In today's lesson, the students learn to relate multiplication and division. 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 the relationship between multiplication and division. The students also illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
I tell the students, "You have learned how to use arrays to represent multiplication. Today, you will use arrays to understand how multiplication and division are related. Name some things that can be put into arrays." Some student responses: desks, books, chairs, and pictures.
To begin the lesson, I call the students to the carpet. I find that the students pay more attention while I'm at the Smart board if they are near me. I begin by sharing a video lesson at the following site:
Sometimes, I like to use video resources to teach the class because it gives the students a different experience in the classroom. I have found that students enjoy class more when they are not doing the same thing.
I let the students watch the video completely before asking them questions. After showing the video, I review the content of the video with the students.
I remind the students that multiplication and division are inverse operations. Therefore, we can use multiplication to help us with division.
Example: 15 divided by 3
I ask the students, "Which number represents the total?" The students know that 15 is the total number being divided into 3 groups. I ask, "3 x what will give you 15?" The students know that 3 x 5 = 15. Therefore, the quotient to this division problem is 5.
I show the students an array of 3 x 5.
I explain to the students that this array represents 3 groups of 5.
I tell the students that they will practice relating multiplication and division in groups.
The students are rotating in centers for this activity. I put the students in groups of 5. Every 15 minutes, I rotate the students to the next center. This is a handout with the instructions for each center activity (Relating Multiplication and Division.)
Group 1: The students go to the computer (Students working on computers) to work on using multiplication to solve division problems at the sites listed below. The students take paper and pencil to the computer so that they can write down the multiplication problems that are helping them solve their division problems. The following websites will help the students with the skill:
Group 2: The students solve real world division problems (Relating Multiplication and Division Real World Problems) using Centimeter Grid Paper or color counters to model the multiplication sentence that help you solve the division problem. The students write the multiplication sentence and division sentence. Last, the students solve for the quotient.
Group 3: What’s on Sale? (Challenge)
The students use a grocery store sales paper (Sales Ad and sales ad2) to find the price of items that are on sale. For example, 2 candy bars for $2.00. How much would it cost for 1 candy bar? The students use multiplication to help you solve the division problems.
Group 4: Name the Multiplication Problem
Before class, print the Name the Multiplication Problem, then cut them out and place them in a bag. At the center, the students receive the Relating Multiplication and Division Activity Sheet with the instructions for this activity. The students pull a division problem from the bag. The students must use the counters to show an array of the multiplication problem that helps them solve the division problem. Then, the students solve for the quotient to the division problem.
To give you an idea of what it looks like in the classroom, this Video shows students working at a center.
Group work is important in the classroom, but independent work is just as important. When students work together, they seem to really enjoy the lesson. However, in order for me to assess mastery, I like for my students to do an independent assignment.
Each student receives the Relating Multiplication and Division Exit Ticket.
Write a division problem. Write the multiplication sentence that helps you solve the division problem. Draw an array of the multiplication sentence. Find the quotient to the division problem.
This is a sample of student work: Student Work - Exit Ticket for Relating Multiplication and Division. In this exit ticket, you can see how the student related the multiplication to the division by drawing an array model of the multiplication sentence.