Problem: You are a wildlife biologist and have been asked to count all the kangaroo rats in a particular area of
Franklin Mountains State Park. Kangaroo rats spend much of their lives underground and come out only at night. How do you count something you
can't see? Do you:
- Forget it, go home, cook up a pot of beans and eat dinner?
- Go home and count all the beans in your kitchen instead?
If you answered the latter, you are partially correct. We are going to count beans and use that as a model for a method we could
use to count the actual kangaroo rats.
Here's what we need:
- A medium sized paper bag with about 1 cup of white beans inside for each group of students. This represents
the total number of kangaroo rats we can't see.
- A marking pen for each group.
- A calculator.
Let's Get Busy!
- Let's trap some of those imaginary kangaroo rats! Without looking into the bag, reach in and
remove some of the beans.
- Count the number of beans and record the result.
- Using the marker, place a marking on each bean taken from the bag.
- Now let's take the k-rats back to where we trapped them and set them free. Place all the marked beans back into the paper sack
with the other beans.
- Fold the top of the bag over and gently shake the sack of beans so that the marked beans mix well with the unmarked beans.
The marked kangaroo rats are dispersing back into their environment.
- Now that all of our kangaroo rats have headed back to their homes in the desert, let's try trapping them again. Without looking into the bag,
reach in and take out part of the beans again. Count the total number of beans removed and then count how many of them are
marked. Record your results.
- It's time to take out that calculator and see if we can figure out how many imaginary kangaroo rats we have in our imaginary desert:
- use this formula:
a/b = c/d
- a = number of marked beans you "recaught".
- b = total number of beans, marked and unmarked, that you "recaught."
- c = total number of beans you marked in step 3.
- d = calculated total number of beans in our bag.
- Let's suppose you originally captured and marked 20 beans. The second time you "captured" the beans you again caught 20
and 1 of them was marked.
- That's 1/20 = 20/d
- d = 400 = calculated number of beans in our bag.
- Repeat steps 4 through 7 two or three more times. Calculate an average number. Round it off to the nearest whole number.
- Now let's check our results by counting the total number of beans, marked and unmarked, in the bag. How close was our calculated
number to the actual number?
- Could we use this method to "count" the number of kangaroo rats?
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