Unit
1 
 MultipleVariable
Models
 Develops student ability to construct and reason with linked quantitative variables and relations involving several variables and several constraints.

 Topics
include:
 Formulas, including the Law of Sines and the Law of Cosines, relating several variables by a single equation; systems of equations with several dependent variables or constraints; patterns of change in one or more variables in response to changes in others; solution of systems of equations and inequalities; and linear programming.

Unit
2 
 Modeling
Public Opinion
 Develops student understanding of how public opinion can be measured. The situations analyzed include elections (where there are more than two choices) and sample surveys, including political polling.

 Topics
include:
 Preferential voting, voteanalysis methods, Arrow's theorem, fairness in social decision making; surveys, sampling, sampling distributions, relationship between a sample and a population, confidence intervals, margin of error; and critical analysis of elections and surveys.

Unit
3 (sample
material) 
 Symbol
Sense and Algebraic Reasoning
 Develops student ability to represent and draw inferences about algebraic relations and functions using symbolic expressions and manipulations.

 Topics
include:
 Formalization of function concept, notation, domain, and range; use of polynomial, exponential, and rational expressions to model relations among quantitative variables; field properties of real numbers and their application to expression of algebraic relations in equivalent forms and to solution of equations and inequalities by methods including factoring and the quadratic formula, and algebraic proof.

Unit
4 (sample
material) 
 Shapes
and Geometric Reasoning
 Introduces students to formal reasoning and deduction in geometric settings.

 Topics
include:
 Inductive and deductive reasoning, counterexamples, the role of assumptions in proof; conclusions concerning supplementary and vertical angles and the angles formed by parallel lines and transversals; conditions insuring similarity and congruence of triangles and their application to quadrilaterals and other shapes; and necessary and sufficient conditions for parallelograms.

Unit
5 (sample
material) 
 Patterns
in Variation
 Extends student understanding of the measurement of variation, develops student ability to use the normal distribution as a model of variation, and introduces students to the probability and statistical inference involved in the control charts used in industry for statistical process control.

 Topics
include:
 Standard deviation and its properties, normal distribution and its relation to standard deviation, statistical process control, control charts, control limits, mutually exclusive events, and the Addition Rule of Probability.

Unit
6 (sample
material) 
 Families
of Functions
 Reviews and extends student ability to recognize different function patterns in numerical and graphical data and to interpret and construct appropriate symbolic representations modeling those data patterns.

 Topics
include:
 Review of linear, polynomial, exponential, rational, and trigonometric functions (including effects of parameters on numeric and graphic patterns) and construction of function rules for function tables and graphs that are transformations of basic types (translation, reflection, stretch).

Unit
7 (sample
material) 
 Discrete
Models of Change
 Extends student ability to represent, analyze, and solve problems in situations involving sequential and recursive change.

 Topics
include:
 Iteration and recursion as tools to model and analyze sequential change in realworld contexts; arithmetic, geometric, and other sequences; arithmetic and geometric series; finite differences; linear and nonlinear recurrence relations; and function iteration, including graphical iteration and fixed points.

Capstone 
 Making
the Best of It: Optimal Forms and Strategies
 A thematic,
twoweek, projectoriented activity that enables students to pull
together and apply the important mathematical concepts and methods
developed throughout the course.
