LESSON PLAN OUTLINE - Jaclyn Stultz's Online Portfolio
LESSON PLAN OUTLINEJaclyn StultzCindy Moyers – John Wayland Elementary School – 2nd gradeFebruary 20, 2013 at 1:15 PMWritten plan is submitted: February 13, 2013 JMU Elementary Education ProgramTITLE/TYPE OF LESSON“We’ve Bean Learning How to Regroup!”Addition and Subtraction Regrouping with ManipulativesCONTEXT OF LESSONThis lesson should be used as a concrete reasoning example of regrouping and borrowing, prior to using a number sentence, in order to give meaning to the process of regrouping and why it is used.CONCEPTS TO BE COVERED This lesson addresses addition and subtraction regrouping of two-digit numbers with concrete examples through the use of manipulatives.RELATED VIRGINIA STANDARDS OF LEARNINGComputation and EstimationFocus: Number Relationships and Operations2.6 The student, given two whole numbers whose sum is 99 or less, willb) find the sum, using various methods of calculation.2.7 The student, given two whole numbers, each of which is 99 or less, willb) find the difference, using various methods of calculation.2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.LESSON OBJECTIVESThe students will explain why and when we must regroup when adding some two digit numbers.The students will explain why and when we must regroup when subtracting some two digit numbers.The students will compare and contrast the way we solve addition problems, versus the way we solve subtraction problems.The students will demonstrate how to use manipulatives to solve word problems.The students will apply their techniques used with the manipulatives to solving problems on paper. ASSESSMENT OF LEARNINGTo assess objectives 1 & 2, I will have the students explain their processes for regrouping, and why it is necessary to regroup to get the correct answer.To assess objective number 3, I will have children identify the difference between borrowing a ten for subtraction, and adding a ten for addition. They will show this through their bean-stick manipulation. To assess objective number 4, the students will use the bean-stick manipulatives to solve word problems, and then use them to solve number sentence problems on their worksheet.To assess objective number nine, the students will use their new technique of bean-stick manipulatives to solve problems in a number sentence on a worksheet. This worksheet will act as their assessment for comprehension of the exercise.MATERIALS NEEDEDBean sticks of ten (25) - MeIndividual beans to act as “ones” - MeCopies of the ten’s frame place value chart (6) - MeCopies of the subtraction sheet (6) - MeCopies of the addition sheet (6) - MeWord problems (5-6) - MeWhite board and marker – Available in the classroomPencils – Students Number line – MeHundreds chart – MePROCEDURESBEFOREANTICIPATED STUDENT RESPONSESWhen I presented this lesson to my cooperating teacher the week before, she took to this idea of using manipulatives and a ten’s frame place value chart, so she has been using it with the students during the past week. They are some-what familiar with it, but the remedial group I am working with will still need extra guidance.To prepare the learning environment, I will set up each child’s space with a ten’s frame place value chart, five ten-bean sticks, and a handful of beans to represent the ones. I will not give them their worksheet yet, because I want them to initially focus on the methods I will be teaching them. To introduce the lesson, I will ask several questions to get their brains thinking about regrouping. This include, but are not limited to:“What have you been learning about in math?”“Who can tell me what addition means? When do we use addition?”“Who can tell me what subtraction means? When do we use subtraction?”“How many ones make up one ten?”“How do you know when you’re supposed to regroup?”“Can someone describe ways they solve addition regrouping problems?” “Can someone describe ways they solve subtraction regrouping problems?”-Regrouping-Addition and Subtraction-Addition is when you add two things together or put two numbers together to find how many you have in all.-Subtraction is when you take one amount from a bigger amount to get how many you have left over.-Ten ones make up one ten.-Teacher: Can you show me with you beans and bean stick?-You have to regroup in subtraction when there is a bigger number on the bottom than on the top in the ones place.-You have to regroup in addition when the answer in the ones place in greater than 9.-When you regroup with addition you have to carry a ten next door to add with the “ten men.”-When you regroup with subtraction you have to borrow a “ten men,” because if there is “more on the floor, you go next door.” DURINGFirst, I will present several word problems for the students. This is meant to help them get acquainted with the manipulatives. Mrs. Moyers has 16 crayons. Student (someone in the group) give her 5 more. How many crayons does Mrs. Moyers have now?“Will we add or subtract to solve this problem?”