“What do you know about odd and even numbers?”
The students turn and talk about what they already know about even numbers. In my class I have 21 students. It happens that one student does not have a partner to turn and talk with. I remind the students about working in partners in class. What happens when one person doesn’t have a partner?
Even numbers are numbers where everyone has a buddy.
I ask the students about one student not having a partner to turn and talk with. Do you think that we have an even number or odd number of students in our class if one person did not have a partner? How do you know?
The students build the number 4 with their ones cubes, and group them into “buddies.” I use the term, "Buddy Up!" Explain that because each one of the cubes has a buddy, or can be grouped into 2, the number is even. Challenge the students to work in partners and use their cubes to find other numbers that are even. I create two columns on the board, one for odd and one for even. I write one digit numbers 1-9 on the board. The students choose a number and build it on their Place Value Mat. Have the students group their cubes into “buddies.” Ask them if every cube has a “buddy.” When they explain that there is one without a buddy, explain to them that this is an “Odd Man Out.” Challenge students to use their cubes to identify other odd and even numbers. As the students build each number, I circulate, checking in with students and having them explain their thinking.
I point out our classroom Odd or Even Poster, which serves as a reminder of what we've just explored.
Next, I read aloud the books One Odd Day and My Even Day by Doris Fisher and Dani Sneed. Before the read aloud, I tell my students that the word "odd" can mean more than one thing. I ask them if they know the meanings of the word odd. Do they think the story will be all about odd number, strange things happening, or both? Students identify the odd and even numbers hidden throughout the book, stopping on each page to identify these numbers.
Before students begin to apply what they've learned, we revisit the list of odd and even numbers that you have made as a class. To make sure my students make sense of what we're discussing, rather than categorizing this as a procedure or a list, I ask the students to think about how the numbers with buddies are “easier” numbers.
I have a list of two-digit numbers on the board, and two columns: odd and even. I have one student choose a number. Before they begin to work, I use one of my teaching tools - socializing intelligence - by having students turn and talk about how they can determine whether the number is odd or even. To continue to stretch student thinking, we come back together to continue the discussion.
My role is to facilitate the expression of their thinking rather than "doing their thinking for them". If necessary, I guide students to think about the one digit numbers as ones.
In our example number we look at the ones place. If the digit in the ones place is even, then the number is even. Let's try this with odd numbers. I use a smaller two digit number, and we look at the ones place to do a quick check. Does everyone in the ones place have a partner? Although the concept of determining whether a number is even or odd by only looking at the ones place, it may not yet make sense for my young students, which is why I've used a smaller odd two digit number. I model the entire number by drawing circles, counting up to my final number while I draw each circle in partners.
We continue to practice with several more examples of two digit numbers on the board. Each time have have students determine whether the numbers are odd or even, in partners if necessary, building each two digit number.
The students then play the Odd or Even Game Page in partners. They roll the two dice and build a two digit number with the numbers shown on the dice, and write it in the boxes. Both partners then build that number on their place value mat, and determine whether the number is odd or even by "Buddying Up" the cubes in the ones place. They then circle their determination.
For students who continue to struggle, showing them a number line beginning at 1 might help, because together they can more readily identify the even/odd numbers up through ten. As we extend to 20, they may begin to detect a pattern. I assist with this thinking not by pointing it out, but by asking students to make comparisons between 1 - 10, and 11 - 20. I may create two number lines for those students who need vertical comparisons but if I do this, I make sure to then "move" the 11-20 number line to its correct place - extending the 1 - 10 number line. We continue on to 21 - 30 to make sure this group of students can apply the pattern to this new range of numbers.
To close our independent work, and our lesson, I have students to turn and talk about what they learned about odd and even numbers. Next, I challenge them to share with everyone why it would be important to know whether a number is odd or even.
This closing thought is a challenge, because most students have yet to consider fractional numbers or division. I'm not looking for a "right" answer. I'm encouraging my students to think more deeply about their learning to consider its purpose.
Some students may say that even numbers are easier to add, but have difficulty sharing why they know this. This is an opportunity to develop student thinking. I do this by encouraging students to "show" when words fail them. Then, they have a concrete example to describe.