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THE CYCLES OF LIFE
MASTER TEACHER Lola Farmer
GRADES 6-8
OVERVIEW
This lesson provides students with an understanding of all the
roles within an ecosystem that keep that system healthy. It also explains
the function of the different organisms within an ecological community and the
specific niche each kingdom of organisms fill. The students will be
exposed to the use of a mathematical modeling of the predator prey phenomenon
that occurs in all ecosystems. It also explains the global abiotic factors
that contribute to the continuity of life.
ITV SERIES
Texas Wild
LEARNING OBJECTIVES
Students will be able to:
*name the types of organisms in a healthy ecosystem
*define the different roles/niches of each kingdom of organisms
*place the animals in the appropriate place on the food web
poster and explain the transfer of
energy
*translate the occurrence of the predator prey phenomenon into a
mathematical formula
*read a table of population coyote/rabbits populations and
explain the trends in data
MATERIALS
Texas Wild video tape
VCR
Remote Control
TV
8 sets of posters and Animals
String/Yarn
Scissors
Labels: Plant, rabbits, hawks, deer, birds, snakes,
grasshoppers, spiders, beetles, ants
VOCABULARY
ecology
"oecos"
ecological community
photosynthesis
herbivores
carnivores
insectivores
scavengers
decomposers
niche
parasites
host
elements
ecologist
evaporation
condense
omnivores
bacteria
fungi
water cycle
oxygen cycle
nitrogen cycle
PREVIEWING ACTIVITIES
Ask the students to turn to a partner and tell each other what
they had for supper the night before. (Have them identify what they ate as
plant or animal.) Ask them to identify whether or not they are herbivores,
carnivores, or omnivores. (Omnivores are animals that eat both plants and
animals.) Ask them to "brainstorm" the plants and animals in the
universal food chain. (The plants convert radiant energy from the sun to energy
for the animals that eat plants, the smaller animals are food for the
larger animals, and man is the top of the food chain.) Have students put
on the labels constructed by the teacher: plants, rabbits, hawks, deer, birds,
snakes, grasshoppers, spiders, beetles, man. Next, have each group of
students get into an circle. Then hand the string to the person wearing
the plant label. Say, "Now, as a group, you decide the appropriate
path the energy will travel with man being the ultimate predator." There
are several ways that this web can be established. Once the students have
completed the web, have a representative from each group explain why they
constructed the web of energy flow the way that they did during the activity.
Pass out the vocabulary worksheet. Arrange students in small groups of
three students. Student A takes definitions
1,4,7,10,13,16,19.
Student B 2,5,8,11,14,17,20. Student C
3,6,9,12,15,18,21. Explain that each student is responsible to acquire the
definitions for their words only and they will be asked to share these
definitions with the other members in their group when the tape ends.
FOCUS FOR VIEWING
To give students a specific responsibility while viewing say,
"You are to identify the categories of organisms discussed in this tape and
how they interact to cause the cycling and recycling of organic matter in this
ecosystem."
VIEWING ACTIVITIES
Begin tape at the beginning where the camera shows
a red flower in the field of flowers. Music is playing. The narrator
is saying, "This is home. Home Sweet Home." Pause tape
where the deer are grooming each other in front of a tree. The narrator is
saying, "Plants and animals of the brush country depend on one
another." Ask, "What is ecology? (The study of an ecosystem.)
What does 'oecos' mean? (Home.) What is an ecological community? (A
habitat with a distinct group of animals and plants.) How do plants and animals
depend on one another?" (The animals eat the plants, the animals eat
the animals, and the plants make O2 for animals. ) Say, "Let's see if
this describes the relationship between animals and plants effectively and
completely."
Resume tape. Pause tape where the tape
shows the prickly pear cactus is behind the red flower in the field. The
narrator says, "That refining process is called photosynthesis."
Ask, "What is the driving force of any ecosystem? (The sun.) What
does the sun do? (It causes the plants to go through the process of
photosynthesis.) What does photosynthesis do?" (Converts the sun's
radiant energy to sugar for the plant to grow or converts the sun's energy to
plant tissue.)
