In today's lesson, the students learn to use models to divide a 2-digit number by a 1-digit divisor. They must consider the multiplication problem that supports their answer. This aligns with 4.NBT.B6 because the students find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
To get started, I ask the students a question. "Why do we need to divide?" I give the students a few minutes to think about the question. I take a few student responses. One student shares, "To split something between people." I tell the students, "Today, we will use models to help divide a 2-digit number by a 1-digit divisor. Our multiplication facts will help us."
I call the students to the carpet as we prepare for a whole class discussion. The 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.
quotient - an answer to a division problem
divisor - a number by which another number is being divided
dividend - the amount you want to divide
remainder - the part that is left after you divide
28 divided by 3
First, divide the 28 pieces evenly among 3 groups. Any leftover will be the remainder.
The quotient is 9 with a remainder of 1. The multiplication sentence that helps with this problem is 3 x 9 = 27.
Another way to model division is with place value blocks. I show the power point slide to the students. I ask, "How many groups will we divide 28 into?" The students tell me 3 groups. I explain to the students that we first divide the greatest place, which is the tens in this problem. "There are only 2 tens. How can I divide them into 3 groups?" The students think about it for a minute. "Can I put one tens block into each group." The students all agree that this cannot be done. I explain to the students that we must regroup. The power point models 2 tens being traded for 20 ones. Now, there are 28 ones. We can divide those into 3 groups. Because 3 x9 = 27, we can put 9 ones into each group. "How many ones will we have left?" The students tell me 1.
The standard algorithm is another way to solve division problems. First, divide your divisor into your dividend. Next, multiply the quotient by the divisor. Last, subtract. This will be your remainder.
Let's try one together.
19 divided by 2
I let the students help guide me through the steps to find the quotient. I draw 2 groups on the board. Together, we count as we divide 19 into two groups. We stop at the number 18. I ask the students how do they know that there will be a remainder in this problem. One student says because "2 is an even number." That is correct because 2 can divide into all even numbers. Because 19 is an odd number, there will be a remainder. We find that the remainder is 1. The multiplication problem that helps to solve this problem is 2 x 9 = 18.
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 Group Activity Sheet Dividing 2-digit by 1-digit. The students must work together to find the quotient to the division problems. They must draw a model to help with the division (MP4) by separating the dividend into groups. They must identify the multiplication number sentence that helps them solve this problem. A multiplication chart is attached to assist the students. The students use place value blocks to get a conceptual understanding of the value of the numbers as they are being divided. They 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. 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 evident in the Video Divide 2-digit by 1-digit. 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 is the dividend in this problem?
2. What multiplication problem will help find the dividend?
3. What is the remainder? How did you find the remainder?
As I walked around the classroom, I heard the students communicate with each other about the assignment. I 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. As I walk around, I hear students say things like "We don't have enough pieces to go around again," or "it's 5 because 8 x 5 = 40."
For this lesson, I wanted the students to use different strategies. The place value blocks are excellent to give the students a conceptual understanding of the value of the numbers, but most students do not have place value blocks to use at home to practice the skill. Therefore, the students also drew models of the division problems. This will allow the students to practice division at home.
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.funbrain.com/math/index.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.
From this example of work, the students used place value blocks to help divide a 2-digit number by a 1-digit number. The standard algorithm was used along with the place value blocks so that the students could get a conceptual understanding of the numbers as they were used in the algorithm.