# PBS Teachers™

Population Simulation with M&M's (Grade Levels: 6 - 9)

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This activity involves two simulations with M&M's® to explore population growth and decay. The follow-up activity, Population Simulations with Calculators introduces NOW-NEXT 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.