Odd and Even
By Carol Underwood
This lesson taught me a lot about how second graders think about odd and even numbers and how to design activities to build understanding.
My objective was for students to be able to identify odd and even numbers from 1-100. However, I also wanted students to be able to explain and prove how a number is even or odd.
I administered the pre-test in the morning on Wednesday, August 28th. About half of the students were able to identify odd and even numbers. Several of these students could tell how they knew it was odd or even. Some of the responses were:
“By the end number.”
“Counting”
“Even numbers have 2,4,6,8 in them. Odd numbers have 1,3,5,7.”
“I can look at the last number.”
“Because you count by two.”
“If you hold up one finger on one hand and two fingers on the other, there are not the same and that’s odd.”
Since the last statement was the only one which reflected real understanding of even and odd numbers, I decided that everyone would benefit by the first activity; building the numbers 1-10.
I handed out the Even and Odd worksheet and the 100’s chart. I decided not to read the book Even Steven and Odd Todd at this time. I thought it would be a good review at a later date.
Using the worksheet, I asked students how we would show the numbers 1-10 with base ten units. Using their answers, I modeled 1-10 on the overhead worksheet. Some were confused. Then I showed a weight scale and explained that if you put one unit on one side and nothing on the other side, the scale is not even, not balanced. Therefore, one is an odd number. That example made this definition of odd and even clear to them. Another student said, “It is like a fair share.” I asked her to explain that to the class. She said somebody gets a number of something and someone else gets one more. That is an odd number. Some students understood her explanation.
I decided to skip the worksheet because the format was confusing to some. I told the class to lay out their pencil in a vertical direction. I modeled at the overhead. Then I put one unit on one side of the pencil and nothing on the other. I asked the students if the number one was balanced or even. I continued putting more units and each time asking if the number was even, the same or balanced. Everyone understood this visual model very clearly. It looked like this:
x x x x x x x
6 4 2 1 3 5 7
Instead of like this:
1 x
2 x x
3 x x x
4 x x x x
When we got to 11, I tried moving to numbers such as 5/6. But many students were not ready for this abstract concept yet.
I asked them to circle the even numbers on their 100’s chart from 1-20. I asked if anyone saw any patterns. Several students volunteered.
Then I asked them to continue circling numbers to 100 and looking for patterns. As they gave their answers, I wrote their ideas on the overhead.
“All the numbers ending in 2 are even and etc.”
The next day I decided to change activities a little. I told the students to make the number 9 with units. Then I told them to show if that number was even or odd. A few students laid out 4 units in one pile and 5 in another. I asked them to show at the overhead and explain their thinking. We continued in this way using numbers from 11-25. Most students were able to make two groups of units and tell whether it was even or odd.
Next we played our even and odd game with cards. I handed out a card with a number on it. The students with the odd numbered cards went to one place in the room. The students with the even numbered cards went to another place. With the face cards taken out, partners put down 2 cards. For the even members, only 2 even cards could win. The opposite was true for the odd group. The students liked this game but it didn’t offer many opportunities for winning. The rules will be changed for the next day.
Our third lesson was on Sept. 2nd after Labor Day. I read Even Steven and Odd Todd. One student said she didn’t get the title. I told her to listen carefully to the story and then she would understand. Also, I told everyone to be thinking about some rules for even and odd numbers. Everyone was very engaged in the story. Sometimes I would re-read sentences for emphasis and hold up my fingers counting. “He knocked on the door knock, knock, knock.” Afterwards the students came up with these rules.
1. All even numbers end in 2,4,6,8 or 0. (We had a discussion about 0.
One girl explained that 0 had to be even because 1 is and odd number.)
2. All odd numbers end in 1,3,5,7,9.
3. An even number + an even number= even number
4. An odd number + an odd number= odd number
5. An even number + an odd number = odd number
* (They will investigate these rules on the next day using 2-digit numbers and a calculator.)
Next, I showed them a function box. A card with a number on it went in one side and came out the other side as the same card with the number as one more. (Of course, it was really a new card.) I showed several examples and they guessed the new number. On chart paper I had drawn.
IN OUT
24 26
33 ?
71 ?
88 ?
They had to guess the OUT number. Students came up and wrote the answer.
I said, “Look at these problems.” What do 22,34,56,and 48 have in common? What do their answers have in common?
22+1
34+1
56+1
48+1
Last, I told them to pick a partner to play a card game. The rules were: each player holds half the deck (minus the face cards). At the same time, they put down the top card. The first player to identify their card as even or odd wins both cards. The game was fast–paced and very motivating. I roamed around to all partners assessing.
The fourth day was a review of explaining or proving that a number is even or odd. I would say a number under 25.The students had to show a strategy on their desk using tools that count by one. I decided to stay with direct modeling and not change to using the abstract number because some students were not ready to break numbers apart in their head. Many students showed their strategy to the class. Lots of practice and discussion helped everyone to be successful. Next, we looked at patterns on the hundreds chart and how to find numbers. I would say four even or odd numbers in a row and then ask, “What is the next even/odd number?”
After questioning, watching and listening to the students, I felt they were ready for the final assessment.
Later that day we went to the computer lab. We tried the even and odd game on www.aaa.Math.com. The class loved it! During the game, they were timed and could see how many right and wrong answers they had. The game used 4-digit numbers so it took a few times playing to get the hang of it. I will be using this web site again for other math concepts and skills.
The post-tests were 100% accurate on identifying even and odd numbers and 60% correct on the explanation. These results were on the expert level for beginning second-graders. Expressing their thoughts in math language is very difficult for this age.
Even though I changed some activities from the original lesson, I thought this was a very productive week. Not only did these students explore even and odd numbers, but also number order, place value, algebraic thinking, computation and problem solving.
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