In yesterday’s lesson students created short story problems using division and solved them with an area model. Today students will apply their understanding of the area model of division to interpret the traditional form of the division equation. Students felt comfortable with completing division problems with the area model but now they must build upon their understanding of division and apply it to the equation. Although I am moving on to the traditional form of division, it is of utmost importance that students understand what is happening within a division problem. In today’s lesson we will transform an area model problem into the traditional division equation and then outline the steps in order to solve the problem.
Think back to our previous lesson and the story problems you were completing with your neighbor. Who can give me a problem they solved yesterday?
I start by jotting down the problem on the whiteboard so that we can refer back to it during the process. I ask the students to then describe how they solved the problem. I add a drawing of the area model they created yesterday.
Is there anyone who has questions or doesn’t understand what this group did yesterday?
Well, if you can do and understand this example you can definitely do division with the equation then.
I begin showing students how to set up the division problem in an equation. While creating the model I call on allow students to interact with my creation.
Okay, what was the total number of bunnies? Twenty. I write the number down.
Alright, what did I have to do to the bunnies to figure out how many each person would receive? Divide. I draw the divide bar around the twenty.
And how many people received the bunnies? Four. I add the four as the divisor.
Finally, how many bunnies did each person end up with? Five. I add the five as the answer on top of the division bar.
Now that we have set up what the equation looks like, I show students how I walk through the problem using the five step method. I think teachers develop their own way of explaining and outlining the steps involved in division. I have created a short video of how I explain division in five steps.
I have students write down the five steps in their vocabulary notebook as a simple list.
I ensure students I will give them a better way to remember the five steps of division. I teach the students the five steps of division using the motions I have created. I ask the students to say the step and do the motion simultaneously. We do this several times and I ensure all students are actively participating.
Now I have the students help me through a couple problems on the board. At this point I don’t want them writing anything down yet. I want them to focus on what I am doing and how I am doing it. I solve the problem asking them throughout what is the next step. I ask them to reply with the motion and the word. I suggest doing an example with a remainder and one without a remainder.
After the whole group practice I ask the students to work with partner to complete the three division problems I provide them with. I set up the three problems on the board and have the students work through them on a separate sheet of paper with a partner. I tell students they need to solve the problems together and verbalize each step as they are doing it. Before starting their problems I ask students to jot down the five steps in abbreviated form and refer back them when completing their problems.
I circulate the room and check for understanding. After allowing the students about 10 minutes to work I ask for volunteers to come to the board and explain their thinking as they walk through the steps of the problem.
I pose one more question to students to wrap up the lesson.
How are the five step method and the area model of division similar and different?
This is definitely the key component to this lesson. Students must understand that the concept shown by the area model is a concrete and visual representation of the five step method. They easily understand the area model and need to view the five step method as an extension.