Extending Algebraic Reasoning I

 

This course will extend and build on understanding developed in the Patterns, Patterns II, Numerical Reasoning, Geometry, and Probability courses.  Algebra will be presented as a language to describe patterns and model relationships.

Participants will develop and/or deepen their understandings of:

 

  • Generalizing patterns using symbols, words, tables, and pictures;
  • Symbol sense by building geometric models of equivalent algebraic expressions;
  • Proof via counterexample and symbolic reasoning;
  • Graph interpretation: analyzing slope (as a rate of change), interpreting intercepts in a given context, and assigning reasonable domain and range in given context;
  • Variables: discrete, continuous, independent, dependent;
  • A variety of functions and relations with particular emphasis on linear functions;
  • representation of functions: connections among, conversions among, interpretation of, and strengths and limitations of verbal, symbolic, numerical, and graphical representations of functions;
  • Functional notation used to represent slope, signed lengths, and signed areas;
  • Simplifying algebraic expressions and solving equations;
  • Anticipating results and judging the reasonableness of results;
  • Appropriate use of technology in the classroom: the TI-84 and CBR2 motion sensor are used as exploration tools that allow students to ask questions; anticipate, check, and explain answers; and distinguish between exact and approximate solutions; and
  • The role and importance of clear communication using proper mathematical language and notation.