Even and Odd

Why do many teachers only teach examples of even and odd numbers, and not properties of even and odd numbers?

What do I mean?  Well, this is what I discussed with a 1st Grade Student when the only thing she could tell me about even and odd numbers was:
Even is 2, 4, 6, 8, and 10
Odd is 1, 3, 5, 7, and 9
And that's all....

First, we built models of the numbers 1 through 10

Then I asked her 2 separate the models into 2 groups that were alike in some way.

This is how she separated the models.  When I asked her what she noticed about the two groups, and she noted this on the models:

"This group doesn't have a partner for each part of the number

and this group does have a partner.  See, how I circled the partners."

Then we discussed how certain numbers can be divided into groups of two, and that we call those numbers Even Numbers.

We went on to talk about odd numbers too.  Since she is in a dual language class, she also wanted to write the Spanish word for even/par and odd/impar on the model.

Next, I asked her to now tell me what she knows about even and odd numbers and she wrote this:

I found it interesting that she put an arrow after the numbers and said "and on and on."  (That put a smile on my face.)

So we talked about how you look at the "on and on numbers" in the ones place to see if they are even numbers or odd numbers. 

I evaluated her knowledge by quickly using a set of teen number cards.

and asked her to classify them as even or odd numbers. 

She was correct, and we even checked our first answer to
 prove that she was correct.

Deborah