An Intro to the Box Method: A Conceptual Approach to 2 digit by 1 digit division

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SWBAT divide 2 digit by 1 digit algorithms and learn to use the inverse to correct their work.

Big Idea

This lesson introduces a method of division that supports a conceptual approach by dividing up two digit numbers by one digit. This lesson is intended to be the entry level and contains modifications for both lower and higher level students.

I Got Six!

15 minutes

To Warm Up: I Got Six

This short movie from Multiplication Rock is a great way to open up thoughts about the relationship between multiplication and division. The clip shows wholes being divided up into six parts, arrays and multiples of 6.

 I led the discussion and used questioning to get them to think about the inverse relationship and make those thoughtful connections. We discovered that the gumball machine is the example of division. I kept asking the through the clip: Is that division or multiplication? Is it both? What do you notice? This helped them stay on task and know that they were looking for the connection and direct them to see that there was a relationship.







New Vocabulary

15 minutes

More New Vocabulary:

I front loaded the lesson with new vocabulary by using a graphic organizer method that I just love! I passed out vocabulary sheets that are divided into boxes and had them set them aside for later. They will fill them out and cut them and glue them into their notebooks as the lesson progresses.  Frayer Model Template

To begin: I drew 18, 3,6 on the board. I asked them: How are these numbers related? What kind of equations can you create that would use all three numbers? How many equations can you make?

Students volunteered one by one to come up and draw how we would write the two multiplication equations. I connected the process using the math mountain.  It is a great visual for students who need to understand that the product of the multiplication equation is at the top and the two factors are at the bottom. I used this model to enhance their understanding of how the product transforms in to the dividend in a division equation. I refer back to this model throughout this lesson. This makes a solid connection for visual learners and those who are having difficulty getting division equations in the right order.

After 18 ÷ 3 = 6 and 18 ÷ 6 = 3 were present and all of the fact family pairs were complete, I introduced the vocabulary and students began filling out the Frayer Model Cards.

 I tied in the vocabulary as we went along. Students worked hard at filling out each section using the questions within the model. They related the dividend, divisor and quotient back to multiplication equations as they looked back on the math mountain model. This relationship solidifies their understanding that the roles of the numbers virtually stay the same on the math mountain, but are named differently in division, much like addition and subtraction.

We continued to fill out all three cards. We repeated the process with divisor and quotient, leaving the "What is isn't" and "Sounds like" blank.I did this because I want them to use these words in the blanks, interchanging them. So, "dividend" is not "divisor" and vice a versa.

"Sounds like" is a  good trigger for students to remember words and helps them to not confuse words that sound alike. They are always confusing divisor and dividend just because it begins with "d" and is part of division. The student can use a  "sounds like" word as the first word that sounds like the vocabulary word that comes to their mind. If we say that divisor sounds like visor, it helps the student focus on its meaning because a visor has no relationship to a divisor. In that process, the student tends to remember the word better. This concept comes from reading instruction authors, Fountas and Pinnell.


It's A BOX!!!

15 minutes

This is a step by step and very straightforward lesson on HOW to divide using rectangular sections or as I call it: " The Box Method". This is done carefully with much enthusiasm because learning to divide in 4th grade is a big deal! It is a milestone in 4th grade.

I started the lesson by asking students if they would like to learn how to divide in a way that they could solve multi-digit numbers divided by one digit?   I explained to them that the standard algorithm is not expected for them to learn in 4th grade and some background as to why.  I told them that I did not expect them to master the regular long division method this year unless they completely understood what they were doing. I brought up the lesson on the SB file: Introduction to Division Using Box Method  I used this SB lesson throughout the whole class instruction and used it to guide them in the process.

 I used students as volunteers to help solve problems as we began. They were gaining confidence as I went through each page systematically, talking about each step, got them to copy the first problem down to try right away. I taught  three different entry points to 54 ÷ 2, by including them in the entry point choices, and then moved on, showing only one to demonstrate the step by step process. I did this to focus on the process at that point. Before I had them try one on their own, then I went back two pages, framing out the idea again, solving the other two and showing that all three had the same answers so they clearly saw how we arrived at the same solution, differently. 

Students then were able to try the 87 ÷ 3 on their own, as I roved and checked on each of them to help support their learning. Students who mastered this problem asked if they could help others. This always is exciting, especially with a new and sometimes confusing concept like this is introduced. I have learned can't be everywhere in this complex process, and have learned that if I teach it very carefully, step by step, the majority of students grasp it and then are ready to help those who aren't yet. I am always happy when there are too many students to be helpers!

This is an atmosphere of cooperative learning as CCSS encourages in Math Practice Standard 5. This method is no fad. It is a CC based approach to division because it moves students toward mastery of understanding of the "why" of division. The diverse entry points really show that students have an opportunity to think about their process. The algorithm limits this understanding, and while they will master it in 5th grade, it is not appropriate now.

 Here are my class's notes from the lesson. I emailed a saved PDF file for them for reference. One of the luxuries of technology! Since textbooks are rarely used, this gives parents insight to what went on in class. Today's Lesson on Learning to Divide



10 minutes

Differentiation: I differentiated my assignments because of the very obvious levels of learners. My middle students were assigned two and three digit problems with no remainders. Two Digit by One Digit and Three Digit by One Digit Without Remainders

My high students were assigned IXL Word Problems Level G, H.4 word problems. If they find those word problems too easy, they can go to the next sections in H and look for more to do with division. They just have to show evidence on paper that they were solving problems. I will get a report from IXL that tells me they were mastering skills because we have a subscription. My high end students need the challenge to dive into division word problems because I don't want them bored with just the process of box division. If they mastered it in class, I want them to apply the knowledge to word problems right away.

I included worksheet that is like a puzzle for those  students wanting to really be challenged to work on 3 by 1 digit. Whirling Fan One by 3 digit Division from Scholastic, is a rigorous assignment. I did not expect that they would completely finish it because of the newness of this skill. I gave them the choice of the straight forward worksheet or the more visual artsy one. I only expect the lower and middle students to work on 4 problems. That is enough! I know they will get home and will be having to really think through the process again. They were allowed time at the end of the day to get started on homework. This lesson took the whole hour...but was worth every moment.

I plan to work with my struggling students one on one as we navigate this new adventure of dividing. I did not expect mastery today from anyone!


Closure: What do you think?

5 minutes

Wrap it up: We shared what we needed to remember in the process of division and insights of the process and the connections we made. I made it a point to emphasize again that everyone's problems may have different amounts of boxes because of how they chose to enter the problem. I reassured them that this method would be new to their parents and that the notes should be reviewed and used.