Understanding Quantity part I: conceptually

To help a child increase their understanding for quantity of a number we must break this understanding down into two parts:
1. conceptual understanding
2. representational understanding

Think about an arbitrary #.
What is its purpose?
*to describe a certain quantity

6 = . . . . . . (we will use dots to represent the quantity whilst you are teaching this I would not just use dots but anything you have a large quantity of : rice, pennies, buttons, beans, candy, rocks, etc)

In order for your child to learn they need the tools to show a concept and to represent their understanding.

First, what are conceptual tools regarding quantity?
* using objects that can be grouped into groups or multiple sets but rearrangement of groups or # of objects with in a group doesn't alter the total # of objects.

OK now she's lost me ; )

Example: (from before with the # of 6 in dots) (b/c of formatting I can't seem to but highly recommend circling the groups as a whole and the sets within each group)

. . . . . .

. . .
. . .

. .
. .
. .

The # of dots in total never change. It is always 6. However, the set within a group have been rearranged.

Did you find your way yet?

Have your kiddo aware of 3 things when looking at groups.

1. When are things the same?
*(each group has 6 dots)

2. When are things not the same?
*(if total # in each group is not the same)

3. When are things the same but not?
*(when quantity is the same but not the # in each set)

Now work with several #'s this way in the set of #'s 1 - 10. later on move up 10 - 30. After working with different numbers your child will have a conceptual understanding of arbitrary numbers and the quantity they represent.