Travel
Time
Lesson
Plan
Overview
In this lesson, students discover the amazing
details of how a migrating bird travels during its annual journey. Travel Time is an extension of the lesson
Osprey Journey, in which students are introduced to “B4”, an osprey bird that
migrates between Minnesota and Mexico each year. In Osprey Journey the students used longitude and latitude
readings to plot the migration path of B4.
In Travel Time, students use the B4 migration map to estimate the
distance traveled by this bird while migrating south. After calculating increasingly accurate estimates of the distance
traveled by B4, the students then determine the relative speed of different
portions of the journey by comparing the distances traveled with the amount of
time elapsed.
|
Suggested Lesson
Sequence |
Please see the Migrations del Mundo module description. |
|
Lesson Level |
|
|
Science
Connections |
·
Students
will investigate the distances that osprey birds migrate. ·
Students
will manipulate
and interpret actual migration data collected by field scientists. |
|
Math Connections |
·
Students
will understand
basic number combinations and the relationships between addition,
subtraction, multiplication and division (including the
distributive property) in order to solve problems using ratio
tables. ·
Students
will compare
varying rates of speed of migrating birds. ·
Students
will investigate
how a change in time or distance affects speed. ·
Students
will use
coordinates to describe locations on a map. ·
Students
will understand
that measurements are approximations. ·
Students
will explore
factors that affect the accuracy of distance approximations. ·
Students
will develop
conceptual understanding of large distances such as hundreds and thousands
of kilometers. |
|
Technology
Connections |
·
Students
will explore the concept and practice of using transmitters as tracking
devices for migrating animals. |
|
Lesson Assessment |
·
Assessment
and Standards Table (Word) |
Materials
Tracking
the Motion slideshow (Powerpoint),
stored in the Osprey Journey folder.
Estimating
Distance activity sheet (Word)
Distance, Time, and
Speed activity sheet (Word)
Completed
Migration Tracking Activity Sheet (from Osprey
Journey lesson)
Note: If students do not have the Migration
Tracking Activity Sheet from the Osprey Journey lesson, you may use the Scientist's
Travel Time Map instead.
Computer with
Internet capabilities (optional)
Globe (optional)
About the slide
show: This slide show is not meant for students to
read through on their own. It is intended to be viewed together, to
outline and illustrate a discussion of the lesson's themes, led by the
teacher. You might have a different student read the text of each slide.
Vocabulary
Note: During this lesson, students
will read passages of text on the activity sheets. Students may be unfamiliar with some of the vocabulary presented
in this lesson. This is done
intentionally, to build reading skills and to spur additional conversations and
discussion about these words and their meanings. Encourage your students to ask about words they may be unfamiliar
with that occur in the readings.
I.
Assessing Prior Knowledge and Contextual Preparation
Because this
lesson is an extension of Osprey
Journey, it is best done immediately
following that lesson. To give students
a little bit different motivation for beginning this lesson, you might mention
that many airline companies offer “frequent flier miles” programs to their
customers. The longer the distance that
a customer flies on the airline, the more free gifts the customer can get. What if there were “frequent flier” contests
for birds? How could we figure out how
far a bird has traveled, or how long it took the bird to travel that distance,
in order to award a prize?
You may also wish
to view the Tracking the Motion interactive
slide show with your students. This
slide show depicts how scientists track the movement of animals using small
radio transmitters mounted on the animal’s body. This will help students to understand the cutting-edge technology
currently being used to understand animal migrations.
II.
Student Activities
After completing
the lesson Osprey Journey, students should have two maps showing the
migration path of the osprey named “B4.”
In this lesson, students will need the map from 1998 to answer the
questions on the Travel Time activity sheets (Estimating Distance
and Distance, Time, and Speed). (If students do not have
these maps from Osprey Journey, they can recreate them using the B4
Travel Time Map.)
