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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.
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