How Many Frogs Live in That Pond?
Yakima WATERS Mini Lesson
Targets and Assessment
WA Science Standards Addressed:
 4-5 SYSC: A system has inputs and outputs.
 4-5 INQD (Investigate): Investigations involve
systematic collection and recording of
observations and data.
 4-5 INQF (Models): A scientific model is a
simplification of an object, event, system, or
process.
 4-5 LS3A: In an ecosystem some populations of
organisms thrive and grow, some decline, and
some do not survive at all.
 4-5 LS2F: People affect ecosystems both
positively and negatively.
Assessments:
 Student performance will be based on completion
of the worksheet.
 Students will also be evaluated at a later time by
using a traditional test that is open note.
Lesson Parameters
Content Area: Biology and ecology.
Overview: Students will learn about what a population is,
about mark-recapture population models, and will
participate in a hands-on activity to determine how many
frogs live in a pond. Students will then examine the
importance of monitoring animal populations.
Grade Level: 5th
Suggested Time: 50-65 minutes
Special Materials:
 About 30-40 plastic frogs.
 Masking tape.
 Guiding worksheet.
 Two buckets.
Learning Outcomes:
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Knowledge:
Students should be able to define what a population is.
Students should be able to describe what causes a population to increase or decrease.
Students should be able to describe what a mark-recapture population model is.
Students should be able to describe what a mark-recapture population model is used for.
Students should be able to identify the parameters of the Petersen-Lincoln population model.
Students should be able to describe why it is important to monitor animal populations.
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Skill:
Students should be able to use the Petersen-Lincoln population model to determine how many frogs
live in the green pond.
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Disposition:
Students should gain an appreciation for the usefulness of math in solving complex problems.
Students should understand that science and math are closely linked together.
Science Concept Background:
The term population refers to a group individuals of the same species that live and interact in the same
location. Within a population individuals interact to reproduce, individuals die, individuals may emigrate
out of the population, and new individuals may immigrate into the population. A mark-recapture
population model is a mathematical relationship between the number of animals re-caught of a given
species and the total population number over two or more sampling sessions. Mark-recapture population
models are used for determining the population number of organisms in a given area. Mark-recapture
population models also allow the determination of survival rates, birthrates, mortality rates, emigration,
and immigration.
The Lincoln-Petersen mark-recapture population model was developed in the early 1900’s, and it was
one of the first population models to be applied to wildlife populations. The basic form of the population
model is displayed below.
N = (n1)(n2)
(m2)
N = The total population number.
n1 = The number of animals caught during the first sampling session.
n2 = The number of animals caught during the second sampling session.
m2 = The number of animals found to be marked during the second sampling session.
“N” is the total population number, which is unknown. The “n1” parameter is the number of animals caught
during the first sampling session. The “n2” parameter is the number of animals caught during the second
sampling session. Finally, the “m2” parameter is the number of animals that are marked that are recaptured
during the second sampling session. It should be noted that there is some error in this equation and many
improvements have been made over the years. Consequently, the population number generated from this
equation should give you a general idea of the population level, not an exact number.
Monitoring the health of animal populations is important for a number of reasons. Populations can be
adversely impacted by many factors including dams, pesticides, construction, habitat fragmentation, hunting,
fishing, and diseases. In fact, many animals like the passenger pigeon have become extinct because of these
factors. Therefore, population information on wild game animals like deer, bears, and turkeys is needed to
ensure the sustainability of the resource for future generations. Similarly, it is vital to understand the
population dynamics of many commercial fish species to ensure that there is a sustainable yield of seafood
that can be harvested for both commercial and recreational fishing. The spread of invasive species can also be
analyzed through population modeling, which will allow for more effective management. Also, population
monitoring is useful for studying the impact of diseases on animal and human populations. Finally, population
monitoring is important for assessing environmental impacts on populations.
Materials:
1. About 30-40 plastic frogs.
2. Masking tape.
3. Guiding worksheet.
4. Two buckets.
Procedure:
Introduce the lesson (3 minutes):
1. Ask students how scientists might determine the number of rainbow trout in a lake.
2. Expand the discussion by bringing up other animals like deer, bear, and moose.
3. Tell students that today they are going to be professional biologists that are going to be tasked with
the job of figuring out how many frogs live in the green pond.
