STANDARD COURSE OF STUDY CORRELATIONS: Science, Grade 6, 7, 8, Goal 1: The learner will design and conduct investi­

gations to demonstrate an understanding of scientific inquiry.

1.05 Analyze evidence to explain observations, make inferences and predictions, and develop the relationship between evidence and explanation.

1.06 Use mathematics to gather, organize, and present quantitative data resulting from scientific investigations.

1.08 Use oral and written language to communicate findings.

1.09 Use technologies and information systems to research, gather and analyze data, visualize data, and disseminate findings to others.

Math, Grade 6, Goal 1: The learner will understand and compute with rational numbers.

1.04 Develop fluency in addition, subtraction, multiplication, and division of non­negative rational numbers.

• Analyze computational strategies. • Describe the effect of operations on size. • Estimate the results of computations. • Judge the reasonableness of solutions.

1.05 Develop fluency in the use of factors, multiples, exponential notation, and prime factorization.

1.06 Use exponential, scientific, and calculator notation to write very large and very small numbers.

1.07 Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

Science, Grade 6, Goal 7: The learner will conduct investigations and use technolo­gies and information systems to build an understanding of population dynamics.

7.01 Describe ways in which organisms interact with each other and with non-living parts of the environment:

• Coexistence/Cooperation/Competition. • Symbiosis. • Mutual dependence.

7.02 Investigate factors that determine the growth and survival of organisms. • Light. • Temperature range. • Mineral availability. • Soil/rock type. • Water. • Energy.

7.05 Examine evidence that overpopulation by any species impacts the environment.

7.06 Investigate processes which, operating over long periods of time, have resulted in the diversity of plant and animal life present today:

• Natural selection. • Adaptation.

INTRODUCTION TO LESSON: Students will work individually or in pairs to calculate the exponential growth of an invasive weed.

EXPLORING NORTH CAROLINA

oooooooooooooooooEpisode: Invaders Among Us

Calculating Exponential Growth of Knapweed

MATERIALS o Photos of spotted knap­

weed (a large laminated image or several smaller photos to pass around). An Internet search will pro­duce many suitable images.

o Graph paper, one sheet per student or pair

o Calculators (optional)

For a follow-along viewing guide for students, see Viewing Guide 15. Spotted knapweed photo courtesy of Joseph M. DiTomaso, University of California, Bugwood.org. •1•

Calculating Exponential Growth of Knapweed

ooooooooo BEYOND THE CLASSROOM • Visit a state park to learn

about invasive species. Most state parks can offer a topic-specific program. The N.C. State Parks system (http:// www.ncparks.gov/) offers free Environmental Education Learning Experiences (EELEs) for educators and students that may be used before, after, during and/or instead of field trips (download from http://www.ncparks.gov/ Education/eele.php). Park staff will provide guided on-site activities with school groups (call ahead to make a reservation). The Parks system has a stewardship program focusing specific­ally on invasive species. Check out www.ncparks.gov/ About/natural_resources_ stewardship.php for more information.

• A nearby public garden may be able to provide a topic-specific program upon request. For a list of public gardens throughout North Carolina, visit http://www.ces.ncsu. edu/depts/hort/consumer/ pgpages.html.

Additional Resources:

Spotted Knapweed Fact Sheet • http://www.nps.gov/plants/ ALIEN/fact/cest1.htm

BACKGROUND FOR TEACHER: A non-native species becomes invasive when it domi­nates, displaces and disrupts native species. When a non-native species is intro­duced into habitats outside its native home, sufficient barriers to limit its growth may not exist. Natural controls include predators, disease, floods, fires and hurri­canes. Human control measures include habitat destruction, collecting/harvest and pesticide application. When a plant species is capable of exponential growth due to the quantity of seeds that it can produce, it can become an overwhelming problem in a non-native habitat.

