Benchmark
9B: The Mathematical World - Symbolic Relationships
(grades 6-8, page 219)
An equation containing a variable may be true for just one value of the
variable. (1 of 3)
Standard 9-1, page 102, Grades 5-8
Understand the concepts of variable, expression, and equation
Standard 9-6, page 102, Grades 5-8
Apply algebraic methods to solve a variety of real-world and mathematical
problems
Mathematical statements can be used to describe how one quantity changes
when another changes. Rates of change can be computed from magnitudes and
vice versa. (2 of 3)
Standard 13-6, page 116, Grades 5-8
Develop the concepts of rates and other derived and indirect measurements
Standard 8-3, page 98, Grades 5-8
Analyze functional relationships to explain how a change in one quantity
results in a change in another
Graphs can show a variety of possible relationships between two variables.
As one variable increases uniformly, the other may do one of the following:
always keeps the same proportion to the first, increase or decrease steadily,
increase or decrease faster and faster, get closer and closer to some limiting
value, reach some intermediate maximum or minimum, alternately increase
and decrease indefinitely, increase or decrease in steps, or do something
different from any of these. (3 of 3)
Standard 8-3, page 98, Grades 5-8
Analyze functional relationships to explain how a change in one quantity
results in a change in another
Standard 9-3, page 102, Grades 5-8
Analyze tables and graphs to identify properties and relationships
Standard 6-3 page 154, Grades 9-12
Translate among tabular, symbolic, and graphical representations of
functions
Standard 6-4 page 154, Grades 9-12
Recognize that a variety of problem situations can be modeled by the
same type of function
Standard 13-1 page 180, Grades 9-12
Determine maximum and minimum points of a graph and interpret the results
in problem situations
