Go
Fish!: Teacher Notes
MA.7.A.1.1
Conceptual Understanding
Data Collection
Interpret Data
Proportional Reasoning
Procedural Knowledge
Solve Proportions
Problem Solving
Reasoning
Communication
Connections
Representation
Imagine that you are asked
to determine the number of fish in a nearby pond. To count the fish
one by one, you could remove the fish from the pond and stack them
to one side, or mark each fish so you would not count them over and
over again. Counting like this could be hazardous to a fish's health!
To determine the number of animals in a population, scientists often
use the capturerecapture method. A number of animals are captured,
carefully tagged, and returned to their native habitat. Then a second
group of animals is captured and counted, and the number of tagged
animals is noted. Scientists then use proportions to estimate the
number in the entire population.
Students work in groups
of three to four.
Each group needs:
 1 paper lunch sack  represents
the "lake"
 A supply of goldfish crackers
 represent the "fish" in the lake
 A supply of pretzel fish
crackers  represent the "tagged fish"
 1 styrofoam cup  represents
the "net"
 1 paper plate
 Collect the Data
Capture:
 Each team receives a paper lunch bag with goldfish crackers
inside.
 With the "net," scoop a sample of goldfish out of
your "lake" onto the paper plate.
 Replace your sample of goldfish with pretzel fish. These are
your "tagged" fish.
 Count the number of "tagged" (pretzel) fish and then
return them to the bag.
 There are _____ tagged fish in the entire lake.
Recapture:
 Shake the bag gently.
 For the first casting, use your net (cup) to remove a sample
of fish. Count the number of "tagged" (pretzel) fish
in your sample and record the total in the first column below.
 Return all of these fish to the lake (bag) and shake gently
to mix them up.
 Repeat this process until you have gathered information on 10
samples and filled in the table below.
Sample
Number

Number
of Tagged Fish in Sample

Total
Number of Fish from Sample

1



2



3



4



5



6



7



8



9



10



Average



 Analyze the Data
 To find the AVERAGE number of tagged fish, add up all 10 samples
of the tagged fish and divide by 10. Do the same thing to find
the AVERAGE number of total fish in your samples. (Using the AVERAGE
number with 10 samples is more reliable than using any one sample's
data.)
 Use the proportion below to estimate the total number of fish
in your lake:
Average
# tagged in samples

=

Total
# tagged in lake

Average
# in samples


Total
# fish in lake

ESTIMATED POPULATION: _____________________
 Now count the total number of fish in your lake to determine
how close your estimate from the "sampling" is to the
actual number of fish in the lake.
ACTUAL POPULATION: _____________________
 How close were you to the actual number of fish?
As a result of this activity,
students learn how to gather information about a large population
based on a representative sample whose makeup is similar.
 Where else would scientists
use this capture/recapture method?
 What are some of the factors that could have caused an estimate
to be close or not so close to the actual number of fish?
