Day 1:
To begin the lesson, I talked about how environmentalists often need to estimate how many fish are in a lake and asked the kids how they thought that it might be done to which they gave me a couple of ways. I then told them about the most common way – the capture/recapture method.
I didn’t do the investigation as it was set up. I first drew a lake on the board and drew in a bunch of “x”s to represent the number of fish. I then “captured” ten of them, tagged them, and threw them back into the lake denoting them with a different color “x”.
I then told the kids that I would wait for awhile for the fish to move around so that all my tagged fish weren’t in one area. Then I showed them that I could recapture a sample, and use that information to write a proportion to solve for the number of fish in the entire lake.
Next, I showed the kids the computer Exploration on page 105 and did the experiment four times. We discussed why the answers weren’t all the same (they ranged from just over 100 to more than 300) and what we could do to with those results to get a better estimate to the true number of fish in the lake.
Then I handed out the beans and told them to come up with their own simulation of what happened on the board and on the computer. After ten minutes, I had two groups come up and show what they had done.
Day 2:
The second day was spent going over all the homework and then doing questions 3 and 4 from the Extra Practice 2.2 worksheet that was put onto the screen. I put the problem up on the board and the students were given about two minutes for each to write a proportion that would represent the problem. I’ve found that it is useful to ask a student for “the ratio where you know both numbers” and then from there, label each part of the ratio, then ask the class what the second ratio must be. This way the kids realize that there is more than one way to write a proportion but that once one ratio is done, there is only one way to write the second.
2.2 Three Extra Practice Problems for Class
At the end of day 2, I gave the following quiz.
