division w/ remainders unit: lap 3 · find whole number quotients and remainders with up to...

Clark University Master of Arts in Teaching Program Learning Activity Plan

Division w/ Remainders Unit: LAP 3 Casey Rothenberg

I. Content: Describe what it is you will teach. What is the content? This is the first lesson where the students will be introduced to remainders and start working with division problems that don’t have an equal quotient. Remainders can be a tricky topic and something that doesn’t seem straightforward at first. Therefore it is important for students have visuals and real life examples to provide a foundation for comprehension. After allowing students time to develop independent thoughts about what a remainder is, the whole class will read a book about remainders. Students will participate in an activity that resembles the story and has students finding remainders for different scenarios. Finally, the class will break into centers where students will either: continue developing skills with remainders, continue practicing the array model they learned the class or create two new vocabulary cards. The vocabulary being taught has to do with the definition of a remainder, and various words related to division problems that students might encounter in future word problems. 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:

• Identify what a remainder is and understand its meaning within a division problem.

• Find remainders in division problems with two digit dividends and one-two digit divisors.

• Use a pre-determined array to visually find how many even groups can be made and how many are left over.

• Work effectively in groups of two, which includes collaborating, agreeing and disagreeing.

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

Unit Plan learning goals. In the real world division is constantly used to help solve big and small problems. However, often there are times where even groups cannot be created, and there is a certain amount left over. It is important for my students to learn what happens in these various scenarios and how they can still solve these problems. A goal of my unit is to have students become comfortable dealing with remainders, and developing the ability to properly interpret a remainder based on the context. In order to think deeply about what should happen with a remainder, students must first be able to actually find a remainder and understand its relationship to the division problem. Everything cant be divided evenly, so students must be comfortable in these situations and know how to solve the problems, find the quotient and then find what is left over.


In this lesson, almost all of the problems derive from some possible real life situation. This is crucial for students as they begin developing their understanding and skills with remainders. Seeing how remainders would naturally appear in an every day situation not only enforces the importance of the learning, but also grounds the concept in a tangible manner. Students will be working with problems that relate back to our over arching fake field trip to Florida and Disney World. IV. Assessment: Describe how you and your students will know they have reached

your learning goals. Throughout the lesson students will be assessed on their abilities to solve a division problem and find a remainder, if necessary. During our whole group lesson students will be working in pairs to solve problems related to how many snacks each person gets on the trip down to Disney World in Florida. There are three different levels of difficulty. For each number of friends sharing oranges, students need a visual representation of all the plates needed and how many oranges end up on each plate. Each pair will be given a problem that looks like: The trip down to Florida will take a very long time, so it is crucial that we travel prepared with snacks, like Florida oranges! However, I have not decided what type of vehicle we will be driving, so I am not sure how many students will be in each vehicle. It is your job to sort out the plates if I bring (22, 35 or 75) oranges. If there are: 2 friends: _____ oranges each with _____ leftover 3 friends: _____ oranges each with _____ leftover 4 friends: _____ oranges each with _____ leftover (group 1) 5 friends: _____ oranges each with _____ leftover 6 friends: _____ oranges each with _____ leftover 2 friends: _____ oranges each with _____ leftover 3 friends: _____ oranges each with _____ leftover 5 friends: _____ oranges each with _____ leftover (group 2) 6 friends: _____ oranges each with _____ leftover 9 friends: _____ oranges each with _____ leftover 2 friends: _____ oranges each with _____ leftover 5 friends: _____ oranges each with _____ leftover 7 friends: _____ oranges each with _____ leftover (group 3) 12 friends: _____ oranges each with _____ leftover 22 friends: _____ oranges each with _____ leftover During centers students will have an opportunity to keep working with division problems that involve remainders. However, this worksheet is very visual and should be accessible for every student. Ability to complete the worksheet will help me assess student’s abilities to visually find a remainder using pre-constructed arrays. The worksheet where


students are finding remainders using visuals will look like:

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?

Throughout this lesson there are a variety of adjustments that make the material accessible for a variety of students needs. Different group work will help scaffold understanding for students who need more time, practice and wording to grasp a concept. During the introduction discussion students will be thinking the problem through and discussing possible methods and solutions. This is a great opportunity for the quiet students to observe the thought process of other students who may have a stronger math understanding and vocabulary. Bringing literature into math class is extremely beneficial, especially for students who need time to think through concepts in different ways and situations. Some students can observe a rule/strategy and be able to replicate it within a couple practices. Other students will different needs might need to look at one concept from a couple different angles, and I think that a read a loud that directly addresses remainders is a perfect opportunity to provide this alternative angle.


Later on in the lesson students will be working in groups to solve problems relating to the story, which will provide a nice background. Students will be working in groups of two, and each set of partners will be strategically set up. Grouping is based on student’s general math abilities, which will prevent one student from doing all the work. However, in order to make sure every group is being engaged but also challenged, the problems are adjusted to three different levels of difficulty. All students will be doing the same work and using the same procedures to solve a division problem and find what’s left over. The only difference is that students who have a harder time with math will be dealing with smaller and easier numbers. The stronger mathematicians in the class will be given problems with larger numbers that require more problem solving. During centers, Josh and I will be at two of the stations to help guide students and answer any questions. One of the worksheets during centers will involve lots of visual representations of what a remainder actually looks like. This will be helpful for ELL’s and students who struggle with language. 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 5-7 min.

