Abby McClureGretchen Buhrke

Mathematics and Literacy Lesson 2DIFFERNTIATED LESSON

Division

Mathematic Objectives: CORE STANDARD: 5.2.1:Solve problems involving multiplication and division of any whole numbers.

*Students will understand double unit division (two digit divisors, 2-3 digit dividend, use of remainders) by thinking of division as backward multiplication and real world practice problems.

Literature: A Remainder of One (Pinczes, E. J. (1995). A remainder of one. New York,

NY: Scholastic Inc.) We chose this book for our lesson because we see it as a tool that students can use to see division in a way that can be manipulated. Students can act out the lesson and physically be the army that is marching or the students can use beans to make the lines. We decided that this book could be a fun way to be introduced to a tougher subject. Division is a more complicated process for students to learn, especially when adding the remainders. We hope that this book can be an introduction that will make the process more simplistic as they learn it.

Grade Levels: 5th grade

Materials Needed: Remainder of One by Elinor J. PinczesBeansWorksheet (Cindy’s Candy Shop)PencilClipboard to write onWhite board and markers

CONTEXT: Demographics for Central Elementary School:Grade 5 Percent Passing ISTEP+ Math Standard: 58%Grade 5 Percent Passing ISTEP+ Language Arts Standard: 50%Ethnicity 2009-2010White: 14%Black: 59%Hispanic: 16%Multi-racial: 7%Asian: 3%

I believe that my lessons challenge students in a way that will help them succeed and do their best in their work. When looking at the ISTEP scores, I take into account that

students need special attention when working in math and language arts, but I make my lessons interactive and hands-on. I give students the opportunity to be challenged and work to their full potential. For this lesson in particular, I worked to make this lesson more beneficial to how the group of students learn. I put them in a smaller group and gave them individualized attention. By doing this, I attended to their needs and could answer their questions right away. Our lesson also focused on strategies they can use on a test; grouping and drawing out the problem helps focus their attention and understands division much better.

DIFFERENTIATION: For our follow-up lesson we will have a group of six low ability students that we will work with. We will adapt the lesson we have already done previously with the whole class. We decided to use the same lesson because the content can be easily adapted to benefit the students that need more individualized attention. Of our six students, two have classified learning disabilities (LD) along with an Individualized Education Plans (IEP); another is in the process of being tested for a LD; the other; the remaining three are considered in the lower ability because they did not pass their ISTEP+ in their 4th grade year and have scored low on tests throughout the semester.

Colin: Colin is autistic, and Mrs. Hazelwood has told us that the school special education teacher believe he may have Asperger’s Syndrome. Asperger’s is generally more of a mild form of autism; children who are classified with Asperger’s do not generally have the language or cognitive delays; their major impairments involve social interactions. According to his IEP, Colin goes to the special education teacher for tests and can have problems read aloud as needed.

Lamaya: Lamaya has an IEP that says she goes to the special education teacher for tests and can have problems read aloud as needed.

Raven: Raven is a phenomenal reader and a strong student in language arts. She is on a 9th grade reading level and her writing is also above grade level. Mrs. Hazelwood is working to get her tested for an IEP in mathematics because she has been falling behind since the beginning of the school year. Mrs. Hazelwood has put her in small groups and even worked one on one with her, but she still struggles to grasp even the basic concepts. This lesson will help her identify different strategies to take when solving multiplication problems.

Gabriel: Gabriel has an Individual Language Plan (ILP). I have actually never heard of this before, but Mrs. Hazelwood explained the Gabriel was only in America for first grade; he was born and spent the rest of the time in Senegal. French is the national language, but Gabriel spoke more slang French. I have worked with him before, and he is a good student, but sometimes is a bit slow in responses. His ILP gives him more time on tests and allows the questions on tests to be read aloud to him.

Farrell and Michael: These students have problems with knowing their basic facts and number operations. I (Abby) have personally worked with all both of these students and they all work very hard when in small groups, but without a grasp on their basic knowledge, they make small errors that mess them up in the answer to the problem. This lesson will help them slowly learn and understand the process of division.

