Fish Population and Proportional Reasoning

Designed for the NYC and NYC Watersheds Trout in the Classroom program


Conceived and written by Nathan Affield and Suzanna Sellars at Brooklyn's Green School.

This lesson plan is designed for middle and upper grade students and could be modified for younger students.

Objective: To build numeracy as well as algebraic and proportional reasoning by using manipulatives, experimentation and investigation to model real life sitations, namely estimating the population of fish in a body of water.  

Background: Water in New York City comes from the Delaware, Catskills, and Croton Watersheds. It falls in the form of precipitation and follows the streams to the man-made reservoirs and controlled lakes. From there it is transported to the city through aqueducts into water tunnels, mainly by the force of gravity. It is then brought to homes, schools and businesses in New York City through water mains and pipes.  The streams and reservoirs which are part of this system are habitat for thousands of brook and brown trout. These species reflect the well being of our watershed streams and reserveoires. 

Many fishery managers use mark-and-capture techniques as well as proportional reasoning to track fish populations. These tecniques help develop models of fluxuation over time and help scientists understand the well-being of a species and the environment they inhabit.

•    Handout: “How Many Brown Trout are in Cross River Reservoir?”
•    Two colors of beans to model the fish population -- 1 bag red beans, 3 bags white beans -- mixed together in a bowl

1.    Divide red and white beans among 10 containers
2.    Give one container to each group
3.    Have students read the hand-out and discuss follow instructions with their group. 

Wrap Up: Provide time for groups to discuss the reservoirs and trout species that live in them. 

(detailed lesson plan below)

Lesson Objective:      
Students will be able to estimate the population of trout in a reservoir using proportional reasoning.

How do scientists estimate population size? 

Do Now:    
Strategize how you would count the number of trout in a reservoir.

Regents Living Environment Standards:    
This lesson is an integral part to understanding ecology mark-and-recapture technique and why it is important for ecologists to study populations. This lesson is interdisciplinary since students must use mathematical concepts of proportion and multiplication to estimate the population size. 

Common Core Learning Standards:     



Structure of the Lesson
(Modeling, Guided Practice, Independent Practice)

- We will discuss strategies for counting the number of trout in a reservoir. 
- Then, we will present students with a tangible way to count using a bucket full of beans. Beans represent the trout and the bucket represents the reservoir. There are red beans (marked trout) and white beans (unmarked trout) in the reservoir population.
- Students will work in groups of two to go “fishing”. Each group will take a cup full of beans and count the number of red beans and the total number of beans to come up with a proportion.
- Student compile data on a white board or projected excel file from computer.
- As a class, we discuss why our proportions may differ, add class data and use cross multiplication to come up with an estimate of the number of trout in the reservoir.
-  Students will work on the post-activity questions to analyze whether or not they agree with this method of estimation and discuss how we could improve our experimental methods.
- If time permits we could do another round of “fishing” to apply our design modifications.

UDL Principles / Differentiation Strategies
- The visual and hands-on component of the bucket and bean representation.

- The post-lab focuses on reflecting and analyzing experimental design.
-Interdisciplinary mathematical concepts help draw students into the potentially difficult concept of how scientists use mark-and-recapture to monitor and study populations.

Student Worksheet

Students should be able to properly use the equipment and use cross multiplication to come up with an estimate of the population. Teachers use observational assessment and questioning to determine student engagement.

Higher order Thinking Questions:    
Why is the mark-and-recapture or “tagging” technique a useful tool for ecologists? What do you think would happen to the population size if the trout’s food source diminished? How long or how often should scientists focus on studying populations?

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