• Stable Order: counting sequence remains consistent

• Order Irrelevance:  you can start counting with any object in a set and that the total will always be the same, regardless of which item you start with

• Conservation:  the total count for a set remains the same regardless of how the objects are spaced

• Abstraction:  quantity can be represented by a variety of things (3 cats; 3 continents; 3 emotions, etc.) 3 small objects is the same as 3 large objects

• One-to-One Correspondence:  each object is only given one count (touch counting)

• Cardinality: the last item counted in a set represents the total number of items in that set

• Movement is Magnitude: as one moves up or down the counting sequence, the quantity counted increases or decreases 

• Unitizing: a set of objects can be seen simultaneously as 1 set and, say, 10 objects (10 pennies = 1 dime; 5 fingers = 1 hand) 

• Hierarchical Inclusion:  Understanding that all numbers preceding a number can be or are systematically included in the value of another selected number. So in a group of 5 there's also a group of 4, and a group of 3 and 2 and 1 is embedded it there. 

• Subitizing: In general, subitizing is the ability to "see" or visualize a small amount of objects and know how many there are without counting. (more detail can be found in the subitizing section of this website)

Check more at: What is Subitizing?

(Kyle Pearce & Jon Orr on The Principles of Counting and Quantity )

• Numbers represent a common organizational structure that we use in our lives and in our world to communicate/represent value.

• Numbers can be taken apart (decomposed) and put together (recomposed). 

• The ability to decompose and recompose is a useful strategy in all aspects of mathematical thinking. 

• We can use objects, pictures, symbols, and/or words to represent number and quantity. 

• There are many ways to count. Each way to count has a proper sequence. (stable order)

• Quantity can be represented in many ways. (Order Irrelevance)

• The same quantity can look different (abstraction). 

• We are learning that as we move up or down the counting sequence, the quantity increases or decreases by the number we are counting by (magnitude).

Cardinality Look fors

Stable Order Look fors

One-to-One Correspondence Look fors

Movement is Magnitude Look fors

Subitizing Look fors

Patterning Assessment