DEVELOPING NUMBER SENSE: PRINCIPLES OF COUNTING
All concepts of number sense need to be actively taught. Cardinality principle is one of the higher order concepts of number sense that children in kindergarten learn.
Cardinality is the ability to understand that the last number which was counted when counting a set of objects is a direct representation of the total in that group.
A child who understands this concept will count a set once and not need to count it again. They will automatically remember and know how many are represented.
Students who are still developing this skill need constant repetition of counting and explicit teaching through modelling that they do not need to count over and over again when it will result in the same number. Students who have difficulty with their working memory may have difficulty with this concept.
Simply counting objects that are meaningful to children’s lives will help them develop a basic understanding of cardinality. How many candies do you have? How many blocks are in your tower? etc.
Practicing to develop subitizing skills helps students develop cardinality. When children automatically recognize a number they know how many are the set. These two principles are closely related but not the same.
These are some of the activities we use to teach cardinality.
Number Line Fluency
I love this activity as it allows me to choose various representations of numbers based upon what concepts I know students already know. They then need to count the objects in order to know how many are in the set/representation if they don’t already know the representation of the number. Then they need to hold that number in their working memory in order to put the numbers in order.
This is a simple tally game. Students flip over a variety of different representations of numbers (sets of bears, tally marks, finger representations etc) and then mark off which number they found. This is a fantastic game to teach cardinality!
I place out a variety of different puzzles which represent different numbers and students need to match the numbers to make a puzzle. Students need to count various objects (such as ten frames, fingers, tally marks etc.) and hold that number in their head. If they play enough or understand the concept of cardinality, they will hold the number in their memory and it will help them solve the puzzles!
Number Talks are a huge support to develop students ability to understand cardinality.
We use Number Talks on a regular basis in our classroom and it has made huge gains in our students understanding of numbers and has helped to solidify their fluency of numbers.
If you want to check it out there is a link to an Amazon affiliate if you click the image below.
Number Sense Freebie
I use this landscape of learning to know where each student is developmentally with number sense and to target small groups with students who have similar needs. Click on the image to be able to download this!