LANGUAGE EXTENSIONS

• TEACH PEERS
Swingers is a great investigation for peer teaching. Have one or more students teach the activity to others. This is an effective way for absent students to be brought up to speed with the concepts.

• MAKE A SWINGING BULLETIN BOARD
Have students make a bulletin-board display outside your classroom that shows the results of the investigation. The poster should include a title, a labeled data display, a definition of pendulum, and a question for readers to think about, such as, “Do long pendulums swing more times or fewer times than short pendulums in 15 seconds?”

• RESEARCH PENDULUM HISTORY
Pendulums have a prominent place in the history of timekeeping. Have students research the following topics to learn about the history:
• Galileo and Christiaan Huygens
• clocks and watches
• metronomes
• Foucault pendulum

Suggest that students prepare a report with diagrams.

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ANSWER:
Shortest to longest, by team number: 4, 5, 2, 8, 6, 3, 1, 7.

 

MATH EXTENSIONS

Measurement Science Stories

No. 24—Student Sheet

 

Measurement Science Stories

No. 31—Student Sheet

• PROBLEM OF THE WEEK
Eight teams of students were experimenting with pendulums to find out how they work. Each team made a swinger of a different length. Their teacher asked them to find out how many times their pendulum would swing. What the teacher forgot to tell the students was how long to count the swings. Below is the data collected by the eight teams. From this information, can you put the pendulums in order from shortest to longest?

 

 

Notes on the Problem. The most direct way to tackle the problem is with a
common denominator. The number 60 is a good choice for this exercise, thus
converting the data into cycles per minute. The data can then be compared
directly. The relationship of length to cycles is inverse.

 

 

• PLAY AN ORDERED-PAIRS GAME
Play the Hurkle Game. Make copies of the student sheet no. 31 called Hurkle Grid.

(Adapted from the book FAMILY MATH (ISBN # 0-912511-06-0), published by EQUALS, Lawrence Hall of Science, Berkeley, CA 94720. © 1986 Regents, University of California at Berkeley.)

Students use ordered pairs of numbers to identify points on a two-coordinate grid. An ordered pair is two numbers enclosed in parentheses, an x-axis value followed by a y-axis value, separated by a comma (8, 2).

The object is to discover the location of the Hurkle hidden beneath one of the intersections on the grid. Two to four students can play. The leader decides on an intersection where the Hurkle is hiding. The other players take turns guessing coordinates, identifying them by their ordered pairs, such as (6, 8). The leader responds to each guess by telling the players the compass direction from their guess to the Hurkle. For example, if the Hurkle is hiding at (6, 8) and the guess is (3, 4), the leader will say, “The Hurkle is northeast.”

The leader should work with his or her Hurkle Grid behind a screen of some kind to mark the Hurkle’s hiding place and the student guesses. Players can share one Hurkle Grid, keeping track of guesses and strategizing together, but each student should make his or her own guess in turn. After each guess the leader should mark the guessed intersection and then give the compass direction from there to the Hurkle. This helps avoid the common mistake of giving the direction from the Hurkle to the guess. Be sure to talk about the best strategy for making guesses.

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MUSIC EXTENSION

• INVESTIGATE METRONOMES AND RHYTHMS
Invite a music teacher, musical parent, or student to bring in a mechanical metronome to show to the class. Ask students to predict what will happen when the sliding mass is positioned farther up the arm and farther down the arm. Compare the number of cycles to that of a pendulum of similar length. If possible, have a volunteer play a tune to demonstrate how it sounds when matched to different speeds of the metronome.

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SCIENCE EXTENSIONS

• INVESTIGATE LINKED PENDULUMS
A double pendulum provides lots of interesting variables to investigate. Have students hang two equal pendulums next to each other and connect them with a soda straw that has been split at each end. They can investigate changing the release positions, or releasing one pendulum after the other. Suggest adding more mass to one pendulum than the other, or trying any other variable that might affect the outcome.

• INVESTIGATE DOUBLE-DECKER PENDULUMS
Have students attach a second pendulum to the paper clip of the first pendulum. They should observe the motion as they change variables in the system, such as mass, length of the different pendulums, and different release strategies.

• INVESTIGATE STRINGLESS PENDULUMS
Replace the pendulum string with some kind of rigid material. Have students compare pendulums made with rulers, sticks, straws, paper-clip chains, or wire. Suggest making two pendulums the same length, one constructed in the usual way and one made with a ruler. Ask students to compare these pendulums. Does something seem peculiar?

What happens to the period of the cycle of the two pendulums as the mass of the bob increases? Students may have to consult a reference to figure out what is going on. [The effective length of the pendulum is determined by the center of mass of the system. In the case of the string pendulum, the center of mass is in the penny at the end. But when using another material, such as a ruler, the center of mass of the system will be somewhere in the ruler. So the effective length of the system is not the actual length.]

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HOME/SCHOOL CONNECTION

Students make second and minute timers with materials they find at home. They work on ways to make their timers accurate. They take a look at a swing as a pendulum.

Make copies of student sheet no. 28, Home/School Connection for Investigation 1, and send it home with students after the first part of this investigation.

 

Measurement Science Stories

No. 28—Student Sheet

 

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