Is that Number Even or Odd? – Commentary on Math Lesson Planning
Let’s teach/plan an elementary lesson on even and odd numbers – first step, compile the basic information on that topic:
The even numbers are all integers with the last digit (i.e. 1's digit) of any chosen number ending in 0, 2, 4, 6 or 8, and it is classified as an ‘even number’. Odd numbers are counting numbers, again with the last digit ending in a 1, 3, 5, 7 or 9. Let’s include a definition from the Internet on even numbers. An even number is an integer which is "evenly divisible" by two. This means that if the integer is divided by 2, it yields no remainder. Conversely, an odd number is a whole number not divisible by 2 and produces a remainder.
Quite frankly, this is not an easy lesson for elementary students to understand and master, especially when both the Common Core State Standards (CCSS) and the Texas Essential Knowledge and Skills (TEKS) specify the ‘determination of even numbers’ as a second grade mathematics standard. Second graders are not about to grasp the meaning of words like remainder, integer or divisible – at least not on a level of physical understanding. Both standards refer to ‘the pairing’ of numbers when determining if a number is even or odd, and this is exactly where this lesson should be begin. Over the years, I have observed several versions of effective ‘pairing’ lessons in primary classrooms, and I would like to share a primary grade level manipulative/tactile lesson in particular on even and odd number pairing.
A manipulative primary grade lesson on even and odd number determination
The classroom teacher taught his or her students if the chosen number was classified as even or odd by using their fingers, and she added a situational story so her students could remember it. For example, examining the number 5. Is the number 5 classified as an even or odd number? Students count to the number five (5) by alternating their number count on each hand and raising a digit (i.e. starting with the thumb on each hand) as they count. In the end, they have two digits raised on one hand and three digits on the other. Bringing the hands together and matching the digits, there is one digit (i.e. finger) that has no matching partner on the other hand. And, the teacher’s story is dance partners – the number five (5) leaves a finger with no dance partner to pair with, so the number five (5) is an odd number.
Why is this activity a great tactile manipulative for determining even and odd numbers?
It is simple, and it has a story that goes with it – easily remembered. The lesson also avoids complicated math vocabulary – easily learned later when the physical concept is mastered.
The manipulative – digits (thumbs and fingers) – students have access to it at all times, and the technique readily transitions to a more abstract paper – pencil number only exercise.
Two students - each counting on one hand and pairing hands - cooperatively talking out the solution. Learning by doing!
A significant number of Title 1 intermediate elementary students do not understand even and odd number classification. This method may be taught students of that age in minutes - time efficient - and they own the content.
It is a first step in sequential lesson planning that may be used with intermediate students so they comprehend the reason whole numbers of any magnitude are classified as either even or odd, by place value of the 1's digit (e.g. ten possibilities, five fingers/thumb on each hand) – affording a thorough mathematical understanding of even and odd numbers.
The divisibility rule of two (2) and a remainder (e.g. odd numbers) can be physically taught to intermediate elementary students using the same manipulative/tactile method as previously learned in second grade.
Even and odd number classification is important, and students must master the content by using highly effective pedagogical methods like this one. However, more importantly, successful elementary math teachers break down complicated concepts to simple ideas so students readily understand and retain the physical meaning of the mathematics.