Enhancing Student Learning:

For all the students, especially Colin, we made the groups small with two of us working with all the students. This way, there is no overload of people but enough people for the students to interact with. We will also structure the lesson by giving clear instructions, establishing patterns, being consistent, and increasing independence. We will also make sure to be repetitive in our lesson to be sure that students can see the message that is linked to what the students are doing, which is multi-digit division with remainders.

Some of the adaptations made in this lesson include input, difficulty, and participation.

o With input, we adapted the way instruction is delivered by re-reading through “Remainder of One” and using the beans with the book, as well as adding a completely new part of the lesson with the assessment and practice of Cindy’s Candy Shop.

o For difficulty, we adapted the problem type so that when the learner approaches the work, they have a better chance at understanding the concept. We did this by continuing to use five’s to divide by with remainders for the worksheet but also did practice problems to go further into other numbers

o We adapted participation by changing the extent to which a learner is actively involved in the task. We partnered students and had them work together to be involved with the lesson, and Gretchen and I worked closely with the pairs to give them the individual help and attention.

We will keep our original lesson plan but designate our differentiation by putting ***

Lesson Procedures:

1. We will begin the lesson with asking students what they already know about division and having them think about what they will be learning. Earlier in the day, the students learned math terms such as dividend and divisor. Gretchen and I will also ask about having a remainder. We will ask students what they think it means in math, and why it is important. We will ask students to think, pair, and share when reviewing/introducing new math problems.

a. ***Since students are in a small group, we will review the basics of division by looking at their notes they were given earlier in the day about division. We will give them 5 division problems that we will do on white boards using our basic division notes we have.***

2. After review, we will have the students sit on their desks. We will begin to read the book “Remainder of One. For each page, we will have students get up in the lines that are marched out. By having students get up and walk around, they are getting to physically see the lines and remainders or each problem.

a. After the students are lined up, we will pause to look at our lines. How many lines did we divide evenly into? How many were left over? I will write down the problem on the chart as we go.

i. Ex: We have 25 people in groups of three, and there are 8 lines of people with one left over.

1. We have 25 peoplewrite dividend2. We are in groups of threewrite the problem on the board3. After the students count the 8 lines with remainder of one,

finish the problemb. We will repeat this step for the entire book.

i. ***We will read the books but use the beans to make the lines. We want the students to have the visual of the page as well as the beans as we go back through the book. We will still stop after the pages and discuss what is in our lines, how many we have left, and how many remain. We will record this in our math journals to see how it changes throughout book. We will record the number of rows, how many it was divided by, and the drawing of our beans. (Repetition: reading the book over again and using the beans as a manipulative) ***

3. After the book, we will discuss remainder of one. “Why are there remainders? / How do we get remainders?” Using a worksheet Mrs.Hazelwood provided, we will do the first set of problems together.

a. First, we will read through the problem. We will ask the students to use their word problem solving skills to go through solving the problem. First, what is the problem asking us to do? We will use the overhead to show the students how we are separating the beans into the equal parts and the reminders we have left over. We will also write the division problem like previously on the board. We will also ask the students to draw their groups of beans on their paper so they may be able to look back on how they solved the problemw.

b. We will do the first three problems as stated above, and once we are on the back of the sheet, we will have students read the problem and do it on their own before we go over it all together.

i. ***We are still using a worksheet, but this worksheet also has manipulative. The students are workers at a factory, and they will be given different bags with a certain number of “candy pieces” in it. The bags will each have a number on them, 1-6. In each bag, there will be a different number of candies in them. We will explain to the students that the candies need to be divided into their smaller bags for selling: Each smaller bag can hold 5 candies. The students will separate and record their answers. We will have students work in partners to do this. Gretchen will help Lamaya and Raven/Michael and Gabriel while I work with Colin and Farrell. We will work closely with the groups to go through the worksheet. Gretchen and I will be modeling how to go through these “shipments” before they actually do it themselves, giving

