Student Exploration: Estimating Population Size (ANSWER KEY)

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.

  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 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.

  1. 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?
C.Suppose you catch 100 fish out of this pond. About how many of these fish would you expect to be tagged?
D.Set the Fish to catch to 100. Click Catch and check. How does the number of tagged fish shown in the Gizmo table compare to your estimate above?
2. On the POND tab, turn off Show total fish in pond. Click New pond. Set the Tagged fish in pond and the Fish to catch to the same number of your choice under 75. A. How many fish were tagged and released? B. Now click Catch and check. Fill in the blanks below to describe the number of tagged fish (and total fish) in your sample.
C.In the space to the right, write a proportion that you can use to estimate the fish population. Solve the proportion. Check your answer on the CALCULATE tab.
D. Turn on Show total fish in pond. What is the actual fish population? 
E. How far off was your estimated population from the actual value? 
F. Do you think your estimate would be more accurate if you increased the number of fish to catch? 
Activity B:
Sample size
Get the Gizmo ready:
  • Select the POND tab.
  • Turn off Show total fish in pond.
 
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 Tagged fish in pond to 75 and Fish to catch to 10. Click New pond.
Click Catch and check. In the space to the right, write and solve a proportion to estimate the total fish in the pond. Select the CALCULATE tab to check.
Turn on Show total fish in pond. What is the actual fish population?    356
In the space to the right, find the difference between your estimate and the actual fish population. Then express this as a percent of the actual population.
D.Fill in the first row of the table for the catch above. Then, change the Number of fish to catch to the numbers shown in the first column and fill in the rest of the table.
2.On the POND tab, click New pond. Be sure Tagged fish in pond is still set to 75.
A.Fill in the following table for the new pond.
B.On the POND tab, click New pond again. Fill in the following table for this pond.

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