The Limits of Tolerance

Learning Resource Type

Classroom Resource

Subject Area

English Language Arts
Mathematics
Science

Grade(s)

9, 10, 11, 12

Overview

They're an important part of the ecosystem. They prevent disease and clean up carrion. Yet, they're also a nuisance to homeowners and a threat to livestock. Their population has recovered and grows at an incredible rate. At what point can we say that there are too many black vultures in America?

This informational material will apply a precalculus concept--limits of functions--to an environmental science issue--how biological and physical changes within an ecosystem can affect the population growth of a species. There are additional links provided for students to explore more about this issue. 

English Language Arts (2021) Grade(s): 11

ELA21.11.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

UP:ELA21.11.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
English Language Arts (2021) Grade(s): 12

ELA21.12.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

UP:ELA21.12.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
Science (2015) Grade(s): 09-12 - Environmental Science

SC15.ES.3

Use mathematics and graphic models to compare factors affecting biodiversity and populations in ecosystems.

UP:SC15.ES.3

Vocabulary

  • interpolation
  • extrapolation
  • anthropogenic
  • limiting factors
  • biodiversity index
  • species richness
  • species evenness
  • population
  • graphic models
  • population pyramid
  • doubling time
  • growth rate
  • slope
  • exponential growth
  • population curve
  • logistic growth model
  • linear growth model
  • constant growth
  • density-dependent limiting factors
  • density-independent limiting factors
  • carrying capacity
  • Biodiversity Treaty
  • demographic transition
  • correlation
  • endangered species
  • extinction
  • survivorship
  • sustainability
  • population properties
  • density and dispersion
  • reproductive potential

Knowledge

Students know:
  • The carrying capacity of an ecosystem results from such factors as availability of living and nonliving resources and from such challenges as predation, competition, and disease.
  • Anthropogenic changes in the environment, including habitat destruction, pollution, introduction of invasive species, overexploitation, and climate change, can disrupt an ecosystem and threaten the survival of some species.
  • Examples of mathematical representations include finding the average, determining trends, and using graphical comparisons of multiple sets of data.
  • The difference between density-dependent and density-independent limiting factors, examples of each, and how each affects populations and biodiversity within an ecosystem.

Skills

Students are able to:
  • Differentiate between constant and exponential growth.
  • Use graphs to compare multiple sets of data.
  • Determine trends in data sets.
  • Use a variety of graphs and charts, including: (e.g., scatterplots, tables, line graphs, bar graphs, histograms) to evaluate the impact of factors on populations and biodiversity.
  • Utilize interpolation, extrapolation and statistical analyses to determine relationships between biodiversity and population numbers.
  • Make inferences and justify conclusions from sample surveys, experiments, and observational studies. (ALCOS Mathematics S-IC)
  • Choose a scale and the origins in graphs (ALCOS Mathematics ALGI. 4.2) in order to accurately compare graphical data.
  • Determine an appropriate graphic model to display relationships comparing populations by biodiversity.
  • Describe how factors affecting ecosystems at one scale can cause observable changes in ecosystems at a different scale.

Understanding

Students understand that:
  • The number of populations in a given area reflects the biodiversity of that area.
  • Ecosystems can exist in the same location on a variety of scales, and these populations can interact in ways that may, or may not, significantly alter the ecosystems.
  • Using the concept of orders of magnitude, a model at one scale relates to a model at another scale.

Scientific and Engineering Practices

Developing and Using Models

Crosscutting Concepts

Scale, Proportion, and Quantity
Science (2015) Grade(s): 09-12 - Environmental Science

SC15.ES.4

Engage in argument from evidence to evaluate how biological or physical changes within ecosystems (e.g., ecological succession, seasonal flooding, volcanic eruptions) affect the number and types of organisms, and that changing conditions may result in a new or altered ecosystem.

UP:SC15.ES.4

Vocabulary

  • ecological succession
  • seasonal flooding
  • volcanic eruptions
  • ecosystem
  • biological changes
  • physical changes
  • keystone species
  • pioneer species
  • habitat alteration
  • density-dependent limiting factors
  • density-independent limiting factors
  • primary succession
  • secondary succession
  • remediation/bioremediation
  • symbiosis
  • abiotic factors
  • biotic factors
  • food chain
  • food web
  • energy pyramid
  • energy flow
  • bioaccumulation
  • ecological system
  • ecosystem services
  • deforestation
  • organism
  • species
  • population
  • community
  • ecosystem
  • biome
  • biosphere
  • desertification
  • overharvesting
  • overgrazing
  • pathogen
  • climax community

Knowledge

Students know:
  • The components of a scientific argument including the claim, alternative claim, evidence, justification, and the challenge to the alternative claim.
  • Factors that affect biodiversity.
  • The relationships between species and the physical environment in an ecosystem.
  • Examples of biological changes (e.g., ecological succession, disease) and physical changes (e.g., volcanic activity, desertification) that affect the number and types of organisms, and that may result in a new or altered ecosystem.

Skills

Students are able to:
  • Use additional relevant evidence to assess the validity and reliability of the given evidence and its ability to support the proposed argument.
  • Describe the strengths and weaknesses of the given claim in accurately explaining a particular response of the ecosystem to a changing condition, based on an understanding of factors that affect biodiversity and the relationships between species and the physical environment.
  • Assess the logic of the reasoning, including the relationship between degree of change and stability in ecosystems, and the utility of the reasoning in supporting the explanation.

Understanding

Students understand that:
  • A complex set of interactions within an ecosystem can keep its numbers and types of organisms relatively constant over long periods of time under stable conditions.
  • When modest biological or physical disturbances occur in an ecosystem, it returns more or less to its original status (i.e., it is resilient).
  • Extreme fluctuations in conditions or the size of any population, however, can challenge the functioning of an ecosystem in terms of resources and habitat availability, and can even result in a new ecosystem.

Scientific and Engineering Practices

Engaging in Argument from Evidence

Crosscutting Concepts

Cause and Effect
Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.7

Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity.

UP:MA19.PRE.7

Vocabulary

  • Limit
  • Convergent
  • Divergent
  • Continuous function
  • Discontinuous function
  • Discontinuity (infinite, jump, removable)

Knowledge

Students know:
  • How to graph the families of functions.
  • How to factor, simplify, and rationalize functions.
  • How to evaluate functions at a given input value.

Skills

Students are able to:
  • Identify continuity and discontinuity (if discontinuous, identify the type).
  • Calculate limits.

Understanding

Students understand that:
  • Functions have various types of continuity and discontinuity.
  • That limits can be determined numerically, graphically, and algebraically.
  • converging means that a limit exists, while diverging means that a limit does not exist.

CR Resource Type

Informational Material

Resource Provider

Other

License Type

CUSTOM

Resource Provider other

CK-12
https://www.ck12.org/c/calculus/evaluate-limits-using-substitution/rwa/The-Limi…

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Accessibility

Text Resources: Content is organized under headings and subheadings

Approved Date

ALSDE LOGO

This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Alabama Learning Exchange © 2002-2023 by Alabama State Department of Education is licensed under Attribution-NonCommercial-ShareAlike 4.0 International

Design by Adaptive Theme