## How Many Bears in the Forest?

### Amelia McCurdySanta Rosa District Schools

#### Description

Students model the tag and recapture of bears and use proportions to estimate the population of the bears in their forest. This is a statistical sampling method used by scientists and naturalist to determine population numbers.

#### Objectives

The student selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

The student describes a wide variety of patterns, relationships, and functions through models, such as manipulatives, tables, graphs, expressions, equations, and inequalities.

The student identifies the common uses and misuses of probability or statistical analysis in the everyday world.

The student knows that a brief change in the limited resources of an ecosystem may alter the size of a population or the average size of individual organisms and that long-term change may result in the elimination of animal and plant populations inhabiting the Earth.

#### Materials

-Paper bags
-Markers
-Box of Teddy Grahams (1-2 boxes per class)
-Small 3oz cups for scoops or laundry detergent scoops
-How Many Bears in the Forest worksheet (1 per student)(see attachment)
-Calculators

#### Preparations

1. Make copies of worksheet.
2. Gather materials.
3. Determine how many groups you will have in your class and put the divided bears into bags. I used a large handful for each bag to save preparation time.

#### Procedures

1. Ask students questions such as: “How do scientists and naturalists know how many animals are in a forest?” - How do they know the number of fish that are in a body of water?” “How do they determine how many endangered species are left?” Lead the discussion so students understand that the animals aren’t actually counted, but that scientist and naturalist use statistical sampling to predict the number.
2. Explain the tag and recapture method. Scientists capture and tag bears. They record the number of bears they tagged. The bears are returned to the forest. After a waiting period, the scientist return to the forest and recapture bears. They count the number of tagged bears and the total number of bears recaptured. Using the following proportion, they determine an estimate of the number of bears:
Original Number Tagged/Number of Bears in Forest = Total Tagged in Samples/Total Recaptured in samples
3. Work out an example for further explaination. Suppose the scientist tagged 52 bears, and returned them to the forest. Later, they recaptured 67 bears and had 33 tagged. We would set up the proportion like this: 52/N = 33/67. Solve using a calculator. Round your answer to the nearest animal/whole number.
4. Ask students if this is a good estimate? Yes it is. How can we get a better estimate? Take more samples. Now we are going to model this method with ‘Teddy Gram” bears. Our forest is the paper bag. Pass out materials and worksheets.
5. Demonstrate tag and recapture method while reading directions on worksheet. Tell students that they will be allowed to eat only after they complete the activity. This will motivate students.
6. Divide students into groups of 4 students. Assign roles: recorder, scientist (bear counter), statitian (calculates), goofer (gathers and returns material). If group number does not work out, assign more than one role to a student.
7. Walk around and monitor students to ensure groups are working together and that the students understand the procedure.
8. After students complete the chart, have them discard the tagged bears and eat the rest!

#### Assessments

See scoring and answer guide at the bottom of attached file.