them clear directions and letting them know the procedure. We are also showing them how we expect them to go through the sheet. When they receive a “shipment bag”, the students will empty the contents and count how many total candies there are and record. Then, the students will divide them into groups of 5. Students will write how many are grouped evenly and then how many remain. The next step is “draw it and solve it”: students will draw their “smaller bags” and then show the problem as a division problem. We will repeat this process for the rest of the bags. (Messages linked with activities: students will get even more individualized attention by putting them in partners; students are also using an example they can all relate to—candy! We are establishing patterns and being consistent with the same problems with different numbers for our practice). We picked 5 because this is a number students know their basic facts on. Their practice problems for homework and with Mrs. Hazelwood will explore other numbers.***

4. Mrs. Hazelhood asked us to give practice problems as homework to the class. We also want students to think of their own example of a division problem. If students can make up their own problems, they can fully explain their thinking on how they think this problem works and the solution.

a. ***We will end the session this same way. We will ask the students to work in their teams to come up with their own division story problem. The students just got finished with learning about word problem solving strategies, and this would be great practice for they just finished studying combined with the new.

i. I got the idea of making up their own question from the strategy “Say it, Play it, Relay it, Weigh It” (Attached to lesson). This strategy is used for special education students in the classroom that need stimulating activities and constant involvement in the classroom. “Create a Question” is under “Play It” and is great for small group processing. Students can come up with their own problems to challenge the other students with and be proud of their work! ***

Assessment: A pre-assessment will be given at the beginning to see how much the students remember from division in 4th grade and to stimulate their thinking on the upcoming lesson. We will keep the pre-assessment simple by having students think, pair, and share about the terms we use when dividing whole numbers. We are also assessing students throughout the process of learning how to divide by numbers that are uneven by doing the first three problems together and having the students draw on their paper their beans of grouping with each problem. Assessing the students in this lesson is important because learning division with remainders is a complicated process for students to understand. Mrs. Hazelwood’s class worked very hard on multiplication, but they are still struggling with their basic facts. Division is using these basic facts to solve the problems, and bringing in the remainder aspect can be even harder for the students. We want to

make sure that our assessments help us estimate how the students are doing and if they understand as we go along.

A description of when you would use the lessons/ activities in relation to the selected mathematics basal textbook: This lesson will replace the basal textbook lesson because the way the book explains it gives students no chance of using manipulative or really seeing. The book lesson gives problems that can be helpful, but there is not other help really besides that. There is a special section that shows how to use a calculator and divide. That could be added on to a lesson, but first we want students to have an understanding of the basic steps of division.

A reflective analysis of your learning in relation to this assignment: We are using ideas that we have discussed in class. We are using the book Remainder of One and adding our different spin on the lesson from help with our classroom teacher (Demonstrate knowledge of and identify and select curriculum materials and professional resources appropriate for specific content and instructional goals [ElEd Dev Stds #1-6: Elem Gen Stds 4]). We understand that division is a complicated process for students to learn, and the more activities and operation sense we use, the better the students can begin to understand. Students can memorize facts easily, but if they can readily understand how division works, they will have an actual understanding of the process of division. This not only helps them knowing multiplication facts but also strategies they may be able to use on standardized testing. When developing this lesson, we thought it would be best to give students the chance to physically see how they can manipulate division. Using the book was our aid in this endeavor. Readers Theater was a great way to present the lesson and allow students to be almost in charge of the lessons. As fellow students read the book, the other students had to figure out how they could evenly make their lines with the amount of people they had (Demonstrate knowledge of instructional strategies appropriate for specific content and for a diversity of student needs. [ElEd Dev Stds #1-6: Elem Gen Stds 4]). Our evaluation of the students understanding was using the beans and going through the problems. Once again, students were able to use the beans and examples as a manipulative to see what division means.

What went well: This lesson was great. I like working in the small groups, and special education is a field I would like to enter so it was great practice and professional development for me. Like all teachers, we had to adapt to what was going on with our students and think quickly on our feet when our lesson may not have gone as planned. We were actually taking them out of the classroom during the time that the students were supposed to be taking notes on division, so we just went through step-by-step how we Colin was feeling queasy and sick, but he wanted so badly to participate in our lesson. I finally got him to go to the nurse’s office with a promise that I would work with him in the afternoon; luckily, he made it to the nurse’s office just in time to get very sick. We had to adapt our lesson without Colin. The students did pretty well with re-reading the book and using the beans! Revisiting this helped make division click; they even remembered how the rest of the book went. Then, we paired off to do the worksheet. I went with Gabriel and Lamaya while Gretchen went with the other group. I quickly

found out that Gabriel and Lamaya do not get along well. Lamaya would not share the bag with him and he would get annoyed quickly with her acting like this. To try to solve the problem, I told them we would all be on a team—myself included. This seemed to work a bit better. The students really enjoyed the worksheet! I think it started to click for them because they would open the bag and start by dividing them by five right away. My group had a great discussion involving what it would be like to have to package candy like that. Gabriel asked me what they do with the left over candy. We decided at the end, we would see if we could package anymore from the remainders! Unfortunately, we ran out of time and could not finish it. The students were not all there later in the day, so we did not get to finish the sheet.

What I learned: Working in this small group with the students was challenging but also rewarding. I liked how I could easily ask them questions and hear all their thoughts; sometimes in a bigger classroom or group, I feel as though this is difficult to give everyone a chance always. We also were individualizing our attention on their needs that I could tell helped. Repeating ourselves, and asking them direct questions they could answer helped them understand it. For example, we would ask them to take us through the “steps” of division and do what they said. If they would ask us if it was right, we would ask them what they were unsure about—why were they questioning their steps?

I also learned that I really enjoy working with special needs students. I love working with all children, but they really did try so hard for me in everything they were doing. I feel like the extra effort put forth to make the lesson better for them to understand encourages me to push not only them but also myself. I still hold them to high standards and expect them to succeed; I want them to hold me accountable for what I am teaching them as well. I felt as though we were al comfortable with each other and that the students trusted me. Lamaya and I had a moment where she was telling me about one of the problems, and she second-guessed herself when I did not immediately say she was right. I asked her why she thought she was wrong, and she told me she did not want me to think she was stupid. After the lesson, I pulled her aside and told her my history with math. I told her no one, especially me, thinks she stupid. I am here to help her understand better. I asked her if there was anything I could do to help her more. She smiled, and told me that no one had ever asked her that. She said she gets distracted by all the people in class and enjoys working with us in the hallway. On Wednesday, we are going to talk about strategies and ideas that she can use when she feels overwhelmed or stressed on a test. Even knowing that I have impacted one student makes me feel like I can really do this—I can be a teacher. It is the best feeling.

These two pictures are reading the Remainder of One book and working on sorting our beans out like the lines in the book. “Hup, two, three, four…”

Above is Gabriel working on the worksheet that we did (Cindy’s Candy Shop). Beside him is our “candy”! Below is Lamaya and I looking at what our division problem would look like for that shipment number!

This is a great tool to use for learners with diverse needs. There are many great ideas to use in different situations encountered in the classroom.

Name: _______________________________

Cindy’s Candy Shop needs your help! They just received 6 shipments of candy that needs to be packaged into smaller bags for selling! Each bag can hold 5 pieces of candy. For each shipment (bags 1-6), we need to figure out how many smaller bags we need! Can you help?Shipment Bag number:Total candies:Number of smaller bags that can be packaged:Leftover:

Draw it and solve it:

Shipment Bag number:Total candies:Number of smaller bags that can be packaged:Leftover:

Draw it and solve it:

Shipment Bag number:Total candies:Number of smaller bags that can be packaged:Leftover:

Draw it and solve it:Shipment Bag number:Total candies:Number of smaller bags that can be packaged:Leftover:

Draw it and solve it:

Shipment Bag number:Total candies:Number of smaller bags that can be packaged:Leftover:

Draw it and solve it:

Shipment Bag number:Total candies:Number of smaller bags that can be packaged:Leftover:

Draw it and solve it: