##
* *Reflection: Developing a Conceptual Understanding
A Remainder of One: Practicing Box Method - Section 3: Game time!

This is a complex process! One of the most difficult parts of this transition is getting used to the idea of diverse entry points into the problems. Prior to Common Core, I was trained to be such a mathematical "this is how you do it" teacher, that this process felt really uncomfortable at first. It is especially hard if parents aren't on board. I begin dialogue with them at conferences in the fall about this process and explain that Common Core will be an adventure in understanding.

Today, I could see students progress before my very eyes. But the painful process of learning to use notes, referring to vocabulary, referring to models, dialogue, talking through and being sure each question I posed was going to pull them forward, is exhausting.But it's worth so much more than just teaching an algorithm. I have learned that well.

I heard happy sounds in my class today. I heard rich questions both to me and to their partners, and thinking out loud about numbers, factors, dividing and getting it right. The idea that they would earn points pushed competitive buttons in them and drove the higher end students to 3 digit by 1 digit problems.

Game playing works really well in this process. It also freed me up to notice things I wouldn't if I had just given them worksheets. I saw number sense. I could tell if they could choose to put the numbers in the correct places in their boxes and understand dividend, divisor, and quotient. We talked about what the quotient really means.

I would miss all of this if we just teach an algorithm. I would cheat them of the experience of the depth of understanding division if it weren't for Common Core.

*This is just too fun...*

*Developing a Conceptual Understanding: This is just too fun...*

# A Remainder of One: Practicing Box Method

Lesson 4 of 21

## Objective: SWBAT divide two and/or three digit numbers by one digit using rectangular sections (or a "box method" ).

## Big Idea: In this lesson students learn about the meaning of a remainder through a whimsical book, "A Remainder of One" and playing games with a choice of dice, dominoes or playing cards to create their division problems.

*60 minutes*

I opened my lesson today with writing two division problems, 47 ÷ 2 and 62 ÷ 3, on the board and asked students to take a few minutes to solve them using the notes from their introduction to division. I had emailed the SB notes from the lesson Introduction to Box Method from the day before.

I let them try to solve the problems for a few moments and asked them if they thought that 62 could be divided by three evenly. They knew that it wouldn't because they used what they remembered about divisibility rules for 3. I was proud that they could use their prior knowledge and transfer it from the work they did in solving factor pairs over the last few months!

At this point, I got out the book *A Remainder of One* and read aloud to them. I used the book to engage their thinking about remainders. They loved it! It is a sister book to *One Hundred Hungry Ants. *

*I connected our class situation to this book since we have 21 students and we often pair up, leaving a "Joe". I asked them to tell me what number I needed to divide by when making groups to make sure no one was left as a remainder. They quickly told me three.*

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#### Reviewing Our Old Notes

*10 min*

We looked together our old SB notes from the lesson yesterday. I brought them up on the SB and we reviewed what we had learned going over step by step. I shifted the attention to the two problems I had written on the Whiteboard. I asked them to look at their work. I asked if anyone had any trouble solving these? Three people said that they were stuck on the first problem.

I decided I needed to simplify the problem and we divided 7 by 2. Through simplifying the numbers, the struggling students could easily see how the remainder worked in the quotient.

I asked them: When do we always have a remainder of one?

Several students tried to answer and then one student said:" For sure when we divide odd numbers by 2. And then it might happen in other times. I just know it happens then for sure."

I asked them to partner up with the person they had worked with in our Ants Ants Ants lesson. They were to go back to their area, bring up the notes in their emial and solve two problems from the notes on the SB lesson. I told them that I would be around to check understanding.

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#### Game time!

*30 min*

I love dice and card games with math! Dominoes work well too when it comes to creating algorithms and playing games to solve problems. Division is much more fun when practicing like this!