Spotted knapweed is an invasive plant that arrived in North America from Europe and Asia in the late 1890s as a contaminant in alfalfa and clover seed. It has spread throughout Canada and almost all of the United States (except Alaska, Georgia, Mississippi, Oklahoma and Texas) and runs rampant in fields, forests, prairies, meadows, pastures and rangelands. Spotted knapweed outcompetes native plant species, reduces native plant and animal biodiversity and decreases forage produc­tion for livestock and wildlife. It has increased at an estimated rate of 27 percent per year since 1920 and has the potential to invade about half of all the rangeland (35 million acres) in the state of Montana alone.

engage f Ask students what they think prevents a species of plant or animal from becoming overpopulated. Have groups of students discuss and compile their ideas on paper.

explore f Show Chapter 4 of the video. Review with students how unchecked growth of non-native organisms can overwhelm ecosystems. Show a photo of spotted knapweed and talk about its natural history and the effects it has had on habitats in the United States. Tell students that they will be calculating the potential exponen­tial growth rate of one knapweed over a 10-year period. Have students work individ-

Spotted knapweed infestation photograph by John M. Randall, The Nature Conservancy, Bugwood.org.

ually or in pairs to complete the assignment sheet. Assist as necessary.

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Calculating Exponential Growth of Knapweed

Solution: • From 100 seeds, four (4 percent) will germinate the first year. • Ninety-six seeds will remain in the “seed bank” (stores of seed in the soil that have not germinated yet). • Twenty-five percent of the sprouts (one of the four) will survive to maturity. That plant will produce

1,000 seeds the next year. • In the second year, 44 seeds (4 percent of 1,096) in the seed bank will sprout; 11 of those plants will

survive, increasing the population to 12 plants (with first year plant added). • These 12 plants produce 12,000 new seeds. Add 96 percent of last year’s seed bank for a total of

13,052 seeds. • Continue counting for five years, taking 1 percent of the previous year’s seed bank and adding to the

previous year’s plants to calculate the number of new plants. • Multiply plants by 1,000 and add 96 percent of the previous year’s seed bank to determine the new

size of the seed bank. • Since the plants live for only five years, subtract Year 1 from Year 6, Year 2 from Year 7, and so on. • Seeds are viable for only eight years, so subtract 100 from Year 8’s seed bank, Year 1’s seed bank

from Year 9’s seed bank, and so on.

*Under ideal conditions, knapweed could reproduce at this rate. Many variables, including soil type and precipitation, may affect population growth.

Year Number of Plants Number of Seeds

0 0 100

1 1 1,096

2 12 13,052

3 143 155,530

4 1,698 1,847,309

5 20,171 21,944,417

6 239,614 260,680,640

7 2,846,408 3,096,661,414

8 33,812,879 36,785,673,858

9 401,667,920 436,982,165,807

10 4,771,469,407 5,190,972,273,123

explain f Have students share their answers and the method(s) by which they arrived at the solutions. Assist any students unable to do the math.

elaborate f Have students graph their results to illustrate the rate of growth over time.

evaluate f Show Chapter 2 of the video to introduce students to other species that have become invasive. Ask students if the bird species mentioned (starlings, house sparrows, rock doves and house finches) might grow in number as quickly as the knapweed. Have them explain in writing why or why not.

Activity adapted from the Montana Weed Project Teacher’s Handbook.

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Calculating Exponential Growth of Knapweed

Assignment

Calculate the exponential growth of knapweed. One hundred knapweed seeds are inadvertently dropped in an area. Calculate how many plants and seeds will be produced over a period of 10 years based on the following growth factors:

• One knapweed plant produces 1,000 seeds. • Four percent of knapweed seeds germinate each year, leaving 96 percent

for the following year. • About 25 percent of seedlings will survive to maturity. • Knapweed seeds remain viable (able to germinate) in the soil for eight years. • The time from germination to seed production is one year. • Knapweed plants live for five years.

Year Number of Plants Number of Seeds

0 0 100

1

2

3

4

5

6

7

8

9

10

Illustration by Tracey Saxby, IAN Image Library (ian.umces.edu/imagelibrary/).

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