Populations (10 minutes):
4. Divide the class up into table groups of about 2-4 students.
5. Handout the worksheet to the class.
6. Ask students what a population is. Have them discuss their ideas in their small groups.
7. Ask the student groups about the ideas they formulated. Then, go over the correct answer and have
students write down the correct definition on their worksheet.
8. Lead a short discussion on what causes a population to increase and decrease in size, namely
reproduction, mortality, emigration, and immigration. Do not use these vocab words directly, just
describe what they are. For instance, just say that animals could enter the population, instead of using
the term immigration. If you want to use the more complicated vocabulary, plan a separate lesson to
do before this lesson. Have students record the appropriate information on their worksheet.
Mark-recapture population models (8 minutes):
9. Ask the student groups to discuss what they think a mark-recapture population model is.
10. Ask the student groups about the ideas they came up with. Then, go over the correct answer and have
students write down the correct definition on their worksheet.
11. Next, ask students groups about what a mark-recapture population model can be used for.
12. Ask the student groups about the ideas they came up with. Then, go over the correct answers and
have students write down the correct ideas on their worksheet.
13. Teach students about the variables that must be controlled if one is going to use a mark-recapture
population model (i.e. time spent catching and location area). Have students record this info on their
worksheet.
The Petersen-Lincoln mark-recapture model (8 minutes):
14. Tell students that today they are going to use the Petersen-Lincoln mark-recapture population model
that was developed in the early 1900’s. Emphasize that the scientists who developed this model
probably worked most of their life to develop it, and at one time they were just kids also. The point
here is to motivate the students and to connect history to them.
15. Explain the population model’s parameters to the students, making sure to reference the parameter
information that they have on their worksheet already. Also, reference information that they have
learned in math class.
16. Explain to students where they will record the data that they obtain from the green pond frog activity
on their worksheet.
The green pond frog activity (10 minutes):
17. Have students gather around the imaginary green pond area. You should have already placed a bunch
of plastic frogs in a designated area that will represent the green pond.
18. Tell students that they cannot touch the frogs or the pond unless instructed to.
19. Tell students that they will have 1 minute to each capture one frog from the pond (there should be at
least as many frogs as students in the pond at this point in the activity). No student should be allowed
to have more than one frog.
20. Once each student has a frog, instruct the students to mark the frog with a piece of tape.
21. Now have students put there marked frogs in a designated bucket.
22. Count the number of marked frogs out loud with the class and record the data on the board for the n1
parameter. Make sure to re-explain that n1 is the number of frogs that we caught as a group the first
time.
23. Give a student the bucket of frogs and have the student release the frogs back into the green pond.
24. Tell the students to close their eyes and pretend like one day is going to go by really fast. This is when
the frogs are going to “move around.” In other words, some unmarked frogs will come into the pond,
some frogs may leave the pond, some frogs may die, and some new frogs may be born. This will
require imagination on part of the students. Perhaps turn the lights off in the classroom to simulate
nighttime and then turn them back on.
25. While the students have their eyes closed take half of the marked frogs out of the pond and add at
least just as many unmarked frogs back into the green pond. Thus, there are now some marked frogs
and some unmarked frogs in the pond. Alternatively, you could just add new unmarked frogs to the
pond (it just requires more frogs).
26. Instruct the students to open their eyes. Once again, have each student catch only one frog over a 1
minute time period.
27. After each student has one frog, have students put the marked frogs in one bucket labeled “marked”
and put the unmarked frogs in a bucket labeled “unmarked.”
28. Count out loud the number of marked frogs with the entire class. Record the number of marked frogs
on the board for the m2 parameter.
29. Tell the students that we now want to count the rest of the unmarked frogs to find out how many we
caught in total. Count the unmarked frogs out loud with the entire class. Record the total number of
frogs caught on the board for the n2 parameter.
30. Have students return to their table groups to analyze the data.
Data analysis (8 minutes):
31. Instruct students to record all of the data (n1, n2, and m2) on their worksheet.
32. Instruct students to put the data into the equation blanks on their worksheet.
33. Handout a calculator to each student group.
34. Explain that the top two numbers must be multiplied together. Have the student groups carryout this
operation and record the number that they get on their worksheet.
