Learning Goals for the Teachable Unit

• Understand that population growth is a multiplicative process.

• Practice how to construct graphs and interpret quantitative data.

• Understand that most population growth is not exponential: factors may limit population growth.

Learning Goals for the Teachable Tidbit

• Students will be able to construct and interpret graphs related to population growth.

• Students will understand the difference between population density and growth rates.

• Students will be able to calculate rates of population growth and make predictions about population size.

Teachable Unit: Population Growth

Preclass Learning Outcome(s)1.Know how to define a population. 2.Know that density is one way of measuring

changes in a population. Activity/assessment1.Reading/lecture on population2.Clicker question or online quiz for self-

assessment

Time Pop. A Pop. B Pop. C1 1 10 1002 2 15 1103 4 23 1214 8 35 1335 16 53 146

Density data for three populations (A, B, C) all taken during the same time intervals.

1. Graph DENSITY VS. TIME. 2. Calculate which population is growing the fastest.

Brainstorm how you might quantify population growth rate.

3. Discuss among your groups how you determined your answer.

4. Combine the graphs on one set of axes. (6 min)

Clicker Question:

Rank the population size at time 10.

A.A>B>CB.C>B>AC.B>A>CD.None of the above.E.There is not enough information to determine the answer.

Time Pop. A Pop. B Pop. C1 1 10 1002 2 15 1103 4 23 1214 8 35 1335 16 53 146

Density data for three populations (A, B, C) all taken during the same time intervals.

4. What is the proportional increase in population size in a given time interval? Is it constant? (2 min)

Clicker Question:

Based on your calculation of the proportional increase of population size per time interval, rank the population size at time 10.

A.A>B>CB.C>B>AC.B>A>CD.None of the above.E.There is not enough information to determine the answer.

Time Pop. A Pop. B Pop. C

1 1 10 100

2 2 15 110

3 4 23 121

4 8 35 133

5 16 53 146

6 32 80 160

7 64 120 176

8 128 180 193

9 256 270 212

10 512 405 233

At time 10: A > B > C

Clicker Question:

Population growth

A.is additive in all cases (Additive: a constant number is added for each time unit within a specific population).B.is multiplicative in all cases. (Multiplicative: the number of individuals added to the population is a function of the number of individuals present; therefore, growth changes as a function of density.)C.may be additive or multiplicative but varies by population.

A > B > C

Population A is growing by 100% (or doubling) in each time interval.Population B is growing by 50% in each time interval.Population C is growing by 10% in each time interval.

Nt + 1 = Nt + [Nt• proportional change]

A: Nt + 1 = Nt + [Nt• (1.0)]

B: Nt + 1 = Nt + [Nt• (0.5)]C: Nt + 1 = Nt + [Nt• (0.1)]

0

500

1000

1500

2000

2500

0 5 10 15

Num

ber

Time

multiplicative

additive

Nt + 1 = Nt + [Nt• (1.0)]Nt + 1 = Nt + (15)

What is the population growth rate?Predict the population size at time 9 and 10.

Summative Question

Timedensity (number/m2)

1 102 143 204 285 396 557 778 1089

10

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Num

ber

Time

A

B

C

Summative QuestionBetween time intervals 3 and 4, which population is

proportionally growing the fastest?Between time intervals 8 and 9, which population is

proportionally growing the fastest?