Resume tape. Pause tape where the caterpillar is
chewing on a leaf. The narrator is saying, "To the herbivore, the
world is a great big salad." Ask, "What is a herbivore?"
(Animals that eat plants.)
Resume tape. Pause tape where the coyote is eating the
rabbit. The narrator is saying, "If the grass looks like supper for
the rabbit, the rabbit looks like supper for the some other meat eater like the
coyote, hawk or owl." Ask, "What are carnivores?" (Animals
that eat other animals.) Say, "Name some animals that are categorized as
carnivores." (The coyote, hawk, owl, or any other native carnivore.)
Ask, "If you are a National Wildlife Park Ranger how would you be able to
determine the population fluctuations within the range of your park?"
Lead the class through a discussion about the mathematical formula: Change
in number of rabbits(prey)/ Change in time (2 weeks) = births - deaths. It
works for the coyotes as well and is dependent upon the food supply of rabbits,
so the equation for the coyote population is Change in number of
coyote(predators)/ Change in time (2 weeks) = births - deaths. Explain to
the students that we will continue this predator prey conversation when we
finish viewing the tape.
Formulas:
^ r / ^ t = rabbit births - rabbit deaths
^ c / ^ t = coyote births - coyote deaths
Resume tape. Pause tape where the grasshopper is
still on the spider web. The narrator says, "This culinary habit has
earned them the name insectivores." Ask, "What are animals who
eat insects called?" (Insectivores.) Say, "Name some of these
animals." (Snakes, frogs, mice, birds, spiders.) Ask, "Can
anyone write a predator prey formula for this situation?" (^ i / ^ t
= insect births - insect deaths.)
Resume tape. Pause tape where the narrator has his
hands in pockets of his pants and he is standing in front of a backdrop of
plants. He is saying, "Like our garbage men, they are not appreciated
always." Ask, "What is the niche a vulture fills in the cycle of
organic matter?" (He is a scavenger. He keeps our earth neat
and tidy.) Ask, "What is a niche?" (The role an organism plays in an
ecosystem.) Ask, "How can we determine if an organism is a
scavenger?" (He/It eats dead animals.)
Resume tape. Pause tape where the narrator says
"It pilfers its minerals and water from this host tree." Ask,
"What are parasites?" (Plants and animals that get what they need to
survive from its host.)
Resume tape. Pause tape where ants are working in a
decomposing tree trunk lying on the ground. The narrator is saying,
"In this way, minerals are constantly being recycled." Ask,
"What are the animals called that assist in the recycling of
minerals?" (Decomposers.) Ask, "Can you name some of these
animals?" (Earthworms, dung beetles, carpenter ants, millipedes.) Ask,
"What is their role in cycling the living to the nonliving?" (They
break the organic matter down into its mineral components.) Ask,
"What breaks these mineral components down even further?" (Bacteria
and Fungi.)
Resume tape. Pause tape where the narrator is
saying, "So the cycle goes, starting all over again." Ask, "What
cycle has he just described?" (The water cycle.) Ask, "How does this
work?" (The water evaporates, condenses to clouds, then falls in the form
of rain back to the surface of the earth.)
Resume tape. Pause tape where the narrator says,
"The plant takes what it needs and gives us back the oxygen." Ask,
"What two global cycles provide us with the elements necessary for life to
exist?" (The oxygen/carbon dioxide cycle and the water cycle.)
Resume tape and play until the end. The narrator
says, "Home is what ecology is all about."
POSTVIEWING ACTIVITIES
At the conclusion of the video, the students should have their
vocabulary worksheet completed. Check to see if students have completed
this worksheet and have students share their answers with the other members of
their group.
Pass out the Cycle Graph worksheet and allow the students to
fill out the graph within their groups. Pass out the interdependence handout and
have the students work together in groups to place the individual animals in
their appropriate locations on the chart. In addition to this
interdependence chart, the students could be asked to divide the animals into
different groups: herbivores, carnivores, insectivores, scavengers, decomposers.
Mathematics conversation continued. Say, "Can any of you
read to me what this formula we wrote on the board says?" (The change
in the population of rabbits divided by the change in time is equal to the
number of rabbits born minus the number of rabbits that die or the change in the
population of coyotes divided by the change in time is equal to the number of
coyotes born minus the number of coyotes that die.) Say, "You are going to
be given the opportunity to experience the use of mathematical tools that
accurately express the natural phenomenon that occur in our planet earth."
