ILLINOIS TEACH & TALK

Students will need a basic ability to count before asking questions specific to cardinality.  However, this connection should be made early in their work with counting. 

For students to truly develop fluency with cardinality, objects should be moved around, spaced apart in different arrangements, and compared.  This also connects directly to K.CC.5.

Students understand that the last number name said in counting tells the number of objects counted.  Prior to reaching this understanding, a student who is asked “How many kittens?” may regard the counting performance itself as the answer, instead of answering with the cardinality of the set.

Students expand their work in addition and subtraction from within 5 to within 10.  They use Level 1 methods developed from smaller totals as they represent and solve problems with objects, their fingers, and math drawings.  Patterns such as “adding one is just the next counting word (K.CC.4c)” and “adding zero gives the same number” become more visible and useful for all the numbers from 1 to 9.  Patterns such as the 5+n pattern used widely around the world play an important role in learning particular additions and subtractions, and later as patterns in steps in the Level 2 and Level 3 methods.  Fingers can be used to show the same 5-patterns, but students should be asked to explain these relationships explicitly because they may not be obvious to all students (MP.3).  As the school year progresses, students internalize their external representations and solution actions, and mental images become important in problem representation and solution.