Adventures
With The Fish Pond: Population Modeling (Grade Levels: 7  9)
Earth Day Concepts: Overview
 What We
Do Adds Up
Recycling
 M&Ms
 Fish Pond
 Answers 
Career Connections
 More Math Concepts
This
activity builds on the population decay M&M activity,
introduces NOWNEXT or recursive equations, and uses
calculators as an efficient tool for exploring population
models. To do this activity you need a calculator that
has an Answer Key, usually designated by ANS. Most graphing
calculators have this feature.
This
activity is best done by pairs of students (but can
be done individually). Each pair of student of students
needs:
 an
activity sheet, and
 their
own calculator (sharing is okay, but it is better
for each to have their own).
Population
modeling is one type of mathematical modeling in which
you produce a pattern or rule that could be used to help
describe the situation. The pattern usually doesn't fit
exactly, but closely describes what is happening in the
situation.
1.
Using the data from the Population Decay simulation
determine a general rule to describe what happens to
the fish population from one year to the next. Finish
the following sentence.
Next
year's fish population will be __________________
NOW
 NEXT equations are another name for recursive equations
which are useful in modeling. You want to write an equation
to describe NEXT year's fish population if you know
the fish population NOW. In this equation, NOW represents
the fish population now, and NEXT represents the fish
population next year.
2.
Your goal is to translate your sentence from problem
#1 into a NOW  NEXT equation that describes the Population
Decay simulation. Start with NEXT =, which means the
same as "Next year's fish population will be". Fill
in the right half of the mathematical equation, and
use the word NOW where you would plug in the number
of fish currently in the pond.
NEXT
= ___________________
(Have
students share their solutions. Some possible solutions
include: NEXT = NOW  .5 NOW, NEXT = .5 NOW, NEXT =
NOW/2)
Now
you need an initial condition to test it out. Suppose
the initial condition is that the pond has 80 fish.
This represents the first NOW for this simulation.
3.
Using the NOWNEXT equation, how many fish will be in
the pond next year?
4.
And the following year?
5.
And the following year?
Many
calculators these days have an Answer key that plugs
the last answer calculated. The Answer function is often
designated by ANS.
To
model this on the calculator we need to tell it two
things:
 the
initial condition (which is the same as the initial
NOW value).
 how
to calculate NEXT.
6.
Our initial condition was that the pond had 80 fish.
To store the value on the calculator, type in the value
80 and press the appropriate key (ENTER, RETURN, =,...).
For us, 80 is now stored as the initial NOW value.
7.
To tell the calculator how to calculate NEXT we need
to enter in the right half of our NOWNEXT equation.
However we need to use ANS in place of "NOW" in our
equation. Then press ENTER. For example if your equation
was NEXT * .5 then you would put in ANS *.5 and hit
ENTER.
8.
Did the calculator return the correct value? If not
you need to start over, you will need to reenter your
initial condition (80) and then ANS expression.
9.
If you hit ENTER again and again the calculator should
give you the value for the next years population. This
is because we taught it the "rule" for our model.
10.
How many years does it take before our population is
under 5?
11.
If we started with 1000 fish, how many years would it
be before the population was below 10?
12.
If we started with 2000 fish, how many years would it
be before the population was below 10?
13.
Knowing what you know about 2000 fish, how many years
would it be before a population of 8000 fish was below
10?
Activity
adapted from lessons in:
Coxford, A., Fey, J., Hirsch, C., Schoen, H., Burrill,
G., Hart, E., Watkins, A., Messenger, M., & Ritsema,
B. (1997). Contemporary mathematics in context: A unified
approach (CorePlus Mathematics Project). Chicago: Everyday
Learning.