Hand out the situation sheet and go through it.
ACTION PLAN
Invite a park ranger from one of the local or federally funded
parks in the area to come and speak to the class about the food chain and the
interdependence of organisms in the park in which they work. They can also
discuss the interrelationship these preserved natural environments have with
man.
Take a field trip to a local ecosystem which is kept wild or
as close to wild as your locality will allow and have the students observe and
record the different living organisms they see. Ask them to categorize
these organisms into one of the categories in the cycle graph. This can be
done in a playground using a tree.
EXTENSIONS
Have the students write a short story where they assume the role
of one of the types of organisms in the cycle chart. A carnivore,
herbivore, scavenger, decomposer. Have them imagine what it would be like
to live like one of these animals on any given day of their lives. Have
them compose a short story from this animals point of view.
Tell the students that there was an unusual catastrophe that
has occurred. One day, someone discovered that all of the decomposers had
suddenly disappeared from our world except for in their own country.
Explain that their collection of decomposers was all the world had left.
Ask them to work in groups to come up with a solution to the situation and a
recommendation on how to put the world back in order the way it was originally
designed. Have the groups present their recommendations to the rest of the
class.
Situation:
You are working as a Park Ranger in a National Park in the South
Texas Brush Country. You have been asked to investigate the relationship
between coyotes and rabbits and their multi-dimensional population. The
National Parks and Wildlife Department is setting up a two year study of your
ecosystem. YOu have the use of satellite tracking.
Job Description: The Park Ranger will:
1.Complete the two year
investigation.
2.Compile population data
onto a table.
3.Interpret data & submit
conclusions in writing.
Ask, "What are the goals I must set up in order
to accomplish this task?" Have a conversation about a goal tree.
This gives the students the opportunity to invest in this situation. The
concepts and conversations that show up with the students will probably fall
into the following categories. Acquiring Technological Information, Field
Study Procedures, time Line Development. Guide the students in a
conversation and using a branching diagram, provide a structure that
organizes their thinking using a metacognative tool and guide them through the
designing of a goal tree. Then, have them transfer the information on the
goal tree to the time line.
Say, "suppose we want to study the interaction
between two species, rabbits and coyotes. For simplicity, we'll assume
that rabbits are the coyotes' only food; that rabbits are eaten b nothing but
coyotes; and that rabbits never die of old age, because coyotes kill old rabbits
when they cease being spry. (There are a few, isolated sites for which
this is essentially true.) We'll let r denote the number of
rabbits, c denote the number of foxes, t denotes time, ^ denotes
the change in."
Because we want to study the interaction between rabbits and
coyotes, we're going to look at two simultaneous equations. Remember in
the video lesson, we saw and wrote the equation:
^(population) / ^time = births - deaths.
We'll use the same structure here:
(1) ^(rabbits) / ^time = rabbit births - rabbit
deaths
(2) ^(coyotes) / ^time = coyote births - coyote
deaths"
The "-sign" is read "the difference
between"
^r = (b-d) ^t
^c = (b-d) ^t
The equations represent the same phenomenon.
"The change in population of any species over the amount of time that
passes is equal to the difference between the number of births and the number of
death over that same change in time."
The Rangers have collected the following information, which will provide you
with the necessary parameters to analyze this situation:
1. The area under investigation contains many different animals and plants.
2. At the South Texas Brush Country State Park, the coyote is an abundant
species.
3. Coyotes eat rabbits.
4. Rabbits have an ecological pressure from coyotes with a coefficiency of 0.05
(i.e. the rate ar witch rabbits are killed by coyotes)
5. The rabbit population grows at a rate of 0.4, and coyotes grow at a rate of
0.001.
6. The coyote competes with itself at a rate of 0.1.
7. The rabbits do not compete with themselves.
8. The current rabbit population is 110.
9. The current coyote population is 8.
Following is a dictionary of terms necessary for making sense of the
mathematics behind this situation:
R = Number of Rabbits at a given time.
M = Growth rate of rabbits if there are no coyotes.
