Division w/ Remainders Unit: LAP 1€¦ · Division w/ Remainders Unit: LAP 1 Casey Rothenberg I. Content: Describe what it is you will teach. What is the content? This is the first

Clark University Master of Arts in Teaching Program Learning Activity Plan

Division w/ Remainders Unit: LAP 1 Casey Rothenberg

I. Content: Describe what it is you will teach. What is the content? This is the first lesson of the unit, so it will be dominated by laying the foundation of the unit as well as some basic review. In third grade students have gone over the basics of division, so this lesson will be a nice refresher and help solidify understandings. It is crucial for student to understand the importance of division and visualize a real life scenario where it is required. This lesson will focus mainly on going through a real life scenario where division is required and students must figure out the best way to split up the treats being passed out. Afterwards the lesson will highlight the relationship between division and multiplication, and how their processes are actually the opposite. Multiplication is achieved through repeated addition and division can be achieved through repeated subtraction. Finally, students will develop their vocabulary related to division, which will be appearing consistently throughout the unit. II. Learning Goal(s): Describe what specifically students will know and be able to do

after the experience of this class. Students will be able to:

• Comprehend what division looks like visually and in a real life example. • Understand that multiplication is repeated addition. • Understand that division is the opposite of multiplication. • Understand that division is repeated subtraction. • Identify and understand these division related words: division, divisor, dividend

and quotient. • Working efficiently and effectively as group, which involves listening and talking

to peers in respectful ways. III. Rationale: Explain how the content and learning goal(s) relate to your Curriculum

Unit Plan learning goals. Throughout the unit there is an emphasis on using division to solve actual problems that can occur in the real world. The ultimate goal of the unit is for students to help plan a trip to a region of the U.S. they have been studying. The trip will be a failure unless every student is able to solve the problems that occur when you are traveling. This lesson gives students a clear example of a real life problem that can be solved using division. Students will have an opportunity to solve the problem using their own methods and train of thought. Another overarching goal of the unit is for students to understand the relationship between division and multiplication. Everything in math is very interconnected and it is important for our students to understand these relationships, because this is what helps them conquer new mathematic equations. In this lesson students will be examining how multiplication (repeated addition) is the opposite of division (repeated subtraction). This


will be represented on the white board as well as physically dividing M&M’s between the students. Understanding vocabulary is crucial for the unit, lessons and the activities students will engage with. During this lesson students will develop an understanding of division related vocabulary words, as well as how they are visually represented. IV. Assessment: Describe how you and your students will know they have reached

your learning goals.

Throughout the lesson students will be informally assessed through my observations. I will be looking for student’s participation during whole group work, as well as general recognition and understanding as I proceed through the lesson. Students need to acknowledge that division can be achieved through repeated subtraction, so I will be looking to see if they understand this during the M&M activity. Students will be assessed on their understanding of how repeated subtraction is one strategy of solving a division problem. Completing a worksheet will allow students to convey their comprehension and abilities to apply this strategy. The worksheet highlighting division, as repeated subtraction will follow this template:


Student’s vocabulary cards will be an assessment of their understanding, and the most formal assessment of the lesson. In order to reach the learning goal students must create an independent card for the words: division, dividend, divisor and quotient. The word will be on the front and on the back will be the definition. On the back students also need to write a model equation, like provided in the visual, and then for each card they will highlight and label the word they are talking about. The visual model of our vocabulary cards will look like:

The definitions that students will be provided are: 1. Division: splitting a number into equal groups. 2. Dividend: the number that is being divided or shared. 3. Divisor: the number the dividend is being divided by. The number of ways something needs to be shared. 4. Quotient: the answer to a division problem. V. Personalization and equity: Describe how you will provide for individual student

strengths and needs. How will you and your lesson consider the needs of each student and scaffold learning? How specifically will ELL students and students with learning disabilities gain access and be supported?

