Name of Unit: Capture/Recapture



Name of Unit: Capture/Recapture

Subject and Grade Level: Math, Middle School

Objectives:

• Students will use proportions to estimate the size of populations.

• Students will calculate descriptive statistics and create a graph/table of population estimates.

Time: 2 days

Minnesota State Standards Addressed:

Bold type indicates standards addressed by this unit.

A student shall:

1. Evaluate and solve problems, including calculating basic measures of center and variability, to demonstrate understanding of basic concepts of probability and calculate simple probabilities

2. Formulate a question and design an appropriate data measurement concepts

3. Organize raw data and represent it in more than one way

4. Analyze data by selecting and applying appropriate data measurement concepts

5. Critique various representations of data

6. Devise and conduct a simulated probability situation

7. Predict future results based on experimental results

Knowledge:

Describe/identify ratios and proportions.

Describe the difference between a simulation and an experiment.

Skills:

Use proportions to estimate a population size.

Organize data.

Create a display of the sampling distribution.

Calculate descriptive statistics—measures of center, measures of spread.

“Conduct a probability experiment to simulate a real life issue” Minnesota Frameworks.

Understandings:

Understand that probability is not an exact science.

“Develop an appreciation for the pervasive use of probability in the real world” Minnesota Frameworks.

Lesson Plan

Pre-requisite knowledge:

• Mean, median, mode, range

• Proportions, fractions, percents

Materials:

Each group of students will need

• Dry white beans in jar (approximately the same number for each group

• Permanent marker

• Small cup

Lesson:

1. “I want to know how many fish are in our lake—how might I do this?”

2. Students will brainstorm—think-pair-share.

3. Teacher introduces the capture/recapture model to estimate population size—use the fish exhibit, but do not show the math at this time.

4. Explain how a simulation using beans can be conducted. Discuss the difference between an experiment and a simulation.

5. Students in small groups will conduct the simulation:

a. Students take a handful/cupful and record the number of beans selected.

b. Mark the beans in this selection and then mix them back in.

c. Students take a second handful/cupful and record the number of marked beans as well as the total number of beans selected.

6. “How could I use these numbers to find the total number of beans (size of population)?” Class discussion.

7. Set up the proportion and find the estimate of the sample size:

1st amount/population total as 2nd marked/ 2nd total

8. Review mean, median, mode, range.

9. Gather all class estimates and have students calculate:

a. mean

b. median

c. mode

d. range

10. Students will each create a visual display of their work. These will include population estimates and descriptive statistics as well as the calculations of these and a graph of the distribution.

11. Post students’ visual displays on the walls and do a “wall walk” and discuss as a class the characteristics of good displays.

12. Homework.

Homework Assignment

Biologists want to come up with estimates for the size of the tadpole populations in the lakes of the surrounding area. To do this, tadpoles are captured, dyed red, and released. A second capture takes place. The total number captured was recorded as well as the number of those that were marked.

At different lakes in the area, the following estimates of population size were obtained: 44, 71, 41, 63, 73, 61, 74

| |1st capture |2nd capture | |

| |Number initially |Total in 2nd capture |Number of 2nd |Population Size |

| |captured and dyed | |total that are |Estimate |

| | | |marked | |

|Fish Lake |61 |68 |36 | |

|Long Lake |98 |111 |60 | |

|Round Lake |70 |84 |27 | |

• Obtain a population estimate for each lake and add to the list above.

• Calculate appropriate descriptive statistics (mean, median, mode, range) for the list of all 10 lakes.

• How could capture recapture be used in another situation? Describe the population and the procedure you would use to do this experiment.

• Create a visual display of your work. Include population estimates and descriptive statistics as well as the calculations of these, a graph of the distribution, and your situation description.

Possible Scoring:

|Criteria |Points Possible |Points Earned |

|Proportions for estimates properly set up. |2 | |

|Population estimates are accurate. |2 | |

|Statistics are calculated accurately. |2 | |

|Visual display is accurate. |2 | |

|Population identified is appropriate. |2 | |

|Description of experiment is accurate and thorough. | | |

| How captured |1 | |

| How marked |1 | |

| How recaptured |1 | |

| How to record data |1 | |

| What to do with data |1 | |

Data for the activity excerpted from:

Additional Resources

Minnesota K-12 Framework for Mathematics

Tadpole dye capture-recapture



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