Division as a Diagram

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Students will deepen their understanding of the traditional division equation by identifying parts of the equation in relationship to the math that is occurring.

Big Idea

Traditional division made simple!


10 minutes

The purpose of today’s lesson is identifying parts of the traditional division equation in order to build a deep and flexible understanding of the math.  Students will make a division problem into a diagram and focus on understanding the vocabulary associated with the equation.  By building a familiarity with the division equation students will feel comfortable with the process and its parts. 

In yesterday’s lesson I created motions to accompany the steps of division.  To open this lesson I will review the steps of division by having students recall them with the motions.  In order to do this I will go around the room and call on students to give the step and motion until I have gone through the steps about 4 times. 

Let’s start out with remembering our division steps we learned yesterday.  Let’s all do them together once and then I will call on someone to give us the next step and someone else to give us the following step and so and so forth. 

When I call upon students I make sure they answer with the motion and with a loud voice.  Sometimes students speak so quietly in the classroom but by reminding them to speak up I build their confidence in speaking in front of others.

The purpose of the round the room review is that I want students to feel comfortable with the order of the steps.  Therefore, when they get to the math they know exactly what to do and are easily able to recall the steps associated with the problem.   


20 minutes

As a class we will build a diagram of a division problem and label all the parts associated with it.  I would like students to be familiar with the academic vocabulary of a division problem and want them to have something to refer back to when completing future problems as we are solidifying an understanding of division.  I have included a copy of what the finished diagram might look like.

Today we are going to create a diagram for a division problem.  Before we get started I would like you to brainstorm with your group the things that might need to be included in the diagram.  Take a few minutes and come up with some ideas. 

While students are discussing in their groups I pass out a brightly colored sheet of paper to each of them on which we will create our diagram.  After a few minutes I ask student responses and we create a list on the board of possible things to include in our diagram. 

I begin by having students create the division problem on their paper.  I only have them draw the division bar, dividend, divisor, and quotient.  The students should put their division problem in the center of their paper to allow for labeling around it. 

After everyone has their division problem copied down I turn the labeling onto the students.

Alright, now that we all have the same diagram, let’s start figuring out what is what.  Tell me about what you know about this diagram and let’s see if you can help me get it labeled.  We can use our brainstorming list to help us figure this out.  Can anyone identify part of the diagram? 

I really just guide the student centered discussion at this time.  I want the students to do the work.  I want them to work the process and think of what the numbers in the equation really mean.  Once a part is identified, I give the students the academic vocabulary to add to our thinking.  I have included a copy of what our finished diagram looks like. 

Remember, it is important to let the students do some thinking about this equation.  They are the ones that need to make the connections between its parts and math involved in a division problem.


20 minutes

To build upon the connections uncovered in creating the diagram, I will now have students create a caption to accompany their diagram.  I thought this would be a great way to tie in a language arts component into this lesson.

You guys did a great job in helping me create this diagram but I feel like it’s missing something.  Normally when I see a diagram or illustration that there is something that goes with it.  Most of the time under it.  (I continue dropping hints until someone blurts out ‘caption’).  Oh, yes, a caption.  We should add one of those to our diagram.  I would like you guys to come up with two or three sentences that summarize or explain this diagram. 

I quickly pull out our language arts basal and show them an example of a caption on a diagram from one of our previous stories.  I read the example to the students and display the diagram.

Just like the author of this text summarized what was going on in this diagram and gave us some ideas about the diagram I would like you to do that for your diagram. 

The students easily understand the task and begin working on the diagram with their neighbor. 

Place holder student sample of diagram with caption.