K = Rate at which coyotes can kill rabbits.
W = Number of Coyotes at a given time.
G = Growth rate of coyotes if there are rabbits.
D = Death rate of coyotes if there are no rabbits.
Wo = population of coyotes at time zero (i.e., at current
time)
Ro = population of rabbits at time zero.
In our situation, these terms are identifies as follows:
K = 0.05 M = 0.4
G = 0.001 D = 0.1
We will attempt to "model" the predator-pret of rabbits and
coyotes, using mathematics.
The TI-82 provides the following equations to model this behavior:
Rn = Rn-1(1 + M - KWn-1) Wn = Wn-1(1 +
GRn-1 -D)
To best understand that these equations express the same statements as
equations(1) and (2), we will re-write them as follows. (Do the algebra by
multiplying the parenthesis by Rn-1 and Wn-1, respectively.)
The Rabbit Equation:
Rn = Rn-1 + Rn-1 * M - Rn-1*Kwn-1
The Coyote Equation:
Wn = Wn-1 + Wn-1 * G *Rn-1 - D
These models represent the following statements:
"The population of Rabbits at any given time "n" (as
in "now") is equal to the number of rabbits at time
"n-1" (1 unit of time before now), plus the number of new
rabbits since time n-1, minus the number of rabbits killed by coyotes
since time n-1.
"The population of Coyotes at any given time "n" (as in
"now") is equal to the number of coyotes at time "n-1",
plus the number of new coyotes since time n-1, minus the number of
coyotes that died since time n-1.
Our equations can be re-written as follows, using the information collected
so far:
Rn = Rn-1 + Rn-1 (0.4)
- Rn-1 (0.05) Wn-1
Wn = Wn-1 + Wn-1
(0.01)Rn-1 - Wn-1(0.1)
For example, the number of rabbits 1 unit of time after the data was
collected by the Rangers was:
t = 1, R1 = Ro + Ro(0.4) - Ro(0.5)
Wo
(The example for the coyotes can be obtained in the same manner)
Say "You have completed a two year survey on the coyote-rabbit
predator-pret situation. The following data has been collected."
| Time |
Rabbits |
Coyote |
|
Time |
Rabbits |
Coyote |
| 0 |
110 |
8 |
|
25 |
103 |
7 |
| 1 |
110 |
8 |
|
26 |
106 |
7 |
| 2 |
110 |
8 |
|
27 |
109 |
7 |
| 3 |
109 |
8 |
|
28 |
112 |
8 |
| 4 |
107 |
8 |
|
29 |
115 |
8 |
| 5 |
106 |
88 |
|
30 |
117 |
8 |
| 6 |
104 |
8 |
|
31 |
118 |
8 |
| 7 |
102 |
8 |
|
32 |
119 |
8 |
| 8 |
99 |
8 |
|
33 |
119 |
8 |
| 9 |
97 |
8 |
|
34 |
118 |
8 |
| 10 |
95 |
8 |
|
35 |
116 |
8 |
| 11 |
93 |
8 |
|
36 |
114 |
9 |
| 12 |
91 |
8 |
|
37 |
110 |
9 |
| 13 |
89 |
8 |
|
38 |
106 |
9 |
| 14 |
88 |
8 |
|
39 |
102 |
9 |
| 15 |
88 |
8 |
|
40 |
97 |
9 |
| 16 |
87 |
8 |
|
41 |
93 |
9 |
| 17 |
87 |
8 |
|
42 |
89 |
9 |
| 18 |
88 |
8 |
|
43 |
86 |
9 |
| 19 |
89 |
8 |
|
44 |
83 |
9 |
| 20 |
90 |
8 |
|
45 |
80 |
8 |
| 21 |
92 |
8 |
|
46 |
78 |
8 |
| 22 |
95 |
7 |
|
47 |
77 |
8 |
| 23 |
97 |
7 |
|
48 |
77 |
8 |
| 24 |
100 |
7 |
|
49 |
77 |
8 |
| |
|
|
|
50 |
79 |
8 |
The following graph is a plot with the number of population counts on
the horizontal axis and the number of coyotes on the right vertical axis and the
number of rabbits on the left vertical axis.
