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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? Explain.

I would guess that 25 marbles out of the 100 are black because from the sample ¼ or a quarter

was black out of the 4 marbles sample.

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?

Explain.

I would guess that the total number of marbles is 400 since the estimated black marble data

is 25%. Based on knowing it is 25%, we can find the total number by multiplying total

number of 100 black marbles by 4 since it is the same ratio between number of black

marbles to total.

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.

1. 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 catch to

50 to show this.) The fisherman’s catch is a sample of all fish in the pond.

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A. Click Catch and check. Look at the Results table. How many tagged fish did the

fisherman catch? He caught 12 of the tagged fish.

B. What percent of the fish in his sample were tagged? The percentage is 24% since 12

of the 50 fish checked had a tag.

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

pond? The total number of fish in the pond is 354.

This number is the population of fish in this pond.

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