Odds and Evens

I went and asked a few Grade 5 students to tell me about odd and even numbers, and this is what they said: Student A: “3 is odd, 2 is even”  Student B:“anything ending in a 0, 2,4,6,8 is even and anything ending in a 1, 3, 5, 7, 9” is odd. The students told me attributes of even and odd numbers, but not one of them explained to me the mathematical meaning of the terms.

The big understanding is that even numbers can be shared fairly into two groups whereas odd numbers always have a left-over and can not be split into two equal groups. I asked a grade 3 student and she explained it well, “Even numbers can be separated into two parts, like the number 8 produces 2 groups of 4, but odd numbers can’t be separated into two equal parts”. I was impressed that she had retained that understanding! When I asked a different grade 3 student to explain what it means to be even, he said, “I dunno”!

It is very important that we teach for understanding. This understanding starts in kindergarten and there are lots of fun ways to get children enthused. The trick is to find resources that show the meaning of odds and evens first. Then you can supplement with songs and stories that are about even and odd, even if they only talk about the numbers and not the big idea behind them.

My top choices are to give the students a manipulative such as Numicon blocks, which can easily be made out of 10 frames, and ask them to sort them into two piles. Students will usually sort those with bumps and those without. This leads to a deeper discussion about the concept of even and odd.

My second favourite way is to use twins. The twins are happy when they share evenly, but they are mad when they can’t and there is a left-over. Once I explain why they are feeling that way, the students can now discover which numbers are even or odd themselves. Watch as Rory easily conceptualizes the idea of two equal parts or left-overs.

Math is a beautiful subject full of patterns and connections and it is my responsibility as a teacher and a parent to make some of these connections transparent while I teach. At the end of this lesson, we tied it all together, labelled the numbers as even or odd and made some observations about the patterns (skip counting by 2) and connections we found. The fact that even numbers always end in certain numbers never entered our conversation, although it will eventually, when we recognize it as an observable pattern that we can use to predict whether something can be shared equally into 2 groups or not.

The next day Rory and I reviewed the concept by using dot cards. I chose this task as a follow-up for two reasons: he gains practice subitizing while reinforcing his understanding of odd and even. The cards we used come from a game called “Tiny Polka Dot”, but you can easily make your own set.

sort

Students that gain a thorough understanding of the meaning of odd and even, can take their learning further. Now students have a starting place for harder problems that develop fluency such as: what happens when you add two even numbers together? What happens with two odd? Or even further: can you ever get an odd number when you multiply two even numbers together? What about multiplying an even with an odd? If the students have a better understanding of what it means to be odd and even, they can make some observations,  discover some patterns, and further develop on their number sense journey.