Estimating Distance:
Possible student responses to questions
Question
1: The first question on the activity sheet
asks students to make a guess about how far it is from Orono, Minnesota to
Villahermosa, Mexico. Although B4 does
not travel in a straight line between these two cities, having students begin
by estimating this distance should help to give them a point of reference as
they calculate more refined estimates of the distance traveled by B4. Teachers may wish to display each estimate
made by students, and discuss those that appear to be more reasonable than
others. Through the discussion, students should begin to recognize that a large
unit of distance measurement (such as kilometers or miles) will be most
appropriate. Throughout the rest of
this lesson kilometers will be used as the unit of measurement.
Question
2: Problem two helps students to see the
benefit of scales on a map when trying to determine distance. Questions one and two are intended to
motivate the need for more precise methods of calculating distances as described
throughout the remainder of the lesson.
Question
3: Although Osprey B4 does not travel directly
south, Villahermosa is almost directly south of Orono. Question 3 uses this information to help
students calculate a more refined estimate of the distance traveled by B4. It might be helpful to show students a globe
to help them see that the distance between latitude lines stays relatively
constant but the distance between longitude lines changes because they meet at
the poles.
Part (a) of problem three asks students to find how
many degrees of latitude B4 traveled from start to finish. (The “N” stands for North, and B4
traveled 27 degrees latitude.)
Although this might help the students understand that B4 is traveling a
great distance, degrees of latitude alone do not indicate linear distances such
as kilometers.
For
that reason, Part (b) helps students
to convert degrees of latitude to kilometers.
The use of a ratio table in Part (b) is designed to help students find
the number of kilometers associated with 27 degrees of latitude. If your students have never seen ratio
tables it might be helpful to spend some time with them developing
understanding of how ratio tables work, and how they can be used.
A context
that is more concrete may help to make the concept of ratio tables clear for
children. For example, if you know that
1 crate of juice holds 16 individual bottles, and you would like to know how
many bottles there are in 13 crates, you might create a ratio table similar to
the one below as an alternative to traditional multiplication algorithms.
In this table we first double sixteen to find out how many bottles there are in two crates. We then can multiply one crate by ten to find out how many in ten crates. Finally, we add the totals in the corresponding columns together (one, two, and ten crates) to find out how many bottles are contained in thirteen crates.
In problem Part (b) of problem 3, students are given one row
of the ratio table and asked to find the other. Eventually students should be encouraged to determine which
calculations will be most beneficial toward the answer they desire. There are always multiple ways to use ratio
tables to find a final answer. (This
is, in part, what makes ratio tables such a powerful learning tool.) Students should have the following ratio
table:
Part (c) illustrates the power and flexibility of
ratio tables. The most common way to
find the solution is to add the totals in the bottom row that correspond with
the top row answers of 20 and 7 (because 20 + 7 = 27). Hence, the correct calculation is: 2970 Kilometers. However, students may have come up with the
correct solution by adding different columns as well. For example, they might have added the corresponding values for
20 + 2 + 5 = 27. As you can see,
students may not need to use all the values in the table to find the final
answer. Allowing students to share
their ratio table strategies for calculating the distance in part (c) could
lead to interesting discussions about multiplication and its relation to
addition.
In Part (d) of problem three, students are
reminded that although they have now used mathematical calculations to find the
distance, this distance is still only an estimate. Students should be aware of the estimation
“error” in their calculations. For
example, the distance between 45N and 18N (directly south) is not the same
distance as the real distance from Orono to Villahermosa. This is true because this calculation does
not take into consideration the east-west distance between the two cities.
Questions
4 and 5: B4 does not travel in a straight line,
and therefore flies a greater distance on his migration than the
straight line between the two cities.
One reason that B4 might not travel in a straight line between Orono and
Villahermosa is the Gulf of Mexico. If
B4 were to travel straight south he would be over water for roughly 650
kilometers. Even for an osprey, this is a very long distance to travel without
any opportunity to rest on land. Some
birds, however, do attempt and succeed at this feat. See extension #4 below to learn more about the amazing migrations
of such birds.
