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.
Unpacked
Certain characteristics are specific to certain sets of numbers. Whole numbers can be
described as odd or even (rational numbers cannot). One way to help students understand
evenness is to ask them to describe a number by representing that number using blocks
and then putting the blocks into two equal groups. If there is one extra block, the number
is odd; if not the number is even.
Second graders apply their work with doubles to the concept of odd and even numbers. Students
should have ample experiences exploring the concept that if a number can be decomposed
(broken apart) into two equal addends or doubles addition facts (e.g., 10 = 5 +5), then that
number (10 in this case) is an even number. Students should explore this concept with concrete
objects (e.g., counters, cubes, etc.) before moving towards pictorial representations such as circles
or arrays.
Students do not always know that counting objects two at a time can lead to a conclusion
that the starting number was even or odd. The understanding of equal groups prepares
them for the concept of rectangular arrays, which is an introductory concept for
multiplication. The concept of even and odd will also be crucial with the introduction of
division. Writing equations for even numbers as the sum of two equal addends lends
itself to adaptation to equations of multiplying by 2 in the following grade.
The focus of this standard is placed on the conceptual understanding of even and odd numbers.
An even number is an amount that can be made of two equal parts with no leftovers. An odd
number is one that is not even or cannot be made of two equal parts. The number endings of 0,
2, 4, 6, and 8 are only an interesting and useful pattern or observation and should not be
used as the definition of an even number. (Van de Walle & Lovin, 2006, p. 292)
Activities that involve taking a number of objects below 20, and partitioning them into
equal groups is the first step to understanding even and odd concepts. Students learn
about “the odd one out” in real life circumstances like picking for teams.
Once students have had practice with sorting objects into equal groups, the use of a
hundreds chart can be helpful for students to see patterns in numbers.