Even and Odd - A Forgotten Concept - The Good Neighbors Math Series

Introduction

Student in 2^nd Grade are expected to determine if a set 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 the sum of two equal addends (CCSSMath.Content.2.OA.C3). The “even and odd” concept/skills are not explicitly addressed in any other grade level standards beyond 2^nd Grade. It is for this reason that the concept of ‘even and odd’ is a ‘forgotten concept’ for many upper elementary students.

The most successful students in 2^nd Grade learn the concept of ‘even and odd’, but only with numbers up to 20. If these students retain this information into the upper grades, they do not always successfully transfer the ‘even and odd’ concepts/skills to large whole numbers. Students who were not successful in 2^nd grade learning ‘even and odd’ concepts/skills within 20, and/or students who did not retain their learning, have no other opportunity in the general education curriculum to relearn the concepts/skills of ‘even and odd’.

Even and Odd Study

I knew this anecdotally from being a Special Education Teacher and Math Interventionist for over 20 years, but I found out empirically just how serious the problem was in my elementary school. Students in 3^rd, 4^th, and 5^th grade took an ‘even and odd’ pretest which asked: “Is 758 an even or odd number? Draw a picture. Explain your answer.” The results from the pretest indicated that: 31% of Gr. 3, 32% of Gr. 4, 23% of Gr. 5 students had “No understanding or Misunderstanding”. Less than 50% of student in all grade levels had a “Good or Excellent Understanding” – 44% of Gr. 3, 41% of Gr. 4, 40% of Gr. 5.

The results clearly indicate that ‘even and odd’ concepts and skills need to be revisited as students work with larger whole numbers in the upper elementary grades. Whether older students never learned the concept of ‘even and odd’ in 2^nd Grade, did not retain their leaning, or fail to transfer their learning to larger whole numbers, there seems to be a need for explicit instruction of ‘even and odd’ concepts/skills in the upper elementary grades.

Whether older students never learned the concept of ‘even and odd’ in 2^nd Grade, did not retain their leaning, or fail to transfer their learning to larger whole numbers, there seems to be a need for explicit instruction of ‘even and odd’ concepts/skills in the upper elementary grades.

Even and Odd Revisited in Upper Elem. Grades

*Onesie’s Odd Job* reviews the definition of ‘even and odd’ and demonstrates how ‘even and odd’ applies to large whole numbers.

Illustration demonstrating the basic definition of ‘even and odd’.

Illustration demonstrating that all multiples of 10 are even numbers.

Illustration demonstrating that all multiples of 100 are even numbers.

Luckily for the math community, there is a unique math picture book that address the basic concept of “even and odd”, and demonstrates how the ‘even and odd’ concept applies to large whole numbers. Onesie’s Odd Job – A Cheesy Mouse Tale of Even and Odd is part of The Good Neighbors Math Series. The series address elementary math skills conceptually through engaging narratives and base ten visual models.

Students learn/relearn the definition of ‘even and odd’ through the character Onesie as he learns about the concept from his neighbors Tenor and Hund-Red. Onesie’s neighbors demonstrate (through base ten visual models) that multiples of 10 and 100 are always even. As Onesie learns, the students learn that even in large whole numbers, the quantity of ones determines if a number is even or odd. Student, from the illustrations, are able to see base ten visual models for why 999 is odd and 998 is even – a powerful teaching tool.

Illustration of question posed at the end of the story: “Is 999 even or odd?”

Illustration demonstrating why 999 is an odd number and 998 is an even number.

Results

The effectiveness of the book on the students’ understanding of ‘even and odd’ was remarkable. After hearing the story/looking at the illustrations, students in Gr. 3 and Gr. 4 who had a “Good or Excellent Understanding” increased to 88% (5^th grade data was not collected). Students who had “No Understanding or Misunderstanding” decreased to 0% for Gr. 3 and 6% for Gr. 4. Two class periods (one period reading the book, second period discussing book/guided activity) of explicit instruction on ‘even and odd’ concepts and skills, made a significant impact on student learning.

3rd Grader Pre-test answer. St. has common error transferring ‘even and odd’ concepts learned in 2nd grade to large whole numbers.

4th Grader Pre-test answer. St. has basic understanding of ‘even and odd’ – numbers that end with 2, 4, 6, 8, 10.

Same 3rd Grader Post-Story. St. now see the number holistically as always having even hundreds and tens, and relying on the ones to determine ‘even or odd’.

Same 4th Grader Post-story. St. has conceptual understanding of ‘even and odd’ – visually shows how the number can be divided in two equal parts.

Conclusion

Teachers cannot assume that students in the upper elementary grades have a good understand of even and odd numbers, and that they can transfer what they learned about even and odd numbers in the primary grades to large whole numbers in the upper elementary grades. Don’t let ‘even and odd’ become a ‘forgotten concept’ in the upper elementary grades. Take time to reteach the basic definition of ‘even and odd’, and help students transfer the concept of ‘even and odd’ to large whole numbers.