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What exactly is the cardinal principle?
This is one of the five counting principles.
Look at this group of tennis balls. How many do you see?
I see six tennis balls.
But how do you really know there are six balls?
Well I counted each ball and when I counted the last ball I said six.
That's right. You have learned that the last number name you say, tells you the total number
in the group.
Children need to learn that the last number tells a property of the group.
It answers the question, how many?
In mathematics, we call this property of a group, its cardinality or numerosity.
For example, the cardinality of this group is four.
How do I help students gain this understanding?
It just takes practice, but try modelling it for children.
For example, say one, two, three, four.
There are four tennis balls in the tube.