After I approved their practice work, I told them they could go to the table and pick their "problem makers"; dice, dominoes or playing cards. They could choose which tool to use. But, I wanted them to create division problems by making the largest dividend from rolling dice, choosing dominoes out of a pile or drawing two cards. To create their divisor, they needed to role a die, add a domino or find one with one set of dots, ( but be sure it added up to a one digit number) or draw another playing card depending upon the tools they chose. There were different kinds of dice to use and they enjoyed choosing their tools.

**Rules:**

Create your division problem by creating the largest dividend from your tools.

Divide by the divisor using box method.

Compare your answers, compare how many boxes you used to get there and check your answers by multiplying and adding the remainder in.

If you are both right, you both get points.

If one of you is wrong, your forfeit your points to the other person.

If you have zero points, you can't give anything, but the other person gives themselves a point.

If you are both wrong, no points are given.

High end students can create three by one digit division problems to challenge themselves.

I roved the room as they played, finding students with interesting questions, getting stuck and forgetting to use their notes as a resource. This was a great opportunity to reinforce use of notes and see what they weren't understanding.Using Notes from the Other Day

They enjoyed the freedom to take the risks of not understanding. Those who did understand played flawlessly, and it freed me up to tutor those who were struggling. Partners supported each other in learning as they had the day before.Dialogue and Learning

As we transition to understanding how to divide on a different level than prior to Common Core, this struggle must be accepted as part of learning. I see it every time I teach it, but in the end, the advanced thinking and connections become their own and they reach a higher level of independence.

The banter and noise in the classroom in the background of my videos is evidence of engagement and joyful learning that Common Core brings to math.

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#### Wrap Up

*10 min*

I gathered my students on the floor to give some closure to the game. I asked them questions about their learning.Checking for understanding...beginning the wrap up.

We all agreed that more practice is needed on a daily basis, but all could see their progress from the day before. I asked them; What was the hardest thing? A wrap up. Those who had mastered two digit by one digit, felt more confident in learning three digit by one digit. I heard comments about how fun the games were.

We will use these tools again as we learn to divide. I explained that they could use the same tools at home.

Homework: Usually on Fridays, I don't assign math homework, except for drills on math facts. I told them they could choose a division activity from IXL math to practice for more practice. This resource is great and I can see their progress because I have a subscription. You can use the site without a subscription, but it will cut off the student after a fair amount of problems.

*Simply log on and go to grade level and pick division problems from there. Go to the tab for standards to set it for Common Core.

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Divison Pretest
- LESSON 2: Ants, Ants, Ants! Using discovery to understand the meaning of division.
- LESSON 3: An Intro to the Box Method: A Conceptual Approach to 2 digit by 1 digit division
- LESSON 4: A Remainder of One: Practicing Box Method
- LESSON 5: Multiply or Divide? Exploring Word Problems that Compare.
- LESSON 6: Developing Our Division Skills
- LESSON 7: Two Games for Practicing Fluency & Dividing 3 -4 Digit Dividends Against 1 Digit Divisors
- LESSON 8: Oranges,Social Studies, Sister Anne and Studying the Whole: An integrated lesson
- LESSON 9: Talk the Talk of Division: Recognizing "Division" Words in One Step Word Problems
- LESSON 10: The Sieve of Eratosthenes: Prime Numbers, Multiples & Inverse
- LESSON 11: Understanding Division Through Bubble Wrap
- LESSON 12: Division: Quiz 1: Assessing division of 2,3, &4 digit by one digit divisors
- LESSON 13: Supporting Their Writing in Math: Class Collaboration and the Google Doc
- LESSON 14: In a Heartbeat! Connecting Informational Text to Multistep Word Problems
- LESSON 15: Assessing Understanding of Division Word Problems
- LESSON 16: Game Day! Review Day!
- LESSON 17: Bowling for fluency: A game for number sense, fluency and equation development.
- LESSON 18: Writing: Showing our Understanding of Entry Points & Place Value in Dividing
- LESSON 19: Division: Getting Ready to Test
- LESSON 20: Dear Mrs. Kanthack: A letter from students about mastering Division Standards
- LESSON 21: Assessing Division