
               
               progression
               
                        ::= learning_object ' "requires" ' learning_object ' "because all of the competencies of the former: " ' modified_competency ( ', ' modified_competency )+ ' "extend the competencies of the latter" '


               
               recommendation
               
                        ::= learning_object ' “matches search for:” ' learning_verbs ', ' modified_competency ', ' DOK_level


               
               search   ::= recommendation


               
               assessment
               
                        ::= learning_object ' “is evidence of:” ' modified_competency ', ' DOK_level


               
               report   ::= ' “set of” ' learning_object+ ' “is evidence of:” ' modified_competency ', ' DOK_level


               
               differentiation
               
                        ::= learning_object ' “is similar to” ' learning_object ' “that” ' learning_verb modified_competency ( ', ' DOK_level )?


               
               learning_verb
               
                        ::= ' “teaches” '
               
                          | ' “practices” '
               
                          | ' “assesses” '
               
                          | ' “exemplifies” '


               
               DOK_level
               
                        ::= ' “at DOK Level” ' ( ' “1” ' | ' “2” ' | ' “3” ' | ' “4” ' )


               
               learning_object
               
                        ::= activity
               
                          | learning_object_map


               
               learning_object_map
               
                        ::= '{' learning_object+ '}'


               
               activity ::= teaching_object
               
                          | investigate_object
               
                          | practice_object
               
                          | assessment_object
               
                          | differentiation_object
               
                          | portfolio_object


               
               teaching_object
               
                        ::= metadata_object


               
               investigate_object
               
                        ::= metadata_object


               
               practice_object
               
                        ::= metadata_object


               
               assessment_object
               
                        ::= metadata_object


               
               differentiation_object
               
                        ::= metadata_object


               
               portfolio_object
               
                        ::= metadata_object


               
               modified_competency
               
                        ::= ( formal_process | knowledge_process ( ' “by” ' knowledge_subprocess )? )? ( math_operation ', ' object | specific_object ) notation_object?
               
                          | math_practice_competency


               
               formal_process
               
                        ::= ' “read” '
               
                          | ' “recite” '
               
                          | ' “write” '
               
                          | ' “represent” ' ( ' “with” ' representation )?
               
                          | ' “randomly sample” '


               
               representation
               
                        ::= models
               
                          | realia
               
                          | glyphs


               
               models   ::= ' “images” '
               
                          | ' “sounds” '
               
                          | ' “activities” '


               
               realia   ::= ' “specimens” '
               
                          | ' “body parts” '


               
               glyphs   ::= ' “words” '
               
                          | ' “symbols” '
               
                          | ' “drawings” '
               
                          | ' “graphs” '


               
               knowledge_process
               
                        ::= ' “identifying” '
               
                          | ' “describing” '
               
                          | ' “comparing” '
               
                          | ' “understanding” '
               
                          | ' “representing” '
               
                          | ' “applying” '
               
                          | ' “relating” '
               
                          | ' “analyzing” '
               
                          | ' “interpreting” '
               
                          | ' “extending” '
               
                          | ' “classifying” '
               
                          | ' “measuring” '
               
                          | ' “iterating” '
               
                          | ' “solving” '
               
                          | ' “converting” '
               
                          | ' “reasoning” '
               
                          | ' “computing” '
               
                          | ' “approximating” '
               
                          | ' “estimating” '
               
                          | ' “inferring” '
               
                          | ' “grouping” '
               
                          | ' “strategizing” '
               
                          | ' “explaining” '
               
                          | ' “constructing” '


               
               knowledge_subprocess
               
                        ::= ' "knowledge_subprocess" '
               
                          | ' "specific knowledge process string" '


               
               math_operation
               
                        ::= ' “naming” '
               
                          | ' “sequencing” '
               
                          | ' “ordering” '
               
                          | ' “adding” '
               
                          | ' “subtracting” '
               
                          | ' “multiplying” '
               
                          | ' “dividing” '
               
                          | ' “negating” '
               
                          | ' “exponentiating” '
               
                          | ' “grouping” '


               
               object   ::= ' "math operations" '
               
                          | ' "string" '


               
               specific_object
               
                        ::= ' "string" '
               
                          | ' "specific object string" '


               
               scope_object
               
                        ::= ' "Whole Numbers" ' sub_scope?
               
                          | ' “Integers” '
               
                          | ' “Unit Fractions” '
               
                          | ' “Rational Numbers” '
               
                          | ' “Real Numbers” '
               
                          | ' “Imaginary Numbers” '
               
                          | ' “Complex Numbers” '
               
                          | ' “Vectors” '
               
                          | ' “Matrices” '
               
                          | ' “Infinite Numbers” '
               
                          | ' “Random Numbers” '
               
                          | ' “Expected Values” '
               
                          | ' “Probabilities” '
               
                          | ' “The Plane” '
               
                          | ' “Space” '
               
                          | ' “Algebraic Expressions” '
               
                          | ' “Numerical Expressions” '


               
               notation_object
               
                        ::= ' “in” ' ', ' ( ' “Fractional Notations” ' | ' “Decimal Notations” '
                  | ' “Proportional Notation” ' | ' “Addition Notation” ' | ' “Subtraction Notation”
                  ' | ' “Multiplication Notations” ' | ' “Division Notations” ' | ' “Radical Notation”
                  ' | ' “Exponential Notation” ' | ' “Scientific Notation” ' | ' “Base Ten” ' )


               
               math_practice_competency
               
                        ::= ' “Make Sense of Problems” '
               
                          | ' “Persevere in Solving Problems” '
               
                          | ' “Reason Abstractly” '
               
                          | ' “Reason Quantitatively” '
               
                          | ' “Construct Viable Arguments” '
               
                          | ' “Critique Reasoning” '
               
                          | ' “Model Problems” '
               
                          | ' “Use Tools Strategically” '
               
                          | ' “Attend to Precision” '
               
                          | ' “Look for Structure” '
               
                          | ' “Make Use of Structure” '
               
                          | ' “Look for Regularity in Repeated Reasoning” '
               
                          | ' “Express Regularity in Repeated Reasoning” '


               
               sub_scope
               
                        ::= ' “0” '
               
                          | ' “1” '
               
                          | ' “to 2” '
               
                          | ' “to 3” '
               
                          | ' “to 4” '
               
                          | ' “to 5” '
               
                          | ' “within 10” '
               
                          | ' “within 20” '
               
                          | ' “within 100” '
               
                          | ' “within 120” '
               
                          | ' “within 1000” '