“What numbers are we adding?” “Ok, we will start with the bigger number on our chart. Can you show me how to represent this on your chart with your bean stick and beans?”After they attempt, I will show them on my chart and explain“We put sixteen first, because that’s how many crayons Mrs. Moyers already has.”I will show sixteen on my chart. “Next, we will add five more, because ‘student’ gave her five more crayons. So let’s add, one, two, three, four, five. Now we have one full ten frame, and one more left over. What do you think we should do with this filled up ten’s frame? I will exchange the ten ones for another ten stick, and then ask, “Now that we have all of our crayons, what will the answer be? How many crayons does Mrs. Moyers have now?’“Can someone tell me how to write the problem we just did?”I will write this problem on the white board. This shows the students that we can turn any word problem into a numerical problem, and neither is any more difficult than the other.I will present them with several other word problems, listed on the attached sheet, alternating between addition and subtraction and increasing with difficulty. I will continue to go through this exact method with the student until they are able to do the process on their own. If one student figures out the pattern/process before the other(s), I will have that student explain their work rather than me explaining the work. If both students understand I will have them each explain their process for solving one problem, and then I will move on to numeral addition problems from their worksheet. I will give them their addition worksheet, and have them write their name on top. We will practice these problems using the same process that we used for the word problems. I will direct them to look at problem number one, because it is the easiest, and I will write it on the white board. I will have them try it on their own as they did with the word problems, and then I will ask, “How did each of you solve this problem?”I will then say, “Now look at your worksheet. Does anyone see something that looks similar to our tens and ones chart next to problem number one?” I will then direct them to problem number two, and ask them to solve it using their beans and bean sticks first, and then check their answer by using the tens and ones next to the problem. I will ask each student what answer they got. If there are any discrepancies I will have the person who did not get the right answer talk their way through their problem aloud until we find the error. Then we will correct the error. After the second problem, I will have them put their addition sheet to the side and I will give them their subtraction sheet, and ask them to put their name on top. I will then direct them to look at the example problem. I will write the problem on the white board, and ask them to solve it with their beans and bean sticks. I will ask them their process and then explain what was shown on the example problem:“This person used the same technique that you have used by taking away tens and ones to get the answer. They just crossed them out instead to show that they took away. Count the amount that is crossed out” “See how the part that is crossed out, the part that they took away is the same as it is in the problem?” “Now you can count the remainder to see if it is the same as the answer this person got.” “Is it correct?”“Now I want you to solve problem number one just like this person solved theirs. I want you to cross out the correct number you are taking away, just like the example showed you, count up your answer, and then use your bean chart to check your answer and make sure you’re right.” I will then have one student explain how they used the worksheet to get their answer, and have another student explain how they used their bean chart to check their answer.-Add-16 and 5-They will show one ten stick and six single beans on the ones side.-We can trade these ten ones for one ten stick. 16+ 5 I will call on a student and have them explain their answer. If they do not count the ten sticks, “ten, twenty…” I will explain that option to them. I will also explain how it is much easier and faster to group by tens, and that’s why we exchange the ones for a ten stick. -I started with the ones and added 8 and 0, which is eight. Then I added the tens column, 2+1, and I got 3, so the answer is 30.-Hopefully they will realize that the photo of the tens and ones frame next to the problem is an exact replica of our beans and bean stick that we have been practicing with.-Some discrepancies may be that the children did not trade the ten stick for the proper amount of ones, giving them the wrong answer. They may also simply count out the wrong number of beans. They may also try to do subtraction, since we will be switching from addition to subtraction in order for them to pay attention to the correct operation.-I started by putting three tens and six ones to make 36. I only had six ones, but I had to take away seven so I had to borrow a ten stick and trade it in for ten ones. Then I could take away 7 ones and one ten-stick for the 17. I was left with 19 as my answer.-They will count 17 crossed out on their worksheet.- I don’t want to use that chart.-Yes-Yes, they got 19 and I got 19.-The students will use the tens and ones on the worksheet first, and then use their bean chart to check their answer.-Worksheet: I crossed off one ten and then two more ones to make 12 that I’m taking away. I have 16 left over.