Course 2, Unit 1 - Functions, Equations, and Systems
This first algebra and functions unit of Course 2 builds on the
units of Course 1 that developed student understanding of functions
and their representation in tables, graphs, and symbolic rules and the
particular properties of linear, exponential, and quadratic functions.
The first lesson provides a review of those concepts and skills. The
subsequent lessons are designed to extend algebraic thinking and problem
solving to functions and equations involving several independent variables
and finally systems of linear equations with two variables.
Key Ideas from Course 2, Unit 1
Direct variation: If the relationship of variables y and x can
be expressed in the form y = kx for some
constant k, then we say that y varies directly with x or
that y is directly proportional to x. The number k is
called the constant of proportionality for the relationship. (See
Inverse variation: If the relationship of variables y and x can
be expressed in the form y = k/x for
some constant k, then we say that y varies inversely
with x or that y is directly proportional to x.
The number k is called the constant of proportionality for
the relationship. (See p. 7.)
Direct variation power functions: power functions of the
form y = axn (n > 0)
Inverse variation power functions: power functions of the
form y = k/xn (n > 0)
Multiple-variable relationships: Ohm's Law is one multiple-variable
relationship that students consider. Current I, voltage V,
and resistance R are related in the relationship I = V/R.
Students consider how keeping one variable constant and changing
a second variable affects the third variable. They also rewrite multiple-variable
formulas by solving for each variable. For example, I = V/R can
also be written as I*R = V.
Solving linear systems of equations: Solving a system of
linear equations means finding ordered pair(s) of values that satisfies
both linear equations. Linear systems have either no solutions, one
solution, or infinitely many solutions. Graphically, the two lines
will either be parallel, intersect in one point, or have the same
graph (represent the same line). Algebraic methods for solving linear
systems developed in this unit are the substitution method and the
linear combination method. The matrix method for solving systems
is developed in Unit 2.