STRAND:

Chance and data

CHAPTER:

Data

Capture — recapture

John Wiley & Sons Australia, Ltd 2004

Fractions are often used to estimate populations that are too difficult to count exactly. An example of this would be the fish population of a lake. A batch of fish will be caught, tagged and released. A second catch is then made, and the fraction of the second batch with tags is used to estimate the entire population. This is called the capture – recapture technique.

We are going to simulate a capture – recapture activity. To complete this activity, you will need to work in pairs.

1. Each person tears or cuts up an A4 sheet of paper into small pieces (you will need to make at least 100 pieces).

Count the pieces and place them in a non-see-through bag. DO NOT tell your partner how many pieces of paper are in your bag.

2. Swap bags with your partner.

3. You now have your partner’s bag. From the bag, take any 20 pieces of paper and clearly mark them with a cross. Then return them to the bag.

4. Shake the pieces in the bag thoroughly and then select another 20 pieces of paper. Note the number of pieces that have been crossed or marked.

5. Write this number as a fraction of 20 and then simplify the fraction.

6. We can now estimate the total number of pieces in the bag. We can assume that the fraction obtained in question 5 is equivalent to the number of crossed out pieces (20) over the total number of pieces in the bag. Based on this assumption, what is the total number of pieces of paper in the bag?

7. Check your estimate with your partner.

Use the method above to answer the following questions:

8. A group of wildlife officers at the South Pole captured and tagged 150 seals. Six months later they made a second capture of 200 seals and found that 25 were tagged.(a) What fraction of seals in the second

capture were tagged?(b) Estimate the seal population of

the South Pole.

LITERACY TASK • Find the meanings of these key terms:

1. fraction:..............................................................................................................................................................................

2. population:.........................................................................................................................................................................

3. estimate: .............................................................................................................................................................................

4. technique: ..........................................................................................................................................................................

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I N V E S T I G A T I O N

INVESTIGATION:

Capture — recapture

John Wiley & Sons Australia, Ltd 2004

9. Wildlife officers catch, tag and release 100 kangaroos in a mountainous area. After some time, they make a second capture of 250 kangaroos and find that 10 are tagged.(a) What fraction of kangaroos in the

second capture were tagged?(b) Estimate the kangaroo population

in this area.

10. A small country town has a high school with 500 students. To estimate the entire population of the town, 300 people in a shopping mall were surveyed, and it was found that 50 of them were local high school students.(a) What fraction of people in the

shopping mall were high school students?

(b) Estimate the population of the town.

11. A naturalist wished to determine the lorikeet population in a local park. She captured 52 lorikeets that were tagged and released. One week later she made a second capture of 72 lorikeets and found that 12 were tagged. Estimate the lorikeet population in the park.

12. A university student wished to determine the approximate number of taxis in the city. Over a period of 2 weeks he caught 25 taxis to various destinations and noted their registration numbers. A month later (over another 2 week period) he caught 40 taxis and found that he had used 8 of them in the previous month. What is the approximate number of taxis in the city?

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STRAND:

Chance and data

CHAPTER:

Data

MQQLD1-capture.pdf