My unit outline on Connections with Galileo consists of four experiments related to the discoveries of Galileo. My teaching method will focus on serving as a guide for my students as they conduct their research. I will focus on the processes of problem-solving, communication, reasoning and proof, representation, and connection within the classroom. I will help my students make connections with the math that we study to other disciplines such as physics, astronomy, and history.
Falling Objects Experiment
Up until Galileo’s time people had accepted the Aristotle’s belief that the heavier an object is, the faster it will fall. Galileo challenged that belief with his falling objects experiment in which he reputedly dropped iron balls of unequal weights from the leaning tower of Pisa.
Goals: To determine if the weight of an object affects its rate of fall (acceleration)
- Students will go to the computer lab to simulate Galileo’s Falling Objects Experiment in which two cannonballs of unequal weights are dropped
- The students will predict which simulated cannonball will fall first and then actually conduct the simulated experiment to determine the results.
- The students will watch a video on the same experiment conducted by a physics professor from the University of Pisa who dropped bottles of water with the same shape but containing different amounts of water from the top of the Leaning Tower of Pisa.
- The students will then conduct the same experiment live dropping containers of water and then a bowling ball and a soccer ball at the same time from the top of the stadium to determine if weight actually affects the rate of fall.
- The students will write a mini-lab report on the experiments they conducted.
- The students will discuss the Law of Falling Bodies. From HOWSTUFFWORKS.com : “A falling body in a vacuum accelerates at the rate of 32 feet, per second (9.8 m/s) during each second that it falls. This acceleration is called the acceleration of gravity, which is expressed mathematically as g.”
- The students will solve math problems to determine the velocity, acceleration, and position of falling bodies on the earth, the moon, Jupiter, and other planets.
- Lab-report on experiment
- Quiz on velocity, acceleration, and position of falling bodies
The Pendulum Experiment
Galileo claimed that one day he became bored during a service at the Cathedral of Pisa and began to watch a swinging chandelier. This led him to experiment with pendulums to determine if the weight of the bob, the height of the release, and/or the length of the string affected the period of the pendulum(the time it take to make one full swing)
Goal: To determine if the weight of the bob, the height of the release, and/or the length of the string affects the period of the pendulum.
- Students will go to the computer lab to simulate Galileo’s Pendulum Experiment using pendulums of different weights, angles, and lengths.
- Teams of students will use the following items to conduct their own pendulum experiment outside to conduct their own experiments: string, cup or small pail with a handle, sand, for weight, a tree limb, stop watch
- Students will write a mini-lab report on the results of their experiments.
- After a discussion about the fact that the square of a pendulum’s period varies directly with its length, students will solve problems related to the pendulum with varying lengths and cycles.
- Lab-report on experiment
- Quiz on the mathematics related to the movement of a pendulum
The Inclined Plane Experiment
- To measure short time intervals with a water clock
- To calculate the acceleration of a rolling ball
- Students will watch the reenactment by an Italian professor of Galileo’s inclined plane experiment on a video
- Student teams will assemble inclined planes and water clocks from materials ordered
- Student teams will pour water into the top of the water clocks that they created
- Student teams will time the ball’s motion down the plane by turning the water clock’s valve on and off
- Student teams will record the time it took for the ball to travel starting at different heights along the inclined plane on a data sheet and then compute the ball’s acceleration from each height using the equation for distance, time, and acceleration ( d = ½ a t2 ).
- Student teams will create posters showing the data they collected and the results of their experiments. This will include graphs related to the experiment. All teams will display their work and a class discussion of the results will be held.
Assessment: Rubric for Students’ Posters for project Grade
In 1609 Galileo first heard of the invention of the telescope and immediately began to make improvements upon it. He used it to make major astronomical discoveries from the mountains of the moon to the moons of Jupiter. His discoveries led him to believe in the Copernican model of the solar system in which the sun rather than the earth was the center of the solar system with all of the planets rotating about it. This led Galileo into serious trouble with the church and eventual house arrest for his beliefs.
- Describe how a reflecting telescope produces an image
- Examine the history of the telescope from Galileo to Hubble
- To build a replica of Galileo’s telescope
- To use the telescopes to examine the planets and stars at night
- To learn more about the development of the telescope by visiting a planetarium
- Students will watch the video 400 Years of the Telescope and answer questions related to the design of a telescope, Galileo’s contribution to the development of the telescope, and the designs and contributions of later telescopes.
- Teams of students will build their own Galileoscopes.
- Students will meet at night with the local astronomy club in order to use their Galileoscopes.
- Students will go to the planetarium in Montgomery to learn more about astronomy
- Students will compute the eccentricity of the elliptical orbit of each of the planets
- Rubric developed for building of Galileoscope
- Journal articles from meeting with astronomy club and from trip to planetarium
- Quiz on ellipses and eccentricity