Population
Simulation with M&M's (Grade Levels: 6  9)
Earth Day Concepts: Overview
 What We
Do Adds Up
Recycling
 M&Ms
 Fish Pond
 Answers 
Career Connections
 More Math Concepts
This
activity involves two simulations with M&M's® to
explore population growth and decay. The followup activity,
Population Simulations with Calculators introduces NOWNEXT
or recursive equations as an accessible way to model
this behavior and expand to other population models.
This
activity is best done by pairs of students (but can
be done individually). Each pair of student of students
will need:
 a
small paper cup with about 30 to 40 M&M's and
 an
activity sheet.
Introduction
You
may want to begin the activity with a short discussion
to address the question, "What is a model?". Models
give us an idea of what the "real thing" is like, but
they lack a lot of detail. Mathematical models are similar
in that they don't tell us exactly what is going to
happen, but they help us to find patterns.
The
important components of Earth Day are that we make a
big impact on this planet and that we are not alone.
Plants, mammals, birds, fish, and insects all contribute
to the existence of life on Earth. Using mathematics
and mathematical models, we can build and refine models
to help us predict how the size of a population will
change over time. Mathematical models don't produce
an exact answer, but they can help us understand either
the patterns or the trends that exist.
You
are going to use M&M's to simulate and model the
population decay and growth in a fish pond. You and
your partner will get a cup of M&M's. Do not eat
them. The M&M's in your cup represent the fish in
a pond.
Simulation
for Population Decay
1.
Count the "fish" in your pond, and record that number
under year 0 in the Population Decay chart.
Have
pairs of students gently pour the M&M's, and remind
them not to eat the M&M's until you say it is O.K.
2.
Gently pour the fish onto your desk. Fish with an "M"
face up represent fish that died or were caught during
the first year. Place them aside (do not eat them yet),
figure out how many fish are left in your pond, and
record that population below year 1. Sometimes the "M"
is difficult to see on the yellow ones, so look hard.
It
is good to walk through this step with the students.
Have them gently pour the M&M's and push the pieces
with the "M" showing to the side to simulate population
decay. You may want to tell the class to assume the
fish with a "W" on them are the same as a fish with
an "M".
3.
Place the "live fish" back in the cup, and repeat the
experiment for year 2. Record the fish population under
year 2 on the chart. Continue the simulation, and record
your data for up to 8 years, or until you run out of
M&M's.
Population Decay
 
Year 
0 
1 
2 
3 
4 
5 
6 
7 
8 
Number
of Fish 









4.
Write a sentence or two describing any patterns you
see in this fish population.
5.
If you started with more fish, do you think you would
see the same pattern? Why?
This
is a good time to stop and talk about what is going
on. It is also a good time to collect and display class
data (or a subset of class data) to increase the size
of your sample and give the entire class one set of
data to consider. This can be done with the whole group,
or you can have four pairs combine their data and consolidate
that for the class.
With
more data, some students will probably recognize that
each year you lose about half of your fish. Ask is
there any reason why we would be loosing half of the
fish? Try to get them to talk about how the M only
being printed on one side of the candy relates to
this process.
Have
students share and talk about their descriptions and
their thinking. Encourage students to write in complete,
grammatically correct sentences when describing their
experiments.
Simulation
for Population Growth
6.
Now you are going to simulate population growth in the
fish pond. Place two M&M's in the cup, and record
2 for your year 0 fish population in the Population
Growth chart.
7.
Pour the M&M's on your desk. This time, for each
fish with an "M" showing, you are to add another fish
to the pond. Record your fish population below year
1 in the chart.
It
is a good idea to talk through this step with students
and model it with them. That is, start with 2 M&M's
in your cup. Suppose when you pour them out, you have
1 M showing (and 1 blank). What do you do? Add 1 more
M&M to the cup to make 3, record that number, and
start the process over.)
8.
Put the fish back in the cup, and repeat this process
for year 2. Record your population, and continue for
up to 8 years or until your run out of fish.
;
Population Growth
 
Year 
0 
1 
2 
3 
4 
5 
6 
7 
8 
Number of Fish 









9. Write a sentence
or two describing any patterns you see in this fish population.
10. What do you
think would happen to the population if you were able to continue this
process? Why?
As with
the population decay model, you may want to collect and display class
data to increase the size of your sample and give the entire class one
set of data to consider.
With more data
some students will probably recognize that each year you add about half
of your fish. The reasons for this are the same as with the decay data.
Students should recognize that the population will just keep getting
bigger and bigger each time.
Have students share
and talk about their descriptions and their thinking.
Ask students:

How long does it take the population in the decay model to become half
its original size?
 How long does it take the population in the growth model to become twice
its original size?
 Why does it take
the growth model 2 years?
Tell students they
and their partners can share the M&M's.
