CORE CURRICULUM GOALS
Earth Systems Core Standard 2
• Objective 3: Examine earth’s diversity of life as it changes over time.
Science Core/Standard V 4th Grade
• Objective 2: Describe the common plants and animals found in Utah environments and
how these organisms have adapted to the environment in which they live.
• Objective 4: Observe and record the behavior of Utah animals.
• Estimate the size of a fish population.
• Practice the mark-and-recapture technique.
• Use real data to estimate the total population of carp in Utah Lake.
• Analyze findings and inferences to generate conclusions.
• 50 Goldfish® crackers (you could also use beans, popcorn kernels or rice).
• Plastic container with lid
1. Mark 20 of the Goldfish® crackers with a marker on both sides. These represent the
“Number Captured and Marked” on the data table below.
2. Place all 50 Goldfish® crackers in the container and cover the lid. Shake the container to
mix the crackers thoroughly. Take the lid off and without looking, withdraw 10 Goldfish®
crackers that represent the “Total Number Recaptured” on the data table. Out of those
10, count the number of marked Goldfish® crackers and record in the table under the
column titled “Number Recaptured (with marks).”
3. Put the 10 Goldfish® crackers back in the container and replace the lid. Shake the container
again and with draw a second set of Goldfish® crackers. Again, record the number of
marked Goldfish® crackers in the sample in the data table. Continue in this manner until
you have completed five trials.
4. Estimate the population size for each trial by multiplying the number of Goldfish® crackers
marked (20) by the number of Goldfish® crackers in each sample (10) and dividing the
product by the “Number Recaptured (with marks)” Goldfish® crackers for each trial.
The result is an estimation of population size. When you have done this for all five trials,
find the average by adding the estimates and dividing by five.
• How does the average value compare to the actual population size of 50? If there is a
difference, explain what might cause the difference.
• What problems might scientists encounter using this method in the field that you may
have not encountered in this simulation?
• The following is real field data. Over a 15-day period, crews captured, tagged, and released
24,064 carp in various locations of Utah Lake. Soon after the completion of tagging,
crewmembers captured another 10,357 carp in random locations of the lake to look for
tagged fish. The total size of the population can be estimated based on the proportion
of tagged fish that are recaptured. Only 208 of the carp in the recaptured sample had tags.
How large is the carp population? Use the following formula to make your estimation:
• What assumptions are made in the mark-and-recapture method? List as many as you can.
(For example, between the intervals that crews are catching and tagging fish, what if
there are a high number of births or deaths? Are there other events that might lead to a
difference in the number of carp that are captured and tagged?)
• Do you think mark-and-recapture is a reliable method for estimating populations? What
other methods could biologists use to estimate the number of carp in Utah Lake?
• Does the estimate become more accurate if you mark a greater number of individuals? Why?
• In a recent lake-wide survey conducted, carp represented an overwhelming 91 percent
biomass in the lake. Carp in Utah Lake are a destructive force within the energy network
of the lake’s ecosystem and cause conditions that promote their survival over the native
species, including the endangered June sucker. What would you suggest biologists do to
reduce the impact of carp in Utah Lake?
• Have older students research other methods of estimating population size such as random
sampling, mathematical models, or genetic markers.
• Have older students discuss the accuracy of the mark-and-recapture model and design
methods to improve its reliability.
• Have younger students retry this experiment with an unknown number of goldfish. Have
teams experiment with larger and smaller sample sizes to see who can make the most
accurate prediction of the sample size. Discuss the results.
• Have a fisheries biologist visit your class and describe the methods they use to estimate