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Topic: Patterns 

Mathematics

 Standard 1.  Uses a variety of strategies in the problem-solving process
  Level III (Grade 6-8)
   Benchmark 3.Understands that there is no one right way to solve mathematical problems but that different methods (e.g., working backward from a solution, using a similar problem type, identifying a pattern) have different advantages and disadvantages
    Knowledge/skill statements
     1.Works backward from a solution
     2.Identifies a similar problem type
   Benchmark 6.Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning)
    Knowledge/skill statements
     1.Provides supportive arguments for conjectures
     2.Generalizes from a pattern of observations
     3.Makes conjectures from generalizations
  Level IV (Grade 9-12)
   Benchmark 1.Uses a variety of strategies (e.g., identify a pattern, use equivalent representations) to understand new mathematical content and to develop more efficient solution methods or problem extensions
    Knowledge/skill statements
     1.Uses strategies to understand new mathematical content
     2.Uses strategies to develop more efficient solution methods
     3.Uses strategies to extend solution methods to other problems
 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level I (Grade K-2)
   Benchmark 4.Understands that patterns can be made by putting different shapes together or taking them apart
    Knowledge/skill statements
     1.Understands that patterns can be made by putting shapes together
     2.Understands that patterns can be made by taking shapes apart
 Standard 6.  Understands and applies basic and advanced concepts of statistics and data analysis
  Level V (Grade (College Readiness))
   Benchmark 3.Identifies patterns in graphical displays of data
    Knowledge/skill statements
     1.Understands graphical displays of data
     2.Identifies trends in graphical displays of data
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level Pre-K (Grade Pre-K)
   Benchmark 1.Understands simple patterns (e.g., boy-girl-boy-girl)
    Knowledge/skill statements
     1.Understands boy-girl-boy-girl patterns
     2.Understands the basic concept of a pattern
   Benchmark 2.Repeats simple patterns
    Knowledge/skill statements
     1.Repeats simple patterns
  Level I (Grade K-2)
   Benchmark 1.Recognizes regularities in a variety of contexts (e.g., events, designs, shapes, sets of numbers)
    Knowledge/skill statements
     1. Recognizes patterns in events
     2.Understands the concept of a pattern
     3.Recognizes patterns in designs
     4.Recognizes patterns in shapes
     5.Recognizes patterns in sets of numbers
   Benchmark 2.Extends simple patterns (e.g., of numbers, physical objects, geometric shapes)
    Knowledge/skill statements
     1.Extends simple patterns in numbers
     2.Extends simple patterns in geometric shapes
     3.Extends simple patterns in objects
  Level II (Grade 3-5)
   Benchmark 1.Recognizes a wide variety of patterns (e.g., basic linear patterns such as [2, 4, 6, 8 . . .] ; simple repeating and growing patterns) and the rules that explain them
    Knowledge/skill statements
     1.Understands the concept of a growing pattern
     2.Understands the concept of a simple repeating pattern
     3.Recognizes linear patterns
     4.Recognizes increasing patterns
     5.Recognizes decreasing patterns
     6. Recognizes the rules that explain simple patterns
   Benchmark 2.Understands that the same pattern can be represented in different ways (e.g., geometrically or numerically; the pattern of numbers [7, 14, 21, 28 . . .] is equivalent to the mathematical relationship 7 × n)
    Knowledge/skill statements
     1.Understands that patterns can be represented numerically
     2.Understands that patterns can be represented geometrically
     3.Represents simple patterns geometrically
     4.Represents simple patterns numerically
  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 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 11.Understands the properties of arithmetic and geometric sequences (i.e., linear and exponential patterns)
    Knowledge/skill statements
     1. Understands the properties of geometric sequences
     2. Understands the properties of arithmetic sequences
     3. Understands the concept of a linear sequence
     4. Understands the concept of an exponential sequence
  Level IV (Grade 9-12)
   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