Ask students to answer the following questions. Conclusion should
be completed in written form.
1. In the graph, you see peaks and valleys in both the graph for the
rabbits and the graph for the coyotes, but the peaks and valleys seem to occur
at different times for the two species.
a. Write a sentence or
two explaining why peaks for
the coyotes come after the peaks for the rabbits.
b. Write a sentence or
two explaining why valleys
for the rabbits come after peaks for the coyotes.
Close this portion of the lesson by asking students to summarize the concepts
they leaned during this activity.
Predator-prey Model
Use sequence graphing on the T1-82 to explore the well known predator-prey
model in biology. Determine the numbers of rabbits and wolves that
maintain population equilibrium in a certain region.
Problem
R = Number of
rabbits.
M = Growth rate of
rabbits if there are no wolves.
K = Rate at which
wolves can kill rabbits.
W = Number of
wolves.
G = Growth rate of
wolves if there are rabbits.
D = Death rate of
wolves if there are no rabbits.
Rn = Rn-1
(1 + M - KWn-1)
Wn = Wn-1 ( 1 + GRn-1
- D)
Procedure
1. Press MODE. Select Seq and the defaults.
press WINDOW >. Select Time FORMAT
and the defaults. Press 2nd (STAT PLOT) and turn off all stat plots.
2. Press Y=. Enter functions to describe the number of
rabbits (Un) and the number of wolves (Vn) for M=.05, k=.001,
G=.0002, D=.03. (Vn-1 and Un-1 are 2nd operations on the
keyboard.)
Un = Un-1(1 + .05 - .001 Vn-1)
Vn = Vn-1(1 + .0002 Un-1 - .03)
3. Press WINDOW and set the initial
population of rabbits (200) and wolves (50), the number of time
periods to plot (400), and the size of the viewing WINDOW.
UnStart = 200 Xmin = 0
Ymin = 0
VnStart = 50 Xmax = 400
Ymax = 300
nStart = 0
Xsci = 100
Ysci = 100
nMin = 0
nMax = 400
4. Press TRACE to plot and explore the
number of rabbits (Un) and wolves (Vn) over time (n).
Determine the maximum and minimum number of each.
5. Enter the program:
PROGRAM : ORBIT
: ClrDraw : FnOff
: PlotsOff :
Dot
: Un(1, 99, 1) ->L1
: Vn(1, 99, 1) ->L2
: Un(100, 198, 1) ->L3
: Vn(100, 198, 1) ->L4
: Un(199, 297, 1) ->L5
: Vn(199, 297, 1) ->L6
: min(L1) - 10 ->Xmin
: max(L1) + 10 ->Xmax
: 10 ->Xscl
: min(L2) - 10 ->Ymin
: max(L2) + 10 ->Ymax
: 10 ->Yscl
: For(I, 1, 99)
: Pt - On(L1(I), L2(I))
: End
: For(I, 1, 99)
: Pt - On(L3(I), L4(I))
: End
: For(I, 1, 99)
: Pt - On(L5(I), L6(I))
: End
6. Execute prgmORBIT, which shows the cycle of the numbers
of rabbits (X axis) and wolves (Y axis) over 297 periods. Use the
free-moving cursor to explore the number of rabbits and wolves.
Name____________________
Definitions Worksheet
Look up the definition or function of each word on this page.
ecology -
"oecos" -
ecological community -
photosynthesis -
herbivores -
carnivores -
insectivores -
scavengers -
decomposers -
niche -
parasites -
host -
elements -
ecologist -
omnivores -
bacteria -
fungi -
water cycle -
condense -
evaporation -
oxygen cycle -
Name____________________________
Fill in the spaces with the following kinds of animals.
Snake
Grasshopper/Insect Earthworm
Raccon
Owl
Mouse
Bird
Deer
Fox
Frog
Follow the arrow from each animal to determine what types of food it eats.
Name_____________________
Cycle Graph
Directions: Fill in the correct name for each category of organism which
appropriately represents the cycle of organic matter
Vocabulary:
photosynthesis
decomposers carnivores
herbivores
insectivores
parasites
bacteria & fungi water &
oxygen cycle scavengers
Updated: April 01, 2008
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