Steps

1. Examine the counting grid above. It represents an area that measures four meters by six meters. What is the total area of this full-size grid?
   (24 square meters)
2. Make a guess before you do any counting. Estimate the number of fish found within these 24 square meters?
   (Accept all reasonable answers)
3. Use a pencil and number the squares one through 24.
4. Devise a method for picking six random numbers from that same range of twenty-four numbers .
5. Examine the six squares identified by the selection of your six random numbers.
6. Tally the total number of fish found in these six squares. Remember, you'll need to devise a plan to deal with fish that lie on a dividing line.
7. Once you've tallied the number of your fish in your sample, multiply this number by four. The number you arrive at is the estimate for the number of fish in the24 square meter grid. Record this as your first estimate.
8. Pick three random squares. Tally the total number of fish in these squares. Multiply your count by eight. Record this value as your second estimate.
9. Randomly select one number. Count the number of fish in that square. Multiple this number by 24 to arrive at an estimate of the number of fish in the entire area.
10. Repeat step 9 two more times.
11. Count the actual fish that are in the entire grid.
    (81 fish)
    Compare and contrast this number to the estimates made based upon 6 samples, 3 samples, and the 1 sample calculations.
    

Questions

1. Why was it important to devise a way of picking random numbers.
   (You needed a random sample and not a sample influenced by selection bias.)
2. Why did you need to develop a method for counting fish that were positioned on a grid line?
   (You needed to assign one fish to one grid block. You didn't want to count it twice.)
3. In step 7, why was the number of counted fish multiplied by four?
   (Since one-fourth of the total area was tallied, you needed to multiply your data by four to represent the full area)
4. How did the number of samples on which the estimate was based affect the accuracy of the estimate?
   (Accept all reasonable answers. Most likely, the greater number of samples produced the greatest accuracy. The fewer the sample blocks, the lower the accuracy and repeatability among the samples.)

More Math
Based upon your count and observed concentration, how many fish can be found in a square kilometer with the same population density?
(To uncover the population size, solve the equation 81/x = 24/1,000,000 ; Answer: 3, 375,000 fish)