-Bean chart: I took away two beans for the two in the ones place, and then I took away one stick for the one in the tens place. I had 16 left over.AFTERAt this point if I feel that all the students are comfortable with the process, I will tell them, “Ok, now that you all are masters at regrouping, can someone tell me about what you have learned?” I will then tell them to complete the worksheets as I have taught them with the bean charts and the pictures next to the problems. As they are doing this I will watch their processes using my observation sheet and their answers as an assessment for the lesson. If any child is struggling or having issues I will be able to help him or her in whatever way necessary. When a child is complete with the worksheets they are excused to leave. -There are ten ones in one ten. -You have to trade one ten stick for ten ones when you are borrowing with subtraction.-You have to trade ten ones for one ten stick when adding if you fill up a whole frame.MODIFICATIONS FOR STUDENTS WITH SPECIAL NEEDS:CHALLENGE problem: For students that are ahead of the rest of the group, I would have a chart with hundreds, tens, and ones with manipulatives that do along with it. This student can solve problems with three digit numbers that regroup in the ones and the tens spot. The really exceptional student could even move up to the thousands. These students may even be ready to move on to the number sentences and skip the bean charts altogether. REMEDIAL problem: For remedial students, I will have them use the ten’s frame place value chart to solve problems without regrouping first. Once they get the hang of it, I will present them with problems that are simpler and only have one step and only have a single digit on the bottom, such as, 20-6. This way, they only have to worry about the ones that come from borrowing the ten from the 20, and they can subtract from that amount. This is easier than having 24-6, which requires two ten frames in the ones section. I chose for them to complete subtraction problems, because these are typically the more difficult problems that cause the most confusion. 283845205030-12 - 26 - 33 - 5 - 8 - 6WHAT COULD GO WRONG WITH THIS LESSON AND WHAT WILL YOU DO ABOUT IT?The students may not understand the concept of the ten’s frame place value chart, or how to convert those ideas onto paper when doing their worksheet.In this case, I think the student may just need more practice and one-on-one guidance. I could possibly work with that student later in the day, and help them to grasp the concept. If they still do not understand I could try using a different process such as a number line or hundreds chart.Since the beans will be glued onto the Popsicle stick, they may fall off; therefore, not representing a full ten.If this were to happen, I would simply exchange it for another. This is why I am making extra sticks, and extra copies of each sheet they will be using.We may run out of time before the students get through their whole worksheet, and/or lesson.If this were to happen, I do not have any worries that we will be able to come back to the lesson later in the day. Since this will be a small group activity, there is a lot more flexibility with scheduling.Other, more advanced students may try to get involved in the activity or feel left out, because they are not getting the chance to engage in it.If this happens, I will simply tell those students that if we have extra time I would be more than happy to show them how to use the bean sticks, or they can practice with them during recess if we have indoor recess.REFERENCES: The bean-stick idea and the ten’s frame place value chart came from Professor Wallace.Addition and subtraction worksheets came from:Fisher, Allyn. Blacklines Practice Book: Bridges in Mathematics 2. The Math Learning Center. Salem, OR. 2009.NCTM PROCESS STANDARDS:Problem Solving Instructional programs from prekindergarten through grade 12should enable all students to— Build new mathematical knowledge through problem solvingChildren are gaining new mathematical knowledge though giving meaning to regrouping through manipulatives.Solve problems that arise in mathematics and in other contextsChildren will learn how to solve word problems and number sentences with their bean-stick strategy.Apply and adapt a variety of appropriate strategies to solve problemsChildren will use a new strategy with the bean sticks and tens and ones chart.Monitor and reflect on the process of mathematical problem solvingI will monitor though observation and worksheet assessment problems.Regrouping Lesson Plan Observation FormNAMEDid student struggle or was the student successful?Could the student describe when to regroup when adding and subtracting?Worksheet assessmentAnything the student should specifically work on after lessonCalebEmeryCaitlynSarahWORD PROBLEMS:Addition:1. Mrs. Moyers has 16 crayons. Student (someone in the group) gives her 5 more. How many crayons does Mrs. Moyers have now?2. Student 1 has 26 socks in her top drawer. She as 12 socks in her bottom drawer. How many socks does she have in all?3. Student 1 spent 19 dollars on a shirt. He spent 18 more dollars on a hat. How much money did he spend in all?4. Student 1 and student 2 were making