**What you need**Cloth bag or a non-transparent container

Marker pen

Notepad

Calculator (optional)

Template of ‘Forty Fine Fish'

Coloured card or paper

Scissors

A friend

**What you do**Draw and cut out 'Forty Fine Fish', preferably on coloured card.

Ask your friend to secretly count out a number of fish tokens and place them into the container or bag. To make it more of a challenge, ask them to make it any number higher than 20.

Now it's time to go fishing. To get an estimate of the number of fish, you need to do several fishing trips:

* On your first trip, pull ten fish out of the container and 'tag' them with a cross using your marker pen before returning them

* On your second trip, shake the container then pull out another ten fish without looking. Count how many of those fish are marked with the cross and write down the number, then return them to the container and mix them up

* Now go fishing a third time, again recording the number of fish with crosses and returning them to the bag, mixing again

* Go fishing one last time, writing down the number of fish you catch with crosses.

Add these 3 numbers and divide the result by 3 to get an average result. For example, if you counted 5 with crosses, then 3, and then 4, this equals 12. 12 divided by 3 equals 4.

The equation which estimates the total number of fish in the bag is:

(Total number caught the first time x total number caught the second time) / average number caught with a cross

In our example, this would be (10 x 10) / 4. This equals 25, which is our total estimate.

Ask your friend for the actual number. Is your estimate close?

**What's happening?**Estimates are guesses based on a small amount of information. Obviously we can't know the exact number of fish in a large area like a lake, so we need some way of getting a small amount of information and then making a guess based on it.

When you go fishing, you are taking a ‘sample' of the larger population. Samples usually represent the population you want to know more about. For example, half of a school might be boys and half girls. If you took a sample of the school, such as one class of students, it should also have about half boys and half girls. If you wanted your estimate to be more accurate, you could count two classes instead to get more numbers.

Your first fishing trip took one sample, and then tagged them all as caught. The second fishing trip counted the same number you caught the first time and compared it with the number of new (untagged) fish being caught. Obviously, if there aren't a lot of fish, you'll catch most of them again. But if there are large numbers of fish in the lake, you mightn't catch any tagged fish at all the second time.

Mark-and-recapture, also called tag-and-release, is a way of using samples to estimate the size of a population when you can't possibly count them all any other way.

**Applications**Many organisms don't sit still long enough to be counted. People aren't all that different –it's difficult to study all of the people in a large area, which is why we do surveys. This means we study a small 'sample' part of a large number of people to provide us with an example of what other people might do as well.

We must be careful that our sample is similar to the whole population we want to study. Would it be accurate to study what breakfast cereal most people prefer if we only asked toddlers? Or what television shows all ages watch by only asking parents? Such is the case with our fish – it is only accurate if we can catch all types of fish we want to count. Imagine catching the fish using a net with holes big enough to let smaller fish through. Would this give us an accurate estimate?

"borrowed" from CSIRO.

either cut your own fish shapes out or use this template:

http://www.csiro.au/helix/sciencemail/activities/images/FortyFineFish.pdf