##
* *Reflection: Developing a Conceptual Understanding
Developing Our Division Skills - Section 2: Metronome fun: Reviewing half as much or twice as many.

This was fun, interesting to be a part of, and gave me a clear understanding of who really didn't understand what half meant. I was surprised! Some students thought that half as fast meant faster!

This little activity really clarified for many that half as fast meant slower and dividing. This supports CCSS demand on us to delve into understanding of the concepts and strive to get students to understand it thoroughly. I think helping students connect math language to their conceptual understanding is one of the best strategies to mastering the standard about multiplicative comparison.

*Math Language and Kid's Perception*

*Developing a Conceptual Understanding: Math Language and Kid's Perception*

# Developing Our Division Skills

Lesson 6 of 21

## Objective: SWBAT solve 4 digit by one digit division problems.

## Big Idea: This lesson reviews some skills about multiplicative comparison while introducing 4 digit by 1 digit division.

*50 minutes*

*What's My Rule? is a great way to review function tables and also strengthen fluency. I like to warm up with different fluency work since we need to be mindful of continually supporting CCSS by spiraling back. I had covered and assessed function tables a long time ago. I wanted to trigger their memory again.*What's My Rule Chart

I set up a blank table on my SB and thought of a division rule to use. I drew in the numbers and told my students to think of a rule that fit. This little game is a great way of getting students to practice mastering standard 4.OA.C.5 by having them generate the rule and increase their fluency. Students took turns figuring out rules and creating the chart. They used the lower chart for ease.What's My Rule...student

**I set up tables going both vertically and horizontally so students understand that the direction of the table doesn't matter.*

*What's My Rule * shows the chart as we solved it in one of our sessions.

*expand content*

**Connecting Music to Understand the Concept of half or twice:*** My students have been writing music to play with their recorders. I got to thinking about CCSS 4.OA.A.2 and how their recent experience in music class writing half, eighth and quarter notes fits this standard. I thought about how fun it might be to play with a metronome for a few minutes and give students a chance to study math language involving multiplicative comparison: half as fast, twice as fast, twice as slow, half as slow. I am hoping this tactile activity will register with their brain in another way to perceive what half and twice really looks like. Eventually, I want them to show me if they understood the meaning of the words and then apply it to an equation. I was thinking that it would be a great way to get my lower students with language difficulties on track with knowing that twice as much meant to multiply and half as much meant they would divide. I wanted them to discover again what the reciprocal of whole numbers mean. This would reach full mastery of the standard as it reads.*

I wrote on the white board: Twice as much or Half as Much? What's the difference? I drew a half note, quarter note and eighth note on the board. They knew exactly how much the notes were worth, ( a credit to their music teacher) , but could not relate it to the mathematical value.

I started the online metronome up at 60 beats per minute, which is pretty slow. I asked students to tap that beat. I then told them to tap the beat twice as fast. Then, I asked them to tap the beat on the beat again. I asked them to tap it half as fast. It was hard, we had to listen carefully and practice it.Half as much means to divide ... for now!

We played with the metronome a little more, changing up the beat and speeding it up.Twice as Fast...Ya Da I really had to guide students to think, catch up or slow down. You can see it in these two little film clips.

*expand content*

After our metronome practice, I reviewed that 1/2 is a unit fraction and that we divide by the reciprocal of a unit fraction in order to find out what portion of the whole number is left. I quickly wrote 1/2 of 2014 on the board. I asked them how I would figure out half of the year 2014. I picked this number because it is the new year and is a good lead in to working on 4 digit by 1 digit division.

Would it be divisible? One student simply said that it meant that we should divide by 2. I asked them if we could do it in our heads? They remembered that divisible meant that the number would go into the number evenly. *We have used it in learning factor pairs.*

I asked them if they could divide 2014 by 2 in their head? *They responded with some protests. Too hard! I coached them on because I was hoping that solving this in their head would lessen any fear of learning to divide in the thousands place on paper.*

I began by asking: What is half of 2000? I then asked: What is half of 14? I got the right answer from about six of them at once.

We were ready to try 4 digit by one digit on paper.

*expand content*

I brought up a blank SB page and wrote a 4 digit by 1 digit division problem. I asked students to copy it down in their notebook. I called on one student and asked her to begin the division with an entry point that she was comfortable with and the fun began. They coached me through the whole problem. I couldn't believe how quickly they got it. I kept checking with three students who really struggle with division to help support them. Divide 4 Digit by 1 Digit

I took the opportunity to have them do the problem again and told them they couldn't pick 1000. The pages show that they picked 300 and continued to pick 300 until it wouldn't work anymore. One student raised his hand and chose 6 for the last quotient, producing 18. Students jumped at the chance to explain why that wouldn't work. We talked about why we wouldn't want a negative number in a division problem remainder.We corrected it to 4 and added the partial quotients arriving at the same quotient as the first problem. As this was being taught, they were taking notes in their math notebook to be used as their reference tool later.

We discussed the meaning of different starting points and why we could start with different numbers. I reiterated that they needed to find numbers they were comfortable with. I told them that they could use that quotient over and over until it wouldn't work, like we did in the second problem. As long as they were multiplying and subtracting correctly, they eventually would find the quotient.

It was good conversation about numbers and tapped into their prior knowledge to give them more confidence in solving larger digit numbers.

The homework would be more practice in helping to get closer to mastering 4.NBT.B.6.I talked again about how it is not a gimmick even though it is not the way their parents learned to divide. It supports understanding of place value and grouping. I reinforced the habit of using their notes. Good notes were essential in their ability to do their homework. I roved and checked notebooks before handing out homeowork.

#### Resources

*expand content*

#### Culminating Practice

*10 min*

Multiplicative Comparison Assignment 3.

This assignment combines multiplicative comparison word problems with lots of fraction words and 4 digit by one digit algorithms. *I did not differentiate this lesson because my pre -test showed that no one really knew how to divide.*We read the word problems aloud to ease the anxiety about being faced with more word problems. We discussed each one to decide if we would multiply or divide.

After we went over the assignment, I allowed them to get a good start on their homework with time to ask questions and ask for help.

*expand content*

##### Similar Lessons

Environment: Suburban

###### Shopping Comparison Problems

*Favorites(4)*

*Resources(44)*

Environment: Urban

Environment: Urban

- 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