ACTIVITY: Goldfish Party! Mark-Recapture Methods

NGSS Science and Engineering Practices
NGSS Crosscutting Concepts
NGSS Disciplinary Core Ideas
The activity below draws from the content in the page Food Resources and Fisheries Science.
Image caption

Fig. 2. Fish populations can be difficult to count, so scientists have developed methods to accurately estimate them.

Image copyright and source

Image courtesy of FreddieMade


Fish populations can continue to be productive food sources even with fishing pressure.


How do scientists, fishers, and resource managers learn about fish populations? How can we maintain fish populations for future generations?

Guiding Questions:

  1. How do scientists estimate fish populations?
  2. What is one way fishers ensure stable fish populations?


Create a mark-recapture model to investigate how scientists monitor the size and number of a fish population and investigate how selective nets may help maintain sustainable populations.


  • Student and Teacher Worksheets (attachment below)
    This teacher guide follows the procedure written here and in the student worksheet with additional instructions and guidelines. We highly recommend starting this activity by introducing the Phenomenon, Inquiry, and Guiding Questions from the top of this webpage.

  • Lunch size brown paper bags
  • Paper plates​ or paper bowls
  • 3 oz. paper cup

Part A: Mark-Recapture:

  • Original Goldfish
  • Colored Goldfish

Part B: Selective Nets:

  • Cheese-Its

Teacher Recommendations:

  • Suggested distribution of supplies
    • per group - 1/2 to 1 bag original goldfish, 1/3 bag of color goldfish, 1 paper cup, 1 paper bag, 1 paper plate
    • per class - 2-3 boxes of cheeze-its
  • Note: This activity uses The Lincoln-Peterson method of mark-recapture. It is used when the population is closed (no births, deaths, immigration, or emmigration) and every individual has an equal probability of being captured.
    • The population size is estimated by catching animals at time 0 (step 4 in the procedures), marking and releasing them, and then catching animals again time X (at times 1–5, step 7 in the procedures).
    • The number of marked to unmarked animals is then compared to estimate population size.
    • The population size is estimated by N = C x M/R, where M = the number of animals marked at time 0,  C = total number of animals captured at time X, and R = number of marked animals recaptured at time X. 
    • This formula is slightly biased for small populations and can be improved to be less biased with the formula N = M(C+1) / R+1. 
    • For more accurate population estimates, researchers often use more complicated designs where they tag animals at multiple time points and use more advanced equations to estimate population size.
    • In this activity, students will only mark fish at time 0, but they will take multiple samples (at time 1 through time 5) to look for recaptures. They will then average their population estimates.


Part A. Mark-Recapture Methods

  1. Follow your worksheet to build your model and explore mark-recapture methods. 
  2. Place Original Goldfish (species of interest) in the paper bag (ocean) or small bowl.
  3. How many fish do you think are in your population?
  4. Capture a sample of goldfish from the brown bag (one cup full), and place them on the paper plate to count. Record this number of fish captured on your data table (represented as M). 
  5. Tag these captured fish by replacing each one with a colored fish (the colored fish represent marked individuals). Note: Since we are tagging by replacement, the goldfish that are tagged and replaced by colored fish can no longer count as part of the population. The replaced fish MUST be disregarded or eaten! 

    Image caption

    Fig. 3. A display of the mixture of population goldfish with "tagged" fish.

    Image copyright and source

    Image courtesy of Kēhau Llanos

  6. Put the colored (marked) fish back into the bag and shake it (or stir the fish in the bowl) to distribute them. 

  7. Recapture another sample from the bag using the cup and pour onto the plate. 

  8. Record the number of color and non-colorfish in the appropriate columns. Return the entire sample to the bag. 

  9. Shake the bag to distrubute them.
  10. Repeat steps 7-9 two or more times. (The number of 1st Capture remains constant for all samples).
  11. This Population Proportion allows you to estimate the total fish in the population (N) for each sampling. Fill in the column on your data table (N = C x M/R).

N (Total Fish in Population)       =   .       C (Fish Captured in Sample)        

M (Total Marked Fish)                     R (Marked Fish Recaptured in Sample)

  1. Calculate the average of your population estimations (average of N).
  2. Finally, count the actual number of fish in your population (total, marked included!).
Original number of fish marked (M): ________________________
Sample Time #

Number of fish

Captured in Sample


Number of fish

Recaptured in Sample


Write out the

Population Calculation

(N = C M/R)





Count of total in actual population: _______________________


Part B. Selective Nets

  1. Replace one-fourth of the gold fish with Cheese-Its. The goldfish are now the juvenile fish and the Cheese-Its are the larger, more mature fish (or larger species not intended to be caught).
  2. Gently shake the bag (or stir the contents of the bowl) to insure randomness.
  3. Cut two dime sized holes in the bottom of the paper cup (net). The holes should be large enough to enable the smaller fish to slip through but not so large as to allow the larger fish to escape. 

  4. Capture a sample of fish from the bag (ocean) using the net (cup). Shake gently to allow the smaller fish to slip through.
  5. Repeat as needed.

Activity Questions:

  1. How do your population estimates (N) compare to the actual population count?
  2. What may account for differences between your count and the actual population? 

  3. In step #13, you counted all of the fish in the bowl. How does this compare to real life (Hint: could you count all the fish in real life)?
  4. How might calculations of population size help scientists and fish regulators determine fish regulations and fish catch limits?
  5. How do selective nets work?
  6. Can a specialized net be successful in releasing smaller juvenile fish?
  7. What are factors that may prevent the smaller fish from escaping?
  8. How might a device such as a specialized net be improved? 

  9. Why is it important to use specialized nets?
  10. Why is it important to sustain fish populations in terms of food chains and food webs?

Further Investigations:

  1. Investigate and discuss the L50 Measurement Ruler!

L50 Background:

In order to maintain a population of fish at sustainable levels, there needs to be enough fish that are sufficiently mature to reproduce and replenish what is being caught. Scientists and fish regulators have identified the length of various fish species at which half (50%) may have been able to spawn and maintain sustainable fish populations. This is called an L50 Measurement Guide (Activity Ruler). One of the ways fishermen (such as yourselves) can directly impact the conservation of living resources and sustain healthy fish populations by learning and implementing the L50 Measurement Guide.



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Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawai?i, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.