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Topic: Graphs and graphing systems 

Mathematics

 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level IV (Grade 9-12)
   Benchmark 1.Understands that objects and relations in geometry correspond directly to objects and relations in algebra (e.g., a line in geometry corresponds to a set of ordered pairs satisfying an equation of the form ax + by = c)
    Knowledge/skill statements
     1.Understands a line in geometry corresponds to a set of ordered pairs
     2.Understands the connections between algebra and geometry
     3.Knows that ax + by = c is the general equation for a line
     4.Understands the concept of a coordinate plane
     5.Knows that geometric figures can be described algebraically
   Benchmark 9.Understands the basic properties and uses of polar coordinates
    Knowledge/skill statements
     1.Understands the properties of polar coordinates
     2.Understands the uses of polar coordinates
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level II (Grade 3-5)
   Benchmark 6.Knows basic characteristics and features of the rectangular coordinate system (e.g., the horizontal axis is the X axis and the vertical axis is the Y axis)
    Knowledge/skill statements
     1. Understands the horizontal axis is the X axis
     2. Understands the vertical axis is the Y axis
     3. Knows that the X axis and the Y axis are perpendicular
     4. Knows the rectangular coordinate system is divided into four quadrants
  Level III (Grade 6-8)
   Benchmark 3.Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them
    Knowledge/skill statements
     1. Understands how algebraic expressions can represent functions
     2. Represents functions using algebraic expressions
     3.Understands how verbal descriptions can represent functions
     4.Represents functions using tables
     5.Understands how tables can represent functions
     6.Understands how graphs can represent functions
     7.Represents functions using graphs
     8.Represents functions using verbal descriptions
     9.Understands the concept of a Venn diagram
     10.Represents patterns using Venn diagrams
     11.Understands how Venn diagrams can represent patterns
     12.Understands how algebraic expressions can represent patterns
     13.Represents patterns using algebraic expressions
     14.Understands how verbal descriptions can represent patterns
     15.Represents patterns using tables
     16.Understands how tables can represent patterns
     17.Understands how graphs can represent patterns
     18. Represents patterns using graphs
     19.Represents patterns using verbal descriptions
     20. Understands the relationship between tables and graphs
     21.Understands the relationship between tables and verbal descriptions
     22.Understands the relationship between tables and algebraic expressions
     23.Understands the relationship between tables and Venn diagrams
     24.Understands the relationship between graphs and verbal descriptions
     25.Understands the relationship between graphs and algebraic expressions
     26.Understands the relationship between graphs and Venn diagrams
     27.Understands the relationship between verbal descriptions and algebraic expressions
     28.Understands the relationship between verbal descriptions and Venn diagrams
   Benchmark 5.Solves linear equations using concrete, informal, and formal methods (e.g., using properties, graphing ordered pairs, using slope-intercept form)
    Knowledge/skill statements
     1.Understands the concept of a linear equation
     2.Solves linear equations using knowledge of properties
     3.Solves linear equations by graphing ordered pairs
     4.Solves linear equations using slope-intercept form
     5.Solves linear equations using concrete methods
     6.Solves linear equations using informal methods
     7.Solves linear equations using formal methods
   Benchmark 7.Understands special values (e.g., minimum and maximum values, x- and y-intercepts, slope, constant ratio or difference) of patterns, relationships, and functions
    Knowledge/skill statements
     1.Understands x- and y-intercepts
     2.Understands the concept of slope
     3.Understands constant ratio or difference
     4.Understands the concept of maximum
     5.Understands the concept of minimum
   Benchmark 9.Uses the rectangular coordinate system to model and to solve problems
    Knowledge/skill statements
     1.Determines whether a problem can be modeled by using rectangular coordinates
     2.Determines whether a problem can be solved by using rectangular coordinates
   Benchmark 10.Solves simple systems of equations graphically
    Knowledge/skill statements
     1.Solves simple systems of equations graphically
     2.Understands the concept of systems of equations
  Level IV (Grade 9-12)
   Benchmark 4.Understands properties of graphs and the relationship between a graph and its corresponding expression (e.g., maximum and minimum points)
    Knowledge/skill statements
     1.Understands the relationship between the graphical and algebraic representations of minimum
     2.Understands the relationship between graphs and corresponding expressions
     3.Understands the relationship between the graphical and algebraic representations of maximum
   Benchmark 7.Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships
    Knowledge/skill statements
     1.Represents functions using graphs
     2.Represents functions using table of input/output values
     3.Represents functions using algebraic formula
     4.Represents functions using written statements
     5.Represents functions using models
     6. Represents patterns using graphs
     7.Represents patterns using table of input/output values
     8. Represents patterns using algebraic formula
     9.Represents patterns using written statements
     10. Represents patterns using models
     11. Represents relationships using graphs
     12. Represents relationships using table of input/output values
     13. Represents relationships using algebraic formula
     14. Represents relationships using written statements
     15.Represents relationships using models
   Benchmark 9.Understands the effects of parameter changes on functions and their graphs
    Knowledge/skill statements
     1. Understands the concept of a parameter
     2. Understands how parameter changes affect functions
     3. Understands how parameter changes affect graphs of functions
   Benchmark 10.Understands the basic concept of inverse function and the corresponding graph
    Knowledge/skill statements
     1. Understands the concept of inverse functions
     2. Graphs inverse functions
   Benchmark 11.Uses a variety of methods (e.g., with graphs, algebraic methods, and matrices) to solve systems of equations and inequalities
    Knowledge/skill statements
     1.Solves systems of equations using graphs
     2.Solves systems of equations using matrices
     3.Solves systems of equations using algebraic methods
     4. Understands the concept of systems of inequalities
     5.Solves systems of inequalities using algebraic methods
     6.Solves systems of inequalities using graphs
     7.Solves systems of inequalities using matrices
  Level V (Grade (College Readiness))
   Benchmark 2.Understands graphs of solution sets of quadratic inequalities
    Knowledge/skill statements
     1. Understands the concept of solution sets
     2.Identifies solution sets of quadratic inequalities
     3.Interprets graphs of solution sets of quadratic inequalities