## Wednesday, December 4, 2013

### Odd and Even Numbers and the Common Core

Knowing about odd and even numbers is one of the big ideas that kids need to develop in grades K-2 that will help them with math concepts as they move through elementary school.  If students understand what odd and even numbers are, they can move on to learning what happens when odd and even numbers are added, subtracted, multiplied and divided.

Where does the concepts of odd and even show up in the Common Core?

• CCSS.Math.Content.2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends
By the end of grade 2, kids should have a solid understanding of the basic concepts of odd and even so they can further develop these ideas as they move through grades 3 and 4 and can start thinking about how they can apply these ideas to help them with arithmetic.

I have a small group of third grader who I have noticed over the last several weeks seem to be struggling with the idea of odd and even.  They certainly had some basic knowledge but some of it seemed fragmented or missing or they were very unsure.  I found 15 minutes to pull them out of class for a quick booster group to address these big ideas.  I want to share with you how we quickly got at what it means for a number to be odd or even, noticed how it extends to numbers beyond 20, and practiced our new found knowledge.

 I started by writing the numbers 1-10 on the board.  I asked the students if they could tell me any of the numbers written on the board that they knew for sure were even.  A student chose 4.  I asked him to prove how he knew 4 was even.  He put up 4 fingers and demonstrated that each one had a partner.  Another student said he knew it was even because it could be written as a double fact (2+2).  We proceeded in this way until we had identified all the numbers between 1 and 10 as odd or even.
 I then wrote the numbers between 11 and 20.  We again identified odd and even and showed some evidence of how we knew we were right.  The idea that the counting numbers go in an odd, even, odd, even pattern came up.  We talked about this but then I asked students how that would help them if I wanted to know if a really big number like 342 was odd or even.  They certainly don't want to count by ones that far thinking odd, even the entire time.
 One boy immediately wanted to answer my question and he decided to point out to me that on my 1000's chart that hangs on my wall 342 is in the same column as 2 and he thinks all the numbers in that column are even.  I pushed on this understanding a bit to see if he really got this big idea or it was something he had been told enough times that he had just memorized it without any meaning.   Then we got into a great discussion about how all the hundreds are even and all the count by 10 numbers are even so we really only care about the ones left over when we are trying to decide if a number is odd or even.
 We finished with a quick odd and even sort.  I made this up simply by writing numbers on scraps of card stock left over from other projects.  I have several sets and they just get paper clipped together and put in a baggie when not in use. I gave each kid their own set and had them sort into odd and even.  When they were finished, their job was to check the sort of another person who was also done.  (not all the sorts use the same numbers.)
 A finished sort
This quick review of the ideas of odd and even really seems to have helped these students solidify their knowledge.  I followed up by adding some of my favorite odd and even literature books to their book boxes for them to explore during independent reading time this week.

How do you find time and staff in your school to give kids that little extra time or practice they need to be successful?  Please respond in the comments below!