APES 110_Gizmo_Student Exploration: Estimating Population Size_2021 | APES 110_Gizmo-Estimating Population Size

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? I would guess around 25. Explain. The reason I would guess 25 is because ¼ is the ratio of black marbles to other marbles being pulled out of 100 and ¼ of 100 is 25. 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? 400 Explain. I would say 400, because ¼ of 400 is 100. 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. A. Click Catch and check. Look at the Results table. How many tagged fish did the fisherman catch? 19 B. What percent of the fish in his sample were tagged? 38% 2. At the bottom of the Gizmo, select Show total fish in pond. How many fish are in this pond? 308 This number is the population of fish in this pond.  Activity A: Capture/recapture method Get the Gizmo ready: • Be sure Show total fish in pond is selected on the POND tab. 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? 186 B. If you catch one fish out of this pond, what is the probability that your fish is tagged? Fraction: Decimal (to nearest hundredth): 0.38 C. Suppose you catch 100 fish out of this pond. About how many of these fish would you expect to be tagged? 38 Explain. The reason I would say 38 is because 100 times .38 is 38. 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? My estimate is close to the actual number of tagged fish. The number is 26 and my number is 38. E. If you don’t know how many fish are in the pond, you can use the results from the catch to write a proportion to estimate the fish population. Fill in the blanks below with words to write this proportion. - - - - - Continued