Mathematical Objects (nouns) 

Mathematical Actions (verbs) 

Types of objects 
Properties of objects 
Practicle use 
Operations on objects 
Number/quantity
 integers
 rational numbers
 real numbers
 measures of:
 length
 area
 volume
 time
 weight

 order
 betweenness
 part/whole relationships
 units
 dimensions


Arithmetic operations
 addition
 subtraction
 multiplication
 division
 expotential

Shape/space
 metric  value between two points
 lines/segments
 polygons
 circles
 conic sections
 spherical shapes
 topological properties  geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.

 distance
 location
 symmetry
 similarity
 connectedness
 enclosure

 mapping and traveling
 designing and building objects

 translation
 rotation
 reflection
 covering, packing, & tessellating
 scaling
 projection
 inversion
 conformal mapping
 homotopies/deformations

Pattern/function
 linear
 quadratic
 power
 rational
 periodic
 transcendental

 input/output
 domain/range
 continuity
 boundedness
 rate of change, curvature, etc.
 maxima and minima
 rate of accumulation
 linearroot, slope/intercept
 quadraticroots, axis of symmetry
 powerroots, asymptotic behavior
 rationalroots, singularities, asymptotic behavior
 periodicfrequency, phase
 transcendental"growth" constant

 expressing how something depends on another  one or more other things
 resolving constraints
 (solving equations and inequalities)

 identifying and describing repetitive relationships
 arithmetic operations (functions on Rn)
 comparison
 equations
 inequalities
 identities
 composition
 translation
 reflection
 dilation/contraction

Arrangements
 combinations
 permutations
 graphs
 networks
 trees

 adjacency
 enumeration
 vertices and edges of graphs/networks

 organizing discrete information

 tends to be closely connected to the idea of repetitive pattern at this level

Chance/data

 determinism
 randomness
 relative frequency
 distribution
 moments

 dealing with uncertainty
 dealing with lack of precision

 sampling (by counts and/or measures)
 composing
 representing
