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# Student Exploration- Estimating Population Size (answers)

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Author: Jack Bauer
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Student Exploration: Estimating Population Size

Vocabulary: percent error, population, sample

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

1. A jar contains 100 marbles total. Some are black. If you pull 4 marbles out and 1 is black, how many out of the 100 marbles would you guess are black?

2.A different jar has 100 black marbles. (The total number of marbles is unknown.) If you pull 4 marbles out and 1 is black, what is your guess for the total number of marbles?

Gizmo Warm-up

In the Estimating Population Size Gizmo™, you will estimate the total number of fish in a pond. You will do this by tagging and releasing a certain number of fish, and then “recapturing” some.

To change the number of fish to tag or catch, drag the slider, or click on the number in the text field next to a slider, type a new value, and hit Enter.

Suppose a scientist tags 100 fish, and releases them. (Set the Tagged fish in pond to 100 to show this.) Later, a fisherman catches 50 fish from the same pond. (Set Fish to catchto 50 to show this.) The fisherman’s catch is a sample of all fish in the pond.

Click Catch and check. Look at the Results table.

A. How many tagged fish did the fisherman catch?

B. What percent of the fish in his sample were tagged?

2.At the bottom of the Gizmo, select Show total fish in pond. How many fish are in this

The “capture/recapture” method lets you estimate the size of a population. To apply this to a fish pond, first catch and tag some fish. (This is the “capture” part.) Then release the tagged fish into the pond and wait. Later, catch a second group of fish. (This is the “recapture” part.) Count the tagged fish in the second group and use a proportion to estimate the pond’s fish population.

Set the Tagged fish in pond to 50. Click New pond.

A. How many fish are in this pond?

B.If you catch one fish out of this pond, what is the probability that your fish is tagged?

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