In December 1995, the probe that had been released by the Galileo
spacecraft in July 1995 entered Jupiter' atmosphere. Galileo had traveled
2.3 billion miles since its launch in October 1989. It spent the first 3 years
in the inner solar system. During one flyby in Venus and two flybys of Earth, it
gathered enough velocity from the gravity of the planets to reach Jupiter.
Throughout its long journey, Galileo had been sending data about solar
system back to Earth.
The Galileo Space
Probe orbiting Jupiter
Studying the passage of time and time versus distance, students are better
able to think about the time required to travel the long distances in space. Of
course, the long time required for this type of travel is exactly why it is
difficult for humans to make journeys to the planets. "Are we there yet?" This
query really has meaning for space travel. Remember, Galileo traveled for
more than 6 years one way to get to Jupiter.
Start the lesson by asking the students how far they can go in 8 seconds.
Typically, students answer in a variety of ways. Some may respond with distances
from a few feet to the length of a football field. Others may ask, "Are we traveling
by foot, on a bicycle, or in a car?" Confine the discussion at this point to
travel on foot.
The passing of time is a difficult concept for everyone. In certain settings,
when we are enjoying ourselves, time seems to fly by; in other contexts, time
seems to stand still. To help students develop their sense of time in a neutral
context, ask them to close their eyes. Tell students when to start, and ask them
to raise their hands after exactly 1 minute has passed. Practice with estimating
the passing of time improves performance. Ask students to share the techniques
they used to guess about the length of a minute. Let students practice with time
intervals less than a minute. Conclude this activity by estimating the duration
of 8 seconds.
After students have practiced estimating the passing of time, they
are ready to see how far a teacher can walk in 8 seconds. Give a student a
stopwatch, and have him or her time the teacher walking from the front to the
rear of the classroom. The teacher's rate of walking might be a topic of
discussion. Ask students to discuss factors which might affect the distance traveled by the teacher.
Activity: Walking Speeds
To gather data about their walking speeds, students mark off in a school
hallway or outdoors distances from 25 feet to approximately 100 feet in
increments of 5 feet. Mark the intervals with masking tape. Have each student
carry an index card that has his or her name and lines for recording as many
trials as you intend to do.
A school hallway marked off in 5-foot increments
For this first experiment, everyone walks 100 feet, and the timers tell
students the time each took to complete the distance. Each mission team takes a
turn timing another team.
Line up students and begin the trials. The teacher tells members of a mission
team when to go. Three students should have stopwatches to time each walker. The
time recorded is the median of the three times shown on the timers' watches.
Using multiple timers avoids losing data because of difficulties using a
stopwatch. If sufficient stopwatches are not available for this scheme, have
each timer pick a participant and keep time for that student. Some students may
need to repeat their walks if a timer makes a mistake.
To facilitate making a graph of the class data, have each student record her
or his time on the reverse side of the index card in large writing. Begin by
making a graph of the class data using the students themselves. Ask five
students to come to the front of the room and stand in order according to their
times, from the least to the greatest. Ask another group to come to the front
and put themselves into the ordered group. If the times are the same, the
students should stand behind one another. When all students are in the ordered
group, the graph is complete.
The teacher should record on the chalkboard or an overhead transparency a
frequency table for the "human" graph. When seated again, each student should
make a bar graph of the data in the frequency table.
Students may choose to use the Bar Grapher Tool to graph the data. Alternatively, students may use grid paper to graph the data.
Bar Grapher Tool
Activity: How Far Can I Walk in 8 Seconds?
The next phase of this lesson requires students to collect data about how far
they can walk in 8 seconds. That is, the time allowed for walking is held
constant and the distance varies from student to student. The marked-off, 5-foot
increments are used to measure the distances.
Only one timer is necessary. The teacher is probably the best timer here
because the stop and go commands need to be authoritative.
At the stop command, each student looks at the distance markers and records
the distance walked. Of course, students do not always stop on a mark. They need
to agree on how to estimate the number of feet they have walked beyond a mark,
add that distance to the marked distance, and record their results for the final
Different students can walk varying
distances in 8 seconds
Closing The Activity
Have each mission team record its results on one graph. The graph should show
distance versus time, with distance on the vertical axis and time on the
horizontal axis. Be sure to talk about the point where time is zero and distance
is zero, which is also a potential data point. Connect each point on the graph
(representing how far each student on the mission team walked in 8 seconds) with
(0,0). The steepness of the lines connecting (0,0) to the data pints shows the
average rate of speed, or slope. Use this opportunity to discuss the concept of
slope and to give a formal definition of the slope of a line.
Students may choose to use the Line of Best Fit Tool to graph the data. Alternatively, students may use grid paper to graph the data.
Line of Best Fit Tool
Adapted from Finding Our Top Speed in Mission Mathematics, Linking Aerospace and the NCTM Standards, a NASA/NCTM project, NCTM 1997.