Most of the lesson will be conducted in groups (whole class and small groups ranging from 4-5), which will help keep the variety of learners on a similar page of understanding. Mainly this will prevent students who might struggle in math (including ELL’s and students on IEP’s) from falling behind. Watching their peers grapple with the problem will help scaffold others understandings and abilities. If group work is conducted successfully, then the more mathematically advanced students will verbally and visually explain to struggling students what they are doing and why it works. Even if students still don’t comprehend how division works within their groups, they will have another opportunity to learn when we reconvene and discuss the strategies used at each


table. This will allow the teacher to put everything in simple and direct language that refers to the content. Creating vocabulary words will be a challenge for ELL’s, students on IEP’s, and students who struggle with writing in general. The words and definitions will be difficult for some students to mentally wrap their head around. Hopefully the visual representations will help provide some concrete area of understanding and allow students to recognize what each part of a division number problem means. The process of creating the cards will be modeled and clearly explained. I will briefly go over each definition and draw its representation on the board to get students thinking about the words, as well as modeling. There are a handful of students (Washington, Katianna, Dung, Irene) who I anticipate pulling aside and talking through each vocabulary card, while the rest of the class works independently. VI. Activity description and agenda

a. Describe the activities that will help your students understand the content of your class lesson by creating an agenda with time frames for your class. Be prepared to explain why you think each activity will help students on the path toward understanding.

Time Teacher will… Student will… Materials

15 min. -Announce to the class that I have brought in M&M’s for the whole class to share. Each table is going to get 20 M&M’s and they have to figure out how many each person gets if they are split up equally. After they have successfully divided the M&M’s they must come up with an explanation for how they solved the problem. -Reconvene as a class and discuss the different methods and explanations students used/had.

-Visually comprehend that there is a certain amount of M&M’s that need to be split up evenly between 22 students -Discuss with students at their table different ways of splitting the M&M’s up -Share out idea formulated at the table -Observe, ask question and make comments about how the strategy is working.

- M&M’s


15 min. -Explain that today just happens to be math opposite day! And that I want everyone to get more M&M’s so I am going to split up 110 M&M’s between the whole class. -Discuss multiplication and break down the process and highlight how it is simply repeated addition. -Now lets do the opposite, which is repeated subtraction. Ask students how I could use repeated subtraction to solve the problem about M&M’s? -Divide M&M’s using repeated subtraction and collect students thoughts on this method compared to our other methods that we tried.

-Listen, ask question and make comments about observations. -Listen and participate ideas about how multiplication is actually just repeated addition. -Think -Observe how division can be turned into repeated subtraction. -Provide ideas on how to use repeated subtraction to help divvy out treats.

- M&M’s

5 min -Introduce the idea that we

will be responsible for planning a trip to a landmark within a region they have been studying. (ex. Disney World, FL) -Explain that the planning will be done in a couple lessons and that we need to work on our division skills to become ready

-Understand that we are planning a pretend trip and that we have real life problems that need to be solved before we can go on our trip -Come up with ideas on destination -Vote on where the destination will be

45 min. Introduce the different centers:

1. Go over the vocabulary words with definitions and visual models. (I am at station) 2. Practicing division through repeated subtraction using

-Listen and ask questions during instructions -work independently and productive at each center

-Note cards -Definitions and visual model of: division, divisor, dividend and quotient. -five ipads (provided by Woodland Elementary)


worksheet. (Josh is at this station to introduce topic and instructions) 3. Practicing division on computers (xtramath) 4. Practicing division on Ipads.

-repeated subtraction worksheet

b. What particular challenges, in terms of student learning or implementing planned activity, do you anticipate and how will you address them?

