Even and Odds
Lesson 2 of 8
Objective: The students will be able to determine whether a group 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 a sum of two equal addends.
(See attachment for video introduction)
To get students excited about learning they watch a brief video “Odd Todd and Even Steven." This video gives clear and precise facts about the meaning and use of odd and even numbers. Common Core mathematical practice MP8 states, “Students should be able to examine numbers to find repeated patterns.
This video clearly exemplifies how to determine what numbers are even, and what numbers are odd. It also, explains how these numbers are used in a real-world setting. After the video, I transition the students into a small group setting to brainstorm what specific facts they learned about even, and odd numbers.
Things to question:
What numbers are even and odd?
How can you determine if a number is even, or odd?
Can you tell me at least three even and odd numbers?
Shortly after the video, I moved students into a smaller group setting. Then I used a simple model of how Even numbers are numbers that CAN be grouped by twos, and Odd numbers are numbers that CANNOT be grouped by twos.
To figure out if a number is odd or even, look at the digit in the ones place.
- If the digit in the ones place is 0, 2, 4, 6, or 8, then the number is even.
- If the digit in the ones place is 1, 3, 5, 7, or 9, then the number is odd.
Examples of Even Numbers
22, 80, 58, 44
Examples of Odd Numbers
We will use the following Mathematical Practices:
MP.2. Reason abstractly and quantitatively.
MP.3, Construct viable arguments and critique the reasoning of others.
MP.7. Look for and make use of structure.
MP.8. Look for and express regularity in repeated reasoning.
Teachers and Students Chat:
Now that students have some idea of what is expected of them, I invite them sit on the carpet. I start to discuss various strategies that can be used when solving problems. For instances, students should be able to make a reasonable estimation on what the total should be, and they should be given several opportunities to learn the best way to solve their own problems.
Therefore, I model how to use basic reasoning skills (MP2) to determine if the given numbers are even or odd, I used a teacher's model to model how even and odd can be used to represent the differences in numbers and shapes. As I explain I ask students what they think I should do to solve the problem. This allows me to check for understanding so far.
After that, I have show at least two or three examples and model aloud how they can be detected. When students are comfortable explaining their findings, I invite student volunteers to come up to the board to illustrate and explain what they have learned so far.
(As students are working I continue to check for understanding, and to point out the various ways students solve their given equations.)
How do you determine what numbers are even and odd?
Can you think of any other ways even and odd numbers can be used?
Work with the students repeating the same mathematical steps until a level of understanding is reached.
Some students are able to respond, however, they are not using mathematical language.
Just about now students are ready to transition into smaller groups to continue working on their own, however, with the teacher guiding them as needed.
Things you will need:
Manila paper, pencils, colors
The students will tri-fold Manila paper into four section, and illustrate how even numbers can be split into two equal groups, and represent how the even number is the sum of those groups. As they are working towards solving their problems, I observe to make sure they are estimating, identifying within reason. I also, check to make sure they are justifying their answers by asking them to explain how they determined their answers.
Show the number 10 using two equal parts.
The number 10 can be split into two equal groups of 5.
The number 10 can be split equally into 5 + 5 = 10.
As the students are working please be sure to actively engaged them in a conversation about how and why they determined their illustrations.
During this part of the lesson I take about five quick minutes to stop and check for understanding. My questions are designed around these concepts:
- How do I know that they learned what I wanted them to learn?
- How well did they learn the objective?
- Who mastered it and who didn't?
- Which parts of the objective did students struggle with? What misconceptions did they have?
I asked the students what they learned, and could they think of other ways to illustrate odd and even numbers?
(Please allow proper wait-time for student’s responses.)
Students were able to illustrate and explain how numbers can be grouped in-order to determine if they are odd or even. Some students were able to determine odd of even numbers by examining the number in the ones place.
Responding to how/why...........helps students break down the standards and creates a positive learning environment. (Note: you can check for understanding through observing, open-ended discussions, or independent response sheets.)
By My Self!
As this lesson unfolds I try to create a mixture of different learning opportunities, to help children encounter new information, develop skills, try out ideas, and build knowledge.
To accomplish this, in this part of the lesson the students will use what they have learned to answer questions about even and odd numbers. First, I briefly go over even and odd numbers as I did in the “anticipatory” part of this lesson. Then I go over the intended outcome of this entire lesson as stated below:
Students will be able to determine whether a group 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 a sum of two equal addends.
(Before the students start working on answering the selected question please be sure they know what the assessment is asking them to do.)
I circle the room to ask students how and why questions to make sure they are getting at those key concepts. For instance; I ask students to explain how they know if a given number is odd or even.
- An integer that can be evenly divided by 2.
- A number whose last digit is 0, 2, 4, 6, or 8.
- All the multiples of 2.
- A number whose last digit is 1, 3, 5, 7, or 9.
- All the numbers that are NOT multiples of 2.
Adding it all up!
Students are now given time to apply what they have learned so far about even and odd numbers to solve the given problems. As they are working I check to see if they can estimate within reason, and explain how they solve their problems.
After students are finished working independently, on their given problems.
I bring them back together in a whole group setting to bring this lesson to a close. Be sure to create with the class a set of guidelines for communicating and co-operating in whole groups.
( Such guidelines may cover making sure that everyone has a chance to talk, criticizing constructively instead of destructively, and finding ways to analyze the work of others.)
Basically, I allow the student to share what they have learned with others.
Some of the students shared orally, some of them wanted to illustrate what they learned on the board. However, this lesson was very engaging and powerful. My students took responsibility for their own learning, and the sharing what phenomenal.