Even and Odd Numbers – Basic, but Not Easy to Learn

Even and Odd Numbers - You think of them as You know about even and odd numbers, right?

I was visiting with my sister yesterday and she was excited that her 8 year old son had finally grasped the idea.

“I know, it’s a pretty basic concept, “ she told me, “but I’m just so excited he finally got it.”

Which made me consider it. Are the concepts of even and odd basic?

Basic but Not Easy

Okay, yes. Even and odd numbers are considered a basic concept. Everyone over the age of 15 or so should have a general idea of which numbers are even and which numbers are odd.

But even-ness and odd-ness are NOT easy concepts.

Think about it:

  • When you list even numbers, they alternate. The same is true of odd numbers.
  • The words even and odd have no corresponding meaning in our standard English vocabulary for kids to anchor to.

So even and odd are arbitrary names for alternating numbers. We might as well say Bob numbers and Fred numbers.

Some Mathematical Definitions

A number* is said to be even if it can be written as the product of another number and the number 2.

A number is said to be odd if it can be written as the product of another number and 2, plus 1.

*Note: “number” here really means integer, but typically we just use whole numbers at the younger ages.

In other words, an even number can be written like 2 x n, where n is some other number and an odd number is (2 x n) + 1, where n is another number.

So 14 can be written like 2 x 7, and 85 can be written as (2 x 42) + 1.

So tell THAT to an 8 year old!

Many grownups don’t know the actual definitions. And if they did, they might not make sense to them, anyway. So it’s less than helpful to introduce the definitions to an 8 year old. (Although, he’s a super smart kid, so he’d probably be able to take it. #ProudAunt #biased)

My sister used the “partners” or “friends” idea. (Not to be confused with the mathematical definition of friends, though.)

A number is an even number if you can partner up that number of marshmallows (or raisins, if you’re healthy like my sis) and have no leftovers.

A number is an odd number if you can partner up that many marshmallows and have someone “friend-less.” With odd numbers, you always have a leftover.

How to Remember the Words

But still, the words are arbitrary.

Turns out, though, the words “odd” and “even” are slightly autological – meaning that they describe themselves. Which is how we can remember them:

The letters in the word “even” can be paired up with nobody left over: EV and EN.

The letters in the word “odd” can be paired so that you have an “odd man out”: OD are partners with leftover D (or more intuitive, O is leftover after DD are partnered).

How about you?

Do you remember learning odd and even numbers? Was it natural or weird? And how do you teach your students?

Share your thoughts in the comments. And don’t forget to share on Twitter, Pinterest and Facebook!

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One Response to Even and Odd Numbers – Basic, but Not Easy to Learn

  1. I think I remembered the difference between odd and even by thinking of even as Even Steven. You could split an even quantity fairly between two people. “You get 5 raisins and I get 5 raisins. Even Steven!”

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