ALEX Classroom Resource

  

Predator-Prey Cycles | Zombies and Calculus

  Classroom Resource Information  

Title:

 Predator-Prey Cycles | Zombies and Calculus

URL:

 https://aptv.pbslearningmedia.org/resource/nvnd-math-zombiecalc1/zombies-and-calculus-part-1/

Content Source:

 PBS
Type: Audio/Video

Overview:

Learn about the math behind predator-prey population cycles in this video from NOVA Digital. In this example, zombie and human populations fluctuate. The zombie population increases as zombies convert humans into zombies. However, without enough humans to eat, zombies die and the population shrinks. The human population increases as humans reproduce but decreases as zombies eat humans. The populations of humans and zombies change through time according to a pair of differential equations. Because human and zombie populations are related, the growth rate of each population depends on the current numbers of both humans and zombies.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
30. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and general piecewise functions. [Algebra I with Probability, 28]
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a function that models a relationship between two quantities,
  • Produce the graph and table of the function and show the key features (intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. and end behavior) that are appropriate for the function.

  • Given key features from verbal description of a relationship, sketch a graph with the given key features.
Teacher Vocabulary:
  • Function
  • Intercepts
  • Intervals of Increasing
  • Intervals of decreasing
  • Function is positive
  • Function is negative
  • Relative Maximum
  • Relative Minimum
  • Axis symmetry
  • Origin symmetry
  • End behavior
Knowledge:
Students know:
  • Key features of function graphs (i.e., intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. and end behavior).
  • Methods of modeling relationships with a graph or table.
Skills:
Students are able to:
  • Accurately graph any relationship.
  • Interpret key features of a graph.
Understanding:
Students understand that:
  • The relationship between two variables determines the key features that need to be used when interpreting and producing the graph.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
28. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a function that models a relationship between two quantities, produce the graph and table of the function and show the key features (intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. end behavior. and periodicity) that are appropriate for the function.


Given key features from verbal description of a relationship,
  • Sketch a graph with the given key features.
  • Know periodicity.
Teacher Vocabulary:
  • Function
  • Periodicity
  • x-intercepts
  • y-intercepts
  • Intervals of Increasing
  • Intervals of decreasing
  • Function is positive
  • Function is negative
  • Relative Maximum
  • Relative Minimum
  • y-axis symmetry
  • Origin symmetry
  • End behavior
Knowledge:
Students know:
  • Key features of function graphs (i.e., intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. end behavior. and periodicity).
  • Methods of modeling relationships with a graph or table.
Skills:
Students are able to:
  • Accurately graph any relationship.
  • Interpret key features of a graph.
Understanding:
Students understand that:
  • The relationship between two variables determines the key features that need to be used when interpreting and producing the graph.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.28.1: Define intercepts, intervals, relative maxima, relative minima, symmetry, end behavior, and periodicity.
ALGI.28.2: For a function that models a relationship between two quantities, find the periodicity.
ALGI.28.3: For a function that models a relationship between two quantities, find the end behavior.
ALGI.28.4: For a function that models a relationship between two quantities, find the symmetry.
ALGI.28.5: For a function that models a relationship between two quantities, find the intervals where the function is increasing, decreasing, positive, or negative.
ALGI.28.6: For a function that models a relationship between two quantities, find the relative maxima and minima.
ALGI.28.7: For a function that models a relationship between two quantities, find the x and y intercepts.

Prior Knowledge Skills:
  • Identify parts of the Cartesian plane.
  • Graph a function given the slope-intercept form of an equation.
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from table.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.28 Given graphs that represent linear functions, identify key features (limit to y intercept, x-intercept, increasing, decreasing) and/or interpret different rates of change (e.g., Which is faster or slower?).
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra II with Statistics
17. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries (including even and odd); end behavior; and periodicity. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a symbolic representation of a function (including polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise),
  • Produce an accurate graph (by hand in simple cases and by technology in more complicated cases) and justify that the graph is an alternate representation of the symbolic function.
  • Recognize if a function is even or odd.
Teacher Vocabulary:
  • Polynomial function
  • Piecewise function
  • Logarithmic function
  • Trigonometric (sine and cosine) function
  • Reciprocal function
  • Radical function
  • Period
  • Midline
  • Amplitude
  • End Behavior
  • Intervals
  • Maximum
  • Minimum
  • Symmetry
  • Even and Odd
  • Intercepts
  • Intervals
Knowledge:
Students know:
  • Techniques for graphing.
  • Key features of graphs of functions.
Skills:
Students are able to:
  • Identify the type of function from the symbolic representation.
  • Manipulate expressions to reveal important features for identification in the function.
  • Accurately graph any relationship.
  • Determine when a function is even or odd.
Understanding:
Students understand that:
  • Key features are different depending on the function.
  • Identifying key features of functions aid in graphing and interpreting the function.
  • Even and odd functions may be identified from a graph or algebraic form of a function.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGII.17.1: Define intercepts, intervals, relative maxima, relative minima, symmetry, end behavior, and periodicity.
ALGII.17.2: For a function that models a relationship between two quantities, find the periodicity.
ALGII.17.3: For a function that models a relationship between two quantities, find the end behavior.
ALGII.17.4: For a function that models a relationship between two quantities, find the symmetry.
ALGII.17.5: For a function that models a relationship between two quantities, find the intervals where the function is increasing, decreasing, positive, or negative.
ALGII.17.6: For a function that models a relationship between two quantities, find the relative maxima and minima.
ALGII.17.7: For a function that models a relationship between two quantities, find the x- and y-intercepts.

Prior Knowledge Skills:
  • Compare properties of two functions each represented in a different way.
  • Identify properties of functions defined algebraically.
  • Identify properties of functions defined by verbal description.
  • Identify properties of functions defined graphically.
  • Identify properties of functions defined numerically in tables.
  • Define standard function types as quadratic and linear.
Tags: changing populations, derivative, growth rate
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

 This resource contains discussion questions.

  This resource provided by:  
Author: Kristy Lacks
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