Part 2. Distance, Time, and Speed
Part Two
of the activities begins the next set of calculations to find an even closer
approximation of the distance traveled by B4 on his migration south. Using original satellite tracking data for
B4 (this data was provided courtesy of The Raptor Center at the University of
Minnesota; www.raptor.cvm.umn.edu/), students
are able to calculate distances for several legs of B4’s southern
migration.
Possible student responses to questions on Activity Sheet Part
Two
Background
information: The table on the activity sheet (re-created
below with the corresponding answers) shows the recorded latitude and longitude
of B4 on a number of occasions during the journey. For purposes of organization, each segment of this journey is
labeled as a “trip” in the table. Although B4 did not make five distinct
“trips” in the way we commonly think of a trip, this notation is used to help
the children distinguish between various stages of his migration. Therefore, each “trip” shows two successive
locations of B4 as recorded by satellite. (Teachers may wish to use the term “leg of the journey” as a synonym for
“trip.”)
To help
complete the table, distance calculators on the Internet can be used to convert
latitude and longitude data into kilometers.
Three websites have been provided for this purpose:
http://jan.ucc.nau.edu/~cvm/latlongdist.html
http://www.csgnetwork.com/longlatdistance.html
Each of
these websites has a calculator that converts latitude and longitude
coordinates into distances. (Only one
of these sites is needed, in case the others are out of order at the time you
do this lesson.) Directions for
submitting the data are included in the websites. To help students understand these directions, the latitude and
longitude of each location is written in the form degrees:minutes:seconds. For example the latitude 44:50:28N means 44
degrees : 50 minutes : 28 seconds north latitude. For more advanced understanding of how these calculations are
made (involving trigonometric relationships), please see the following website:
www.mathforum.com/library/drmath/view/51711.html
|
|
Start of Trip |
End of Trip |
How Many days? |
How Many
Kilometers? |
|
Trip 1 |
September 19
44:50:28N 93:38:49W |
September 22 40:35:20N
96:28:26W |
3
days |
473
Kilometers |
|
Trip 2 |
Sep 22 40:35:20N
96:28:26W |
Sep 24 33:11:17N
96:28:26W |
2
days |
855
Kilometers |
|
Trip 3 |
Sep 24 33:11:17N
96:28:26W |
Sep 26 29:31:23N
97:50:46W |
2
days |
426
Kilometers |
|
Trip 4 |
Sep 26 29:31:23N
97:50:46W |
Sep 28 29:31:23N
97:50:46W |
2
days |
826
Kilometers |
|
Trip 5 |
Sep 28 29:31:23N
97:50:46W |
Oct 1 17:48:47:N 92:31:30W |
3
days |
750
Kilometers |
Question
1: After filling in the table with the values
illustrated above, students use these
calculations to estimate the number of the kilometers traveled by B4. By adding the number kilometers from each
leg of the trip students should arrive at an answer of approximately 3330
kilometers.
Question
2: Problem two asks students why their
calculations in problem six are still only an estimate of the distance traveled
by B4 on his migration south. Possible
answers might include the notion that no bird flies completely in a straight
path. It is likely that B4 stopped
along the way, diverted his flight path, etc.
Question
3: Problem three helps students to understand
that although their answer in problem two is only an estimate, it is the most
accurate estimate that we are able to make with the data available to us (and
better than the other two options). As
an extension to this question, you might ask students what data would need to
be collected to make an even better estimate.
Hopefully students should start to see that by calculating the distance
between smaller and smaller legs of B4’s journey the estimate would become
increasingly accurate.
Question
4: Problems 4 and 5 help students begin to
understand the concept of speed
(velocity). Speed is a ratio that compares distance and
time.
Part (a):
Answers will
vary. Teachers should be sure to
encourage students to share their reasoning about how they determined the speed
of B4 on each trip of the journey.
Part (b):
B4 travels the
slowest during Trip One.
