Some scientists believe that there is a growing shortage of fish in the sea. They believe the reason is that we have captured too many fish. This is called “overfishing.” To help prevent overfishing, government has to set limits, called “quotas”, on how many fish fishermen can catch in a year. In order to decide on quotas, the government needs to know the total number of fish that live there. They rely on scientists to find out.

But how can scientists tell? They couldn’t possibly count every fish, especially when they can’t see them all. The ocean is so big and fish spend all of their time underwater!

The truth is, scientists don’t count every animal. Instead, they count some of the animals, then make an estimate using basic math.

Scientists are especially interested in the number of fish that live within limited areas. This is called the “population density.” For example, scientists believe that, at certain times of the year, certain kinds of fish generally keep to a “neighborhood” or habitat off the coast of New England. They can find out whether the population density of this kind of fish is growing or shrinking by keeping track of the population density within a habitat over a number of years.

One method researchers use is fairly simple. They go out in boats, catch the fish, place “tags” on a certain number of them, and release them back into the ocean. One week, for example, they will tag twenty fish. The next week, they will return to the same area of the ocean and count every fish they see. Maybe they will see and count two hundred. Out of that two hundred, they find that ten of those fish have tags on them. They can assume that if they saw another two hundred fish, they would find the other ten tags. They can then estimate that there are about four hundred fish living in that habitat.

Do it yourself

This mathematics experiment is similar to the way scientists estimate population density. Guess the number of pennies/buttons without having to count every one.


  • Small jar or bowl
  • lots of small objects such as pennies or buttons
  • water-based paint
  • pen/pencil


  1. Place the pennies/buttons in a jar or bowl.
  2. Remove a big handful of the objects and paint a mark on each of them to “tag” them.
  3. Count how many you have “tagged” and write this number next to “A” in the space provided.
  4. When the paint is completely dry, place the marked pennies/buttons back into the container. Mix very well with the unmarked objects by shaking or stirring the jar.
  5. With your eyes closed, again remove a big handful of the pennies/buttons. Count the number of items you have removed and write this number next to “B” in the space provided. If there are no marked objects in your sample, you need to collect more and add those to your total in B.
  6. Count the number of “tagged” objects in your sample and write that number next to “C.”
  7. To estimate the total number of objects in the jar, multiply “A” times “B,” and divide the result by “C.”
  8. Thus, (A x B)/C = approximate number of objects in jar.
    Repeat this several times, trying different size samples: two handfuls, a cupful, etc.
  9. Make sure to mix them back into the total population of objects every time. Remember, this is only an estimate. The larger the sample you take, the closer your guess will be to the exact total.
  10. After many guesses, count all of the pennies or buttons and see how close your guesses were.