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II.5 APPORTIONMENT AND FAIR DIVISION
  prerequisite:  II.3

  A. APPORTIONMENT
 

A student will learn how to: 
  • describe the goals of apportionment
  •  define quota and apply methods of calculating quotas
  •  reproduce and implement algorithms for calculating the Hamilton method of apportionment
  •  analyze data which illustrate difficulties and identify unfairness
    • the Alabama paradox
    • the Population paradox
    • the New States paradox
  •  apply the Webster and other divisor methods of apportionment
    •  the Adams divisor method
    •  the Jefferson divisor method
    •  the Hill divisor method
  •  compute and apply an adjusted quota to overcome difficulties
  •  use the Apportionment Impossibility Theorem to describe deficiencies of various apportionment methods
 

  B.  FAIR  DIVISION
 

A student will learn how to: 
  • describe the goals of fair division
  • produce and implement fair division algorithms for dividing a cake
  • produce and implement fair division algorithms for dividing an estate
  • work with a prepared spreadsheet template to fairly divide an estate
  • produce and implement fair division algorithms for dividing property
 
  TECHNOLOGY:  graphing calculator with capability to produce numerical tables, spreadsheets, other prepared software 
TEACHING METHODS:  mostly group activities 
IMBEDDED CONCEPTS: ratio and proportion, rounding off decimals, geometric regions 
 CONCEPTS:  logical reasoning, apportionment, fair division 
 

II.6 ALGEBRA  SKILLS  -  Level A
 
 

A student will learn how to: 
  • transform expression involving a multi-step process  (for example, verify an identity) 
  • factor polynomials of degree less than or equal to 4 
  • transform expressions using the properties of exponents and logarithms, using the concept of one as the inverse of the other 
  • solve problems within a context by formulating equations and inequalities
 
 
 CONCEPTS:   domain and range of functions
 

 to the writer:  modeling should drive both of the algebra modules
 

II.7 ALGEBRA  SKILLS  -  Level B
  prerequisite:  II.6
 

A student will learn how to: 
  • simplify algebraic expressions that involve fractional and negative exponents
  • solve linear inequalities
  • apply the rules of exponents and logarithms to solve exponential and logarithmic equations
  • apply skills to solve many different kinds of equations found in a variety of
  • application problems (include roots, quadratic, cubic, quartic, logarithmic, exponential, etc.)
 
 suggestion for project:  write a paper that discusses how these functions are used in the real
world
 to the writer:  modeling should drive both of the algebra modules
 
 CONCEPTS:  domain and range of functions 
 
II.8 SYNTHESIS I
  (related to modules II.1 and II.2)
  see discussion of Synthesis Module in Level One ideas:  
 

II.9 SYNTHESIS II
  (related to modules II.1 and II.4)
  see discussion of Synthesis Module in Level One ideas:

 
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Last Date Modified: October 3, 1997