The first principle of counting involves the student using a list of words to count in a repeatable order. This “stable list” must be at least as long as the number of items to be counted. For example, if a student wants to count 20 items, their stable list of numbers must be to at least...

# Playlist - Counting and Quantity

The order in which items are counted is irrelevant. Students have an understanding of order irrelevance when they are able to count a group of items starting from different places. For example, counting from the left-most item to the right-most and visa versa. For a full summary of all...

Conservation is the counting and quantity principle referring to the understanding that the count for a set group of objects stays the same no matter whether they are spread out or close together. If a student counts a group of items that are close together and then needs to recount after...

Abstraction is the counting and quantity principle referring to the understanding that we can count any collection of objects, whether tangible or not. For example, the quantity of five large items is the same count as a quantity of five small items or a mixed group of five small and...

One to One Correspondence is the counting and quantity principle referring to the understanding that each object in a group can be counted once and only once. It is useful in the early stages for children to actually tag or touch each item being counted and to move it out of the...

Cardinality is the counting and quantity principle referring to the understanding that the last number used to count a group of objects represents how many are in the group. A student who must recount when asked how many candies are in the set that they just counted, may not understand...

In general, subitizing is the ability to “see” or visualize a small amount of objects and know how many there are without counting. While this idea may seem simple on the surface, subitizing is actually quite complex. If we dig deeper, we can see that there are two types of subitizing...

Hierarchical Inclusion is the counting and quantity principle that refers to understanding that all numbers preceding a number can be or are systematically included in the value of another selected number.

For a full summary of all counting principles, read the original blog post.

Movement is Magnitude is the counting and quantity principle that refers to the understanding that as you move up the counting sequence (or forwards), the quantity increases by one and as you move down (or backwards), the quantity decreases by one or whatever quantity you are going...

Unitizing is the understanding that you can count a large group of items by counting smaller, equal groups of items from within the large group.