Five Math Counting Principles: Instructional Strategies (2024)

This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance. When students master the verbal counting sequence they display an understanding of the stable order of numbers. Then, students may apply the counting sequence to count a set of objects with one-to-one correspondence – each object is paired with one and only one number word. When students are able to count a set of small objects and then answer the question, “How many?” they show an understanding of cardinality. The principle of abstraction is shown when students understand that any set of objects may be counted as one set, regardless of whether the objects are all the same. When children understand that objects may be counted in any order (e.g., left-to-right, right-to-left, in a random fashion) they have developed an understanding of the order irrelevance counting principle. Counting skills are considered a gateway to other mathematics skills, such as simple arithmetic. Students should be provided with multiple practice opportunities to show that they have an understanding of the five counting principles and can apply skills to novel situations.