The main challenge for students will be completing the vocabulary cards and generally understanding the information being covered. In following lessons students will practice using repeated subtraction as well as using the inverse of multiplication to solve division problems. These activities will ensure students understandings of the material being covered in this class. The vocabulary cards will be a time consuming task for some of our students. Students have had practice making vocabulary cards, so the process will be familiar. Also there will be extra time for students to finish completing their cards during extra-recess and literacy circles. VII. List the Massachusetts Learning Standards this lesson addresses. 4.NBT.B6 Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. VIII. Reflection

a. In light of all areas of planning, but especially in terms of your stated purpose and learning goals, in what ways was the activity(ies) successful? How do you know? In what ways was it not successful? How might the activity be planned differently another time?

b. What did you learn from the experience of this lesson that will inform your next LAP?

Leading up to the unit Josh and I had occasionally mentioned to the students that

we would learning about division, so most of the students had anticipated what I would be teaching them. Because of this there was some excitement when I introduced the topic and the gist of what we would be doing for the rest of the week during our math block. After discussing how today was ‘math opposite day’ and that we would be sharing M&M’s to celebrate I was able to obtain students attention and engagement. I started off by passing plastic bags filled with M&M’s out to each table and asking them to try and figure out a way to split them up evenly. In each bag was 20 M&M’s, and all except one of the tables had four students. I wasn’t completely sure how much knowledge


concerning division students had starting the unit, so a lot of the time I wasn’t sure what to expect. Three tables had one or two students that quickly realized the situation was asking to divide 20 by 4. Even though they recognized the number problem, I wanted them to really think about what the process of sharing looked like. I encouraged students to put the numbers into sentences that relate to the actual real world problem. Instead of saying the answer is five, I guided students to saying something like, ‘each student gets five pieces of M&M’s in order to split 20 evenly between four students’. Also, I made these tables give five to each student and see if they had any left or not. One table decided to solve the problem by divvying out the M&M’s one by one, which I think is a great way to visually represent the action of sharing. Afterwards we had a whole group discussion, where tables shared out their method and solutions and we talked about what strategies worked, what didn’t work, what was easier and what was more time consuming. Students seemed to comprehend that the process we just played out utilized division to solve a real life situation. They recognized that if one person had more M&M’s then that was unequal and something went wrong. Students copied down the definition of division, which helped solidify the notion that we are simply equally sharing. Going back to the ‘opposite day’ theme students, as a class we started dissecting multiplication, where I was able to solicit responses I was looking for by asking questions. Students highlighted how multiplication is simply repeated addition, and since division is the opposite of multiplication, they were able to guess that division could be repeated subtraction. As a group we figured out how to split up 110 M&M’s between the whole class using repeated subtraction. Afterwards we tried one more problem as a whole group and then students completed one on their own. In stations students were able to work effectively. By looking at student’s worksheets on repeated subtraction it was clear that most students were able to successfully use this method to find a quotient. Some students were able to find the quotient by recognizing the inverse. Only a small group of two-three students didn’t understand the directions and struggled finding an answer. One student successfully subtracted to zero, but was unable to acknowledge that every time they subtracted they added +1 to the quotient. I think that the vocabulary station was mostly productive but some students didn’t fully understand the relation between words and their definition/what they look like in a problem. The first group that came to this station I actually forgot to have them draw an example and label the different vocabulary words within the equation. Copying down the visual was very beneficial for students who got to, because it provided them a simple and clear way of referring back to their vocabulary cards and identifying the word they need to know. Throughout the unit students showed their understanding of the vocabulary words by using them appropriately within sentences and answering my questions about, “what that number is called?.” Overall I think time management was my biggest struggle, which resulted in some students not finishing their vocabulary cards. However, I anticipated this and understood there would be time in the next class to finish. Both the vocabulary cards and worksheet took students so long that they only a few were able to actually use ipads and computers, which worked out well because time on these devices can be unproductive and/or unrelated. Time could’ve been utilized better by knowing when to stop and move on, and being more prepared for transitions.



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Division w/ Remainders Unit: LAP 1€¦ · Division w/ Remainders Unit: LAP 1 Casey Rothenberg I. Content: Describe what it is you will teach. What is the content? This is the first