Outcomes, Fall 2012

Students will be able to
apply mathematical knowledge and reasoning to communicate mathematics concepts
as a result of:

- Understanding algebra as generalized arithmetic:

- Recognizing and applying the concepts of variable, function equality, and
equation to express relationships algebraically.

- Manipulating simple algebraic expressions and solving linear equations and
inequalities.

- Justifying algebraic manipulations by application of the properties of
equality, the order of operations, the number properties, and the order
properties.

- Using algebra to solve word problems involving fractions, ratios, proportions,
and percents.

- Identifying variables and deriving algebraic expressions that represent
real-world situations.

- Recognizing and applying the concepts of variable, function equality, and
equation to express relationships algebraically.
- Understanding the concept of function:

- Understanding the definition of function and the various representations of
functions (e.g., statements, input/output machines, tables, graphs, mapping
diagrams, formulas).

- Recognizing and extending patterns using a variety of representations (e.g.
verbal, numeric, pictorial, algebraic).

- Identifying and analyzing direct and inverse relationships in tables, graphs,
algebraic expressions and real-world situations.

- Using qualitative graphs to represent functional relationships in the real
world.

- Translating among different representations (e.g., tables, graphs, algebraic
expressions, verbal descriptions) of function relationships.

- Understanding the definition of function and the various representations of
functions (e.g., statements, input/output machines, tables, graphs, mapping
diagrams, formulas).
- Understanding linear functions and linear equations:

- Recognizing the formula and graph of a linear function.

- Distinguishing between linear and nonlinear functions.

- Finding a linear equation that represents a graph.

- Analyzing the relationships among proportions, constant rates, and linear
functions.

- Interpreting the meaning of slope and the intercepts of a linear equation that
models a real-world situation.

- Selecting the linear equation that best models a real-world situation.

- Recognizing the formula and graph of a linear function.

Students will be able to apply mathematical knowledge and reasoning to communicate mathematics concepts as a result of:

- Understanding non-linear functions
- Representing functions in multiple ways: graph, function rule, table, and words
- Recognizing characteristics of functions in different representations
- Given one representation of functions, generating other representations of functions

- Using mathematical models
- Recognizing patterns and functions in everyday life
- Recognizing the power of algebraic reasoning in everyday life
- Recognizing the power and limitations of mathematical models.

- Developing mathematical ways of thinking and habits of mind
- Persevering in making sense and solving complex problems
- Constructing and analyzing mathematical arguments
- Consider precision and estimation
- Looking for patterns, common structure, and repeated reasoning in mathematics.