Benchmark 9B: The Mathematical World - Symbolic Relationships

• 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