Tag Archives: Free Response Items


Last month my husband and I decided to take our kids to a local state park for a picnic and some fishing.  We had scouted the best places in the park to fish and took off for an afternoon adventure.

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For those of you who don’t have a lot of experience fishing with a 7, 5, and 1-year old time is of the essence.  You have a very important 15 minute window in which to have someone catch their first fish.  If you don’t get any action in about the first 15 minutes you can pretty much bet on the fact the the kiddos you brought fishing will be ready to put away the fishing poles and start to build a fire for the s’mores.

Well on that fateful day in the middle of August, that 15 minute window slipped right through our fingers.  And then, the 15 minutes turned into 30 without so much as a nibble.  My husband was able to entertain the kids a little while longer by letting each of them practice casting their own finishing line (while everyone else crouched in the bushes to avoid an accidental snag), but even the novelty of doing that wore off about an hour into the fishing expedition.

Soon, the excitement of going on a fishing trip turned in to:

“When can we make s’mores?” –My 5 year old

“How come that person is catching fish?!?”–My 7 year old

“Dad are you sure there are even fish in this lake?”–My 5 year old again

(Just as a side note we stayed at the park for 3 hours and did not catch ONE. SINGLE. FISH., but to make up for it we made s’mores and then stopped for ice cream on the way home.)

Anyway, this fishing trip reminded me of a method for estimating the fish population in rivers and streams called the Mark-Recapture method.

The Iowa DNR has a really nice explanation of the Mark-Recapture method, although the whole using real crickets thing creeps me out a little; but this is basically how it works:

1. Catch fish and tag them (or Mark them).  Record the number of fish you’ve caught and tagged.

2. Go fishing again.  Record the total number of fish you catch and the number of caught fish that you tagged previously (that’s the Recapture park).  Then set up the following proportion to estimate the population of fish in the the lake/river/stream you were fishing.

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Now that you know the basics of Mark-Recapture, lets think about a few things:

1. Taking a census of the fish in the lake is not practical in this case.  Why?

2. If I’d really like this to be an accurate picture of the population of fish in this lake, what are some things that I will have to consider when collecting the data (ie fishing, tagging, and counting)?  Think about things like location of the fisherman, time of day for fishing, weather conditions during the Mark-Recapture data collection.  What are other items that should be considered?

3. Why might the Iowa DNR or any naturalist for that matter be concerned with the fish population of a particular lake or stream?  How can the Mark-Recapture method help address those concerns?

P.S. If you’re an AP Statistics Teacher or Student, this is a great sampling example to consider.  Did you know sampling questions occur the most frequently on AP free response exams, and they are also the most often missed on the exam too?  Don’t believe me?  Check out this article.