35. Now have the student groups divide the number that they just got by m2 and record the resulting
number on their worksheet.
36. Ask each student group what number they got from the calculation.
37. Write the correct number on the board and explain that this is the estimated total number of frogs
that live in the green pond, not the exact number.
Discussion about the importance of monitoring animal populations (10 minutes):
38. Ask student groups to list three things that could negatively impact a population on their worksheet
and then lead a short discussion.
39. Ask student groups to discuss why it is important to monitor animal populations. Tell students that
they will need to write down two reasons on their worksheet.
40. Ask student groups about the ideas that they came up with and go over the correct information.
Extension(s):
Population knowledge applied to a hands-on population activity at a real pond:
 Students will use their knowledge about populations and models to figure out how many frogs or other
organisms live in a pond by using the Lincoln-Petersen population model.
Have students solve similar mark-recapture population model problems during a math class:
 This is another way of emphasizing the connections between science and math. Math skills that
students have developed throughout the year will be applied through using the Lincoln-Petersen
population model.
Population knowledge applied to the sustainability of seafood:
 Students will be challenged critically to think about the seafood that they and other people consume
each day. A major goal will be to educate students about unbiased seafood guides that they can use
when they go shopping. Case studies of fisheries that collapsed completely should definitely be
highlighted also to give an historical framework (i.e. Atlantic salmon). Information from the Monterey
Bay Aquarium and NOAA Fisheries Division would be very useful for this extension (see Supplements
section).
Teaching Tips:
Students should have had a prior lesson addressing basic population principles. This lesson serves to
reinforce previous knowledge and extend it in an applied manner. Additionally, make sure to explain the rules
and expectations to the students clearly before you start the hands-on activity. The variables that must be
kept constant throughout the sampling process if you are going to use a mark-recapture model (i.e. time
catching and location area) should be explained clearly to the students (step #13). Furthermore, make sure to
explain the components of the Lincoln-Petersen model clearly to the students. Also, make sure to explain the
computing process to the students in a simple straightforward way. Lastly, make sure that the students have
had the proper mathematics background before giving this lesson. This includes fractions and more complex
math like word problems.
Formative Assessment:
The formative assessment component will be accomplished through guided in-class questions that each table
group will discuss. The feedback from students that is obtained verbally in class will be used directly to assess
comprehension of the presented concepts. The lesson can then be adjusted appropriately in class to better
meet the students learning needs. Please see the worksheet or procedure section for the questions.
Summative Assessment:
The summative assessment component will be accomplished through using a worksheet and a follow-up open
note test that will be given at a later time. The worksheet functions to make sure that the students were
actively participating during the lesson, and that they completed the data analysis. The worksheet should only
contain the correct answers, not brainstorming ideas. If desired give each table group a blank piece of paper
so that they can record their brainstorming ideas down on it.
The follow-up test will function to evaluate the students understanding of populations and mark-recapture
population modeling. In addition, there will be an applied population math problem that the students will
have to solve on the test. The test will also work to emphasize the importance of taking good notes and
participating in class. The ultimate goal of the test will be to determine the level of understanding of the
students after the lesson.
Answers for the worksheet and test will be based on the following grading scale:
1. Answer is correct and stated clearly (6pts).
2. Answer is largely correct but may not be stated clearly (4pts).
3. Answer is flawed or completely incorrect (2pts).
4. The answer is missing (0pts).
Supplements:
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NOAA Fisheries (Atlantic salmon population decline example): www.nmfs.noaa.gov.
Monterey Bay Aquarium Seafood Guide: www.montereybayaquarium.org.
References:
Amstrup, S.C., T.L. McDonald, and B.F.J. Manly. 2005. Handbook of Capture-Recapture Analysis. Princeton
University Press: New York City, USA.
Sutherland, W.J. 1996. Ecological Census Techniques: A Handbook. Cambridge University Press: Cambridge,
UK.
By: Jonathan Hegna, Fall 2011, for Lincoln Elementary School