In today's lesson, the students learn to identify a whole number as prime or composite. This aligns with 4.OA.B4 because the students find all factor pairs for a whole number in the range 1-100. Determine whether a given whole number in the range 1–100 is prime or composite.
To get the students started, I review by asking a question. "How can we find the factors of a whole number?" I give the students a few minutes to think about the question. I take a few student responses. One student says, "By looking at the number of the multiplication problem." I asked the class could someone explain that more. Another student adds, "Multiply the numbers that equal that number." Today, you use what you learned yesterday by using multiplication to help find the factors of numbers. Then you will identify that number as being prime or composite.
I call the students to the carpet as we prepare for a whole class discussion. The Prime and Composite Numbers 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 begin by going over important vocabulary for this lesson. The students will have to know these terms to understand the lesson.
A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself.
A composite number is a whole number greater than 1 that has more than two factors.
Factors are numbers that are multiplied together to find a product.
I read the vocabulary with the definition, then the students repeat it after me. We begin to practice the skill by finding the solution to a problem. The following problem is displayed on the Smart board:
Identify 23 as prime or composite
In order to determine if a number is prime or composite, we must find all of the factors. What are the factors of 23? Let's find out.
I send the students back to their seats because I want the students to work hands on while we are solving this problem. Each student has their manipulative kit at their desk. The students use the counters for this activity.
"We learned yesterday that making arrays can help find factors.
How many equal groups can we separate the number 23 into? Take your counters and separate the 23 pieces into equal groups. Write down the multiplication facts as you do this."
I allow the students to work independently at their desk to discover the number of even groups that they can separate the 23 counters into. I walk around to monitor as the students do this. I have to remind the students that equal groups mean that each row has the same number of counters because some of the students are having difficulty separating the counters. I asked one student, "What can you multiply to get 23?" The student knew right away that 1 x 23 = 23, so the student made the array of one row with 23 counters in the row. After giving the students about 5 minutes to do this, I call the students back together as a whole class. I ask the students to share their discovery. Based upon the student responses, they all only had 1 array for this problem. We discover that 23 can only be put into one group of 23. We review the definitions for prime and composite number. Based on the definition, the students determine that 23 is a prime number because the factors are 1 and 23.
This one example is just to expose the students to the skill. Because I want the students to have plenty of time to explore and learn with the counters, we move on to working in groups.
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 group a Prime and Composite Numbers Group Activity Sheet and counters. The students must work together to find all the factors of a whole number, then identify the number as prime or composite. They must use the counters to make arrays to represent the multiplication equations that correlate with the whole number (MP4). Multiplication charts will be available for students who have not mastered their multiplication facts. The students must communicate precisely to others within their groups. 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. 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?
4. Is this number prime or composite? How do you know?
As I walked around the classroom, I heard the students communicate with each other about the assignment. 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. I always tell my students that they must justify their answer by referring back to the problem.
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.aaamath.com/fra63ax2.htm#section2
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 student's 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. In the Video, Prime or Composite, you can see a sample of student work. 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.
The biggest problem I noticed with this lesson is that some students had a difficult time identifying all of the factors of some of the numbers. I feel that this is because they did not apply what they have learned previously of using models to represent multiplication problems. A few of the students wanted to take the counters and just separate them into rows, not being conscious of the fact that they should be equal rows. I discussed with these students that in order to multiply two numbers, the same number must be repeated. With their models, the same number was not being repeated throughout the array.