Lesson Plan

Hoofin' It! - The Bean Counters: Mark-Recapture

Grade Level:
Fifth Grade-Twelfth Grade
Mathematics, Wildlife Biology, Wildlife Management
30 - 45 minutes
graphing, observation


The lesson plans in our 'Hoofin' It!' unit help students learn the basics of animal classification and what characteristics are common to mammals, mainly through studying Dall sheep.

Lesson fifteen explores how scientists estimate populations.


Students will be able to estimate population size through sampling rather than with a complete count, and be able to compare different methods.


The "Hoofin' It!" unit explores the natural resource management of Dall sheep in the national parks of northwest Alaska. Students will learn about Dall sheep, where they live, how they have adapted to their environment, and how wildlife biologists study them to understand how to protect their populations within national parklands. Links to other lessons in the unit can be found at page bottom.

Dall sheep are a wild sheep that lives on steep mountain slopes across the Alaska. The sheep are an integral part of the natural ecosystem, and they are prized by subsistence and recreational hunters. In the early 1990s, the Dall sheep population in the Baird Mountains of Noatak National Preserve declined dramatically, losing half its population in two years. Wildlife managers closed the sheep hunting season for seven years to allow the population to grow again.

Why did the population drop so suddenly? What are the natural and human factors that affect the Dall sheep population? In the spring of 2000, Brad Shults, a wildlife biologist for the National Park Service, began a research project to learn more about Dall sheep population dynamics. Shults hopes to better understand sheep by studying the number of lambs that are born, how long sheep live, what are the most common causes of death, where do they go from season to season, and just how many sheep are there?


Each group will need a marking pen, a bag of beans, a container, a small scoop, and a copy of the Mark-Recapture Data Table.


Before You Begin 

Read and review Dall Sheep and People: Wildlife Management of Dall Sheep.


  • Have the students get into two or three groups and give each group a copy of the Mark-Recapture Data Table. Discuss as a class how mark-recapture works, in general terms. 

  • Discuss with the class that scientists can investigate questions in more than one way. Why might a scientist use mark recapture rather than a complete census? Hint: mark-recapture techniques are often used with small mammals and animals that are not often seen but can be caught in traps and released. As scientists learn about population and research techniques, they can create new techniques that are improvements over older techniques. Mark-recapture allows scientists to count a population they cannot see well. 

  • Give each student a container of beans (more than 100 beans) and a small scoop, be sure they can’t get all the beans into the scoop at once. The beans will represent a Dall sheep population. Explain to students that the purpose of this activity is to learn how biologists estimate population size with statistics when they can’t count each and every animal. 

  • Have each student estimate the number of beans in their jar. Do not take a long time at this, just have them make a guess. Record their guesses on the board. 

  • Have each group take one scoop of beans from their container, mark each bean in the sample with a pen (i.e. put a dot on the bean). Write the number of beans you marked in the “M” column for Round 1. Once all the beans in that sample have been marked, return them to the container with the rest and mix thoroughly. This represents the initial marking of the population. 

  • Each group now takes another sample of beans from the container with their scoop. This will be Round 1. This time, count the total number of beans in the sample (n); the total number of unmarked beans in the sample(u), and the total number of marked beans (m) which equals the number you marked the first time plus the number you just marked. Record the data in the table. Before returning the beans to the container, the students mark all the beans in the sample that were not already marked. Return the materials back to the container, mix, and repeat this step 4 more times. To calculate M in each round, add the M and u from the last round (the number had already marked and the number you just marked). 

  • After the students have completed all the rounds and recorded their data should complete the table by calculating the sum for each column. 
  • Students now calculate the estimated population size using the following equation: 
N = [ ( ∑M x ∑n ) / ∑m ] / the number of rounds

B = actual population size (parameter)
N = estimated population size (estimater)
n = number in bean sample drawn
m = number of marked beans in sample of drawn beans
M = cumulative number of marked beans in container
∑ = the symbol for "sum"

  • For younger students use the form: 
the estimated population = [(total number of beans sampled x number of marked beans) / total number of recaptured beans] / the number of rounds

  • For example, using the data in the Example Mark and Recapture Data Table, the estimated Dall sheep population size would be: 
N = [(159 x 78) / 49] / 5

  • After the students have calculated their estimated bean population size, they should empty out the container and count all the beans. Compare the estimated population size with the counted population size. 

