# Even and Odd: The Importance of Conceptual Understanding

I can’t tell you how many times I learn through the eyes of my five year old.  She asks amazing questions, especially when it comes to numbers.  While we were doing some daily math play today, I thought about introducing her to the concept of even and odd numbers.  I was taught even and odd by being told to memorize the numbers: 2,4,6,8.  As a tiny child I don’t think I truly understood why a number was even vs. odd.

So we built the numbers 1-10 (in hindsight I wish I had included zero) with unifix cubes. Then I told her to put them in pairs. We put the pairs together, and lined everything up. During this process she was uncomfortable whenever one was left over, and wanted to pair it up with one from another number set! This is how it looked once we had it all situated.

Then I asked her what she noticed.

“There is ‘ones’ all by itself!”

We pointed out which numbers had an “odd one out” as I put it. That was when I introduced the words odd and even.  I think it is essential to introduce the vocabulary to kids after they have explored the concept, so that they have a way to name what it is they are seeing.

She then noticed that every other number was odd.  So we looked at and extended the pattern: odd, even, odd, even….until we got to the 10. I then asked her what she thought 11 would be, odd or even?  She shouted out “odd!” without even thinking about it.

I still have a few third graders that are struggling with this concept (can you even believe that?). I am going to try to see if this could help them understand this very basic concept.

## 5 thoughts on “Even and Odd: The Importance of Conceptual Understanding”

1. Thanks for sharing this! Gives me a new way of teaching odd/even numbers that is more relatable to kids than just lecturing!

• You are so welcome! It totally makes sense doesn’t it? I wonder what kind of math student I would have been if I had learned it that way.

• It does make more sense. I recently saw a post somewhere (not a blog) that showed student answers to test questions. One was as follows:

the following number is even or odd: 68 ______
How do you know this? _____

The kid said “because I’m smart” and I had to sit for a minute and think, because even I didn’t know what the right answer was!

Gotta make it make sense!

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