.com
OVERVIEW FOR THE TEACHER
M
ost children have ridden on a carousel or merry-go-round and are very eager to share their
experiences. How did the horses move? Did the rider next to them have a horse that followed the
same path? These valuable insights into the operation of the ride will be built upon through the
exploration of the K’NEX Education Carousel Ride model. Like the Ferris Wheel and the Boom Ride,
the Carousel is a circular ride, but its circular motion is in a horizontal plane as opposed to the vertical
plane observed in the Ferris Wheel and Boom Ride.
The Carousel also introduces a more sophisticated gearing system in that it is not only responsible
for moving the ride in its circular motion, as is the case with the Ferris Wheel and the Boom ride, but it
is also responsible for making the “horses” or “animals” in the Carousel menagerie travel in the up and
down motion associated with the ride. Students will be asked to investigate the famous question about
whether or not riders on the outside row of horses move faster or slower than riders on the inside row.
Most students will have a preconceived notion as to the answer to that question. A unique mathematical
connection is made here to slope, with the intent that students begin to understand that slope is more
y
2
- y
1
x
2
- x
1
than
, that it has a much deeper meaning as a measure of the rate of change. In this case
slope will be a measure of the speed of the riders on the Carousel.
REVIEW
Your students will be more successful if they have an understanding of the following concepts and
vocabulary:
• Distance traveled: Total length of the path traveled by a person or object, which can be on either a
curved or straight path.
• Speed: Rate of change where a measured distance is compared to a unit of time.
• Slope: Rate of change which measures how one variable changes as another changes, typically in
algebra:
Change in y values
Change in x values
ACTIVITY 1: MOVING FASTER WHERE?
PROCESS
Whole Class
1. Encourage the students to discuss their experiences of riding on a carousel compared to, for
example, a roller coaster. Ask them to describe the features associated with a carousel, such as
the circular and vertical motions, the artistic design of the overall structure, including the horses,
and the music. Discuss the fact that, although carousels are not nearly as thrilling as roller coasters,
their motions are just as complex and rely on many of the same concepts from physics that are
associated with other rides.
2. Explain that in this lesson they will build the K’NEX Education Carousel Ride, (or use a previously
built model,) to investigate the following questions:
a. Do the horses on the inside and outside of the ride move at the same linear speed?
b. How does the computed slope of the graph of distance traveled versus time compare with the
speed of the riders?
… 46 …


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