  • At the end of this activity, have each group present to the class their findings for both the estimated population size and actual population size. Students can either make a poster describing the research question, techniques, results, and conclusions, as in the Field Sampling activity; or students may create a poster describing field sampling and mark-recapture techniques, how each one is conducted, what their differences are, why a scientist might use one or another, and what conclusions can and cannot be drawn about true population size from a population estimation technique. 
Discussion Questions

  • Why might a biologist use an estimation instead a total census (i.e., counting each and every individual)? 
  • What are advantages and disadvantages of estimating a population vs. conducting a census? 
  • What might affect the population estimate (i.e. number of samples drawn, number of sampling rounds, number of marked beans, etc.)? 
  • How might the population estimate change if there were fewer rounds or more rounds? 
  • What would happen to the population estimate if there were fewer beans in container, or if the beans were not marked after each round? 
  • Were student guesses of bean population size accurate? What is the role of evidence in science? 
  • Why do scientists and wildlife managers want to know the population size? 
  • To use the mark-recapture technique in the field, what types of instruments or tools would a biologist need? (traps or airplanes, something to record their data with, maps). 

Have the students conduct the same activity but have them sample for only two rounds. Record the same data for each round and then calculate the estimated population size based on two rounds. Have the students conduct the same activity, but with ten rounds. Record the data and calculate the estimated population size. Compare the estimated populations sizes from two rounds, five rounds, and ten rounds with the actual number of beans. What did the students find? How does the number of rounds affect estimates of population size?

Apply what they found in estimating population sizes to a real-life example. How would this information be useful if a biologist wanted to find out the population of Dall sheep? Invite a local biologist to come in and discuss how they use statistics in their work.

Suggested Assessment

Have the students define mark and recapture. Have the students describe two ways that an estimate in population size might be influenced.

Have the students describe why a biologist might use mark and recapture as a means of estimating population size versus counting the whole population.

Additional Resources

The "Hoofin' It!" unit explores the natural resource management of Dall sheep in the national parks of northwest Alaska. Students will learn about Dall sheep, where they live, how they have adapted to their environment, and how wildlife biologists study them to understand how to protect their populations within national parklands.

This unit is designed for grades K-12. Many of the lesson plans are appropriate for younger grades, although the later part of the unit are geared towards middle and high school. A class needn't do every lesson in the unit to gain insights into wildlife management - each can be approached as a stand-alone lesson on a particular biology-related topic.

Lesson 1
Hoofin' It! - What Do You Know?

(Understanding taxonomy; k - 12th grade)
Lesson 2
Hoofin' It! - Vertebrate Grab Game

(Exploring types of vertebrates; 3rd - 6th grade) 
Lesson 3
Hoofin' It! Vertebrate Mysteries

(A vertebrate matching game; 8th - 12th grade)
Lesson 4
Hoofin' It! Special Parts

(Animal adaptations; k - 12th grade)
Lesson 5
Hoofin' It! Hard to See?

(Camoflague; k - 8th grade)
Lesson 6
Hoofin' It! - Sheep Maneuvers

(A predator-prey game; k - 12th grade)
Lesson 7
Hoofin' It - Year of the Sheep

(Life cycle of a Dall sheep; 3rd - 12th grade)
Lesson 8
Hoofin' It! - Who's Got My Habitat?

(Habitat and wildlife populations; 3rd - 12th grade)
Lesson 9
Hoofin' It! - Habitat Grid

(Exploring wildlife habitat; k - 3rd grade)
Lesson 10
Hoofin' It! - Through the Seasons

(A game looking at seasonal impacts on wildlife; 2nd - 11th grade)
Lesson 11
Hoofin' It! - Population Art

(Intro to counting wildlife populations; k - 2nd grade
Lesson 12
Hoofin' It! - Population Calculation

(Graphing and analyzing sheep population data; 6th - 10th grade)
Lesson 13
Hoofin' It! - Scavenger Hunt

(A game connecting students to wildlife; k - 6th grade)
Lesson 14
Hoofin' It! - Field Sampling

(How scientists count wildlife populations; k - 12th grade)
Lesson 15
Hoofin' It! The Bean Counters: Mark-Recapture

(Learning to use the mark-recapture method for population surveys; 5th - 12th grade)