Explanations will vary. Some
students will solve this problem intuitively as they recognize that the total
kilometers traveled (473 vs. 426) is relatively close, but that it took a whole
extra day for B4 to travel that distance during Trip One.
Question
5:
Speed
Rankings (from fastest to slowest):
Day 2, Day
4, Day 5, Day 3, Day 1
Teachers
should look for possible misconceptions that students might generate when
working with the notion of speed. For
example, students tend to assume that a greater distance traveled equates to a
greater speed. This may not be true
after the length of time necessary to cover those distances is factored in.
The two
most difficult trips to place in the correct order are trip 3 and trip 5. During trip 3, B4 travels 426 kilometers in
2 days. During trip 5, B4 travels 750
kilometers in 3 days. In order to
compare these speeds, students may need to think about altering the data so
that time becomes constant in the comparison.
One way to do this is to calculate how far B4 traveled per day during each trip. Another solution method might take advantage
of the ratio tables used earlier to find out how far B4 would travel in 3 days
if trip 3 were extended to three days and B4’s speed remained constant. The table below shows how this might be
done. It can be seen that B4 traveled
faster during trip 5 than he did during trip 3.
|
Kilometers Trip 3 |
426 |
213 (found by one-half of 426) |
639 (found by 426+213) |
|
Days |
2 |
1 (found by one half of 2) |
3
(found by 1+2) |
In
this lesson, students learn about the distance traveled by an Osprey as it
migrates south from Minnesota to Mexico.
Students should be able to calculate distances between lines of latitude
using the ratio of 5 degrees of latitude to approximately 550 kilometers. Students should also be able to explain why
the distances they calculated are only estimates of the actual distance
traveled by B4. The students’ intuitive
understanding of the concept of speed as a ratio of distance and time can also
be assessed using simple variations of the problems and values presented above.
Lesson Extensions for Authentic Assessment
1. Students can calculate the distance
traveled by B4 during the year 1997 and compare this information with the year
1998. For information about the
locations of B4 during his migration in 1997 please see the website www.raptor.cvm.umn.edu/.
2. To explore the concept of speed in more
detail you might have students go outside and run 50 meter and 100 meter dashes
versus running for 30 seconds and 60 seconds.
Collecting data about time for different distances and distances for
different times might help students to explore how change in one variable can
affect change in another variable. This
activity will also provide students with a concrete experience to which they
can refer when trying to compare speeds.
3. Students can explore the relation of
distance to latitude and longitude readings by using maps with scales and
latitude and longitude lines. For
instance they could calculate the distance between the latitudes of 30N and 31N
and then 10N and 11N and then the distance between various longitude lines at
the above latitude locations. These
explorations should help students to see that although the distance between
lines of latitude stays constant, the distance between lines of longitude
changes depending on how far you are from the equator or pole. Students will discover that, at the pole,
the distance between lines of longitude is zero. Therefore, if a student were at the pole, s/he could run “around
the world” (across all lines of longitude) in an instant!
4. Throughout this lesson, students discovered
that the shortest distance between two points is a straight line. Could there be any birds that fly directly
over the Gulf of Mexico when on their migrational path, to shorten the distance
they have to fly? In fact, there
are. Some small warblers are among the
“all-stars” of migration. Some warbler
species will fly directly over the Gulf of Mexico during their migration
between the Yucatan Peninsula of Mexico and the Eastern United States. In order to do so, they must double their weight prior to their
migrational feat. Share this story with
your students and discuss with them the possible advantages and disadvantages
of traveling in a “straight line” when migrating.
5. “Ratio tables” can be extremely helpful as
a computational tool and, in the process, help learners develop rich number
sense. With practice, students can
become highly proficient at using ratio tables for multiplying large numbers as
well as smaller ones. Help develop
students’ ability to construct and solve ratio tables in their own mind by
asking them to calculate simple multiplication tasks without a piece of
paper. As students become familiar with
performing simple ratio table calculations in their head, challenge them to
build their own mastery of this powerful tool by providing progressively more
difficult examples.