-Ask the class what 38 ÷ 5? -Write the problem on the board, and ask the class to solve the problem using models, pictures, numbers and/or words to solve. -After reconvene as a class and discuss what students did and if it makes sense or not.

-Listen and ask appropriate questions. -Participate thoughts on what to do if you cant split up dividend into equal amount of groups.

10 min. -Read Bean Thirteen -Listen and ask questions. -Think about what bean thirteen represents. -Think of ways to split up bean thirteen.

25 min. -Break students into pairs. -Instruct students that they will be replicating a similar scenario from Bean Thirteen, except what they will be doing is going to help us divvy out snacks on our trip to Disney World. -Introduce the question and

-Listen to directions and ask appropriate questions. -Work with partner to first use the dividend to create equal groups, which is the quotient. Understanding if there is a left over that cant be

-Dividing up oranges worksheet. Includes remainders.


model on the board how many oranges each student gets if there are 18 oranges being split between 5 students. Show using array that involves ‘plates’. -Students will be given a variety of manipulatives to help solve their problems. (go to assessment to see the different problems.)

broken into groups equally and labeling this the left over.

50 min. Stations: 1) Solving division

problems with remainders using the worksheet that uses visuals. (Josh)

2) Practicing using the array model to solve division problems with NO remainders. (I will be at this center to provide problems and assistance)

3) Creating two new vocabulary cards following the models provided at that station. One for remainder and one titled: division key words. For the latter, students will write down: how much/many will each have, divided among, split up between, per, each, share, equally.

4) Once students finish their worksheets and vocabulary cards they can practice division on iPads or computers (xtramath)

-Create a new vocabulary card for the word: remainder. -Create a new vocabulary card that highlights all the words associated with division word problems. -Complete worksheet that has students dissect arrays to find a quotient and remainder. -Practice solving division problems with two-three digit dividends using the array model.

-Worksheet using visuals to find quotients and remainders. -Five iPads provided by Woodland Academy -Classroom computers -Two vocabulary cards for each student. (44 in total)


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

I anticipate that students might struggle working effectively in partners and continue working the whole time. Students definitely struggle working together in an appropriate and valuable way. Often one student will take a back seat as the other does most of the hard work. Or students will disagree and/or not get along, which leads to quarreling and minimal work getting accomplished. Thankfully there are two teachers in the room who can walk around answering questions, asking questions and generally keeping students on track. Also, hopefully the strategic grouping will keep students respectful and on task. 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?

Overall I thought this lesson went pretty well. Students were a little unsure of how

to approach the original problem of 38 divided by 5. They understood that something was wrong when we evenly most of the dividend, but then had a number left over that couldn’t be split up equally into five groups. A couple students recognized that we needed to create a fraction. After drawing different visuals and talking through a couple options, students knew that we had found our quotient but still had some left over. I introduced the word remainder, and designated our left over’s to be called a remainder.

Even though Bean Thirteen is geared more towards a 2nd and 3rd grade level, my students were engaged throughout the entire read a loud. Most of the quickly picked up on the fact that bean thirteen would always be a left over, which gave them an opportunity to practice using the word remainder.

As we solved problems as a whole class, before splitting off into pairs, students copied down the different equations. During this process students were able to effectively duplicate the visual representations we were creating as a whole class. These visuals really help students understand the notion of having something left over, and that a certain amount cannot be split up equally into the groups we created.


During group work I was pleasantly surprised at how comfortable and complaint students were with the partners they were designated. The read aloud, the connection to our field trip and the mystery of the new concept all worked together to maintain students engagement. Almost all of the groups stayed on task and worked effectively during the whole activity. Most students struggled briefly in the beginning and had a hard time deciphering the quotient and what is left over. However, through either problem solving with their partner or receiving some assistance from Josh or I, most groups were able to adequately solve the different problems and find the correct quotient and remainder. Even for the groups that were struggling, it mostly only took one reminder or pointer in the right direction for them to get on track. There was one group in particular who thought they were solving the problems correctly but were actually overlooking some crucial steps and self-checks. Unfortunately I was unable to meet with the group and only realized their struggles after I collected everyone’s work. It seems they ignored the fact that the amount in each group cant exceed the dividend. In multiple instances their quotient was too high, and would need a larger dividend to make the equation equal. In order to recognize their errors, the students should’ve been checking their work by multiplying their quotient by the divisor and then adding the left over’s to see if they reach the dividend. If I teach this lesson again, I might require students to double-check their answers using multiplication. Also I could have students check in with a teacher after solving two or three of the problems, in order to make sure they are on the right track.

During centers students did an awesome job finding quotients using arrays. This was a perfect and easy opportunity for students to practice working with remainders by using visuals to represent what a particular division problem actually looks like. Every student was able to successfully split up the arrays into equal groups and then find what is left over. Some students struggled on question number eight, because making the group of three required them to create an odd looking circle/shape.

Before breaking off into centers I took time to quickly and clearly explain what students would be doing at each center. I also strategically had the group’s starts at particular centers, which allowed me to adjust the time I spent with each group, depending on ability, and not worry if some student’s didn’t receive that much personalized attention.

division w/ remainders unit: lap 3 · find whole number quotients and remainders with up to...

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