I have seen the many cute anchor charts to remind students how to tell if a number is odd or even with Even Steven and Odd Todd. The charts include a list of numbers to look for in the ones place–even 0, 2, 4, 6, 8 and odd 1, 3, 5, 7, 9. If this is all that is being done at the primary level, when the concepts of even and odd are introduced, the “boat is being missed”.
What Should Be Taught?
At second grade, the Common Core Standard reads as follows:
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.
In order for students to CONCEPTUALLY understand the odd or even, a few things can be done. Keeping in mind, the standard at the second grade level is written for objects up to 20.
First, students should be exploring the concept of odd and even with objects (up to 20) as stated, not simply be shown a number and asked if the number is odd or even by looking at the digit in the ones place. We also need to keep in mind a prerequisite of odds and evens at this level is the ability to count by 2 to 20 in second grade. If a student is not able to count by 2 to 20, he or she cannot successfully use the skill of counting objects by two to determine if the number of objects is odd or even.
Breaking Apart the Standard: How to Teach the Concept
One of the most common ways kids are taught to determine if a number of objects is odd or even is by pairing them to determine if there are any objects left without a pair–in which case the number of objects is odd. If all objects are paired, the number is even. This can easily be done with any objects, and kids like to explore the concept with lots of different objects.
Another way is to count the number of objects by two to determine if there are any objects left that cannot be counted by two. If the sum of objects can be counted by twos, it is even.
Lastly, students should be able to write an equation to express an even number as a sum of two equal addends. There is some work that needs to go into a child’s understanding of this. Starting with objects, a child can try to sort the objects into two equal groups. This is most easily done by sorting objects one-by-one into two groups and counting the number in each group to determine if the number of objects is equal. If the groups have an equal number of objects, the number of objects is even. The child can then write an equation to represent the model. Example: 4 + 4 = 8 to represent two groups of four object with a sum of 8. If the groups are not equal, the addends in an equation will not be equal, therefore making the number of objects odd.
Why Teach it This Way?
Why is it SO important for students to CONCEPTUALLY understand the concept of odd and even in these ways? Because, as a child works with equal groups of objects he/she is gaining foundations for multiplication. That is why the skill of determining a number of objects as odd or even falls under the heading, Work with equal groups of objects to gain foundations for multiplication, in the Common Core Standards. We have to continuously remind ourselves that developing our students’ conceptual understanding, rather than teaching them a set or shortcuts or tricks, is the best way to prepared them for what they will encounter as they progress in mathematics. In this way, we give them the power to apply their understanding to different situations and make connections.
At this time of year, I like to give students the opportunity to explore the concept of odd and even with candy corn. The pictures below show how students build understanding of the concept by pairing and creating equal groups. Students must prove if the number of candy corn is odd or even BOTH ways. They may then choose which way to model on their activity sheet.
Please feel free to download Candy Corn Odds & Evens. It that can be used as a whole group lesson, small group lesson, or an independent workstation.
All the best for the week ahead–