In today's lesson, the students learn to factor whole numbers. This aligns with 4.OA.B4 because the students find all factor pairs for a whole number in the range 1-100. This lesson will lead to future lessons on identifying prime and composite numbers.
To get the students started, I ask a question. "How can you show different arrangements for a number?" I give the students a few minutes to think about the question. I take a few student responses. One student responds, "You can put them in groups." Another student says, "You can use arrays." I tell the students "Today, you will learn to use multiplication to help find the factors of numbers. You will draw arrays to model the number."
I call the students to the carpet as we prepare for a whole class discussion. The Factors.pptx power point is already up on the Smart board. I like for my students to be near so that I can have their full attention while I'm at the Smart board.
I pose a scenario to discuss this skill. "There are 36 chairs in a closet. The teacher wants the chairs set in arrays. How many different arrays can you make with the chairs?"
I remind the students that multiplication can help with solving this problem. "What multiplication facts can we use to make 36?" The students think about this for a minute. I call on a few students to give me the multiplication facts. Student responses: 1 x 36, 9 x 4, and 6 x 6.
In the power point, the students see how to make arrays for 36. An array must have an equal number in each group. I remind students of the properties of multiplication. The identity property tells us that any number times 1 is that number. If we make an array of 1 x 36, then we know that 36 x 1 is also possible because of the commutative property. I explain to the students that we only need to write down the factors one time even though we can use the commutative property to change the order of the factors. I let the students know that 1 and the other number will always be factors of that number.
We can use patterns to help us find factors as well. Because 36 is an even number, we know that 2 is a factor. We learned in previous lessons that the multiples of 2 end with 0, 2, 4, 6, and 8. I point out to the students that earlier, they did not give me 2 as a factor. I let them know that always use 2 as a factor for even numbers. We can use division to help find the other factor that multiplies by 2 to get the product of 36.
Also, we learned that the multiples of 9 added together will equal 9 or a multiple of 9. 3 + 6 = 9, so 9 is a factor of 36.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
I let the students know that if they are not sure if a number is a factor, then they can divide that number into the product. If the number can go evenly without a remainder, then it is a factor for that number.
I give the students practice on this skill by letting them work together. I find that collaborative learning is vital to the success of students. Students learn from each other by justifying their answers and critiquing the reasoning of others.
For this activity, I put the students in pairs. I give each pair a Factors Group Activity Sheet.docx. The students must work together to find all the factors of a whole number. They must draw arrays to represent the multiplication equations that correlates with the whole number. Multiplication Chart.pdf will be available for students who have not mastered learning their multiplication facts. The students must communicate precisely to others within their groups (MP6). They must use clear definitions and terminology as they precisely discuss this problem.
The students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and must agree upon the answer to the problem. Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students. From the Video, you can hear the students discuss the problem and agree upon the answer to the problem. As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6). As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.
As they work, I monitor and assess their progression of understanding through questioning.
1. What multiplication facts have a product of this number?
2. What patterns can be used to identify the factors?
3. How does drawing arrays help solve the problem?
As I walked around the classroom, I heard the students communicate with each other about the assignment. From the video, you can hear the classroom chatter and constant discussion among the students. Before Common Core, I thought that a quiet class working out of the book was the ideal class. Now, I am amazed at some of the conversation going on in the classroom between the students.
Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.mathplayground.com/factortrees.html
To close the lesson, I have one or two students share their answers. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.
I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples, as well as work that may have incorrect information. More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.
I find that some of the students are only going for the obvious factors. If it is not on their multiplication chart, then they feel that they have found all of the factors. We will continue to work on using division to help figure out if a number is a factor of another number.