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.
Understanding the Standard:
- 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 board can be helpful for students to see patterns in numbers.
- Once students can identify and continue even and odd patterns, a mathematical generalization can be made regarding numbers that are equal. One of those generalizations may include the use of a “doubles fact” that can produce the digit in the ones place. For example, in the number 16, students would be instructed to look specifically at the digit in the one position, which is the six. They will then determine if a doubles fact exists, that would produce a sum of six. Since 3 + 3 (a doubles fact) equals six, then the number 16 is also even.
Questions to Focus Learning:
- Can students sort a set of objects into two equal groups?
- Can students express that when there is nothing left over after sorting objects, then that set is said to be even? Conversely, if an object is left out, then that set is said to be odd.
- Can students use their knowledge of “doubles facts” to determine if a number is even or odd?
- Can students write an equation to express an even number as the sum of two equal addends?
Students have had practice in sorting sets of objects. Students have previous experience with hundreds boards and can skip count by 2s.
At Grade Level:
Students will demonstrate their ability to determine a number’s property of being even or odd through a variety of strategies and will then use that information to later multiply numbers.
Students will write equations for odd numbers as one more than the sum of a pair of identical numbers, for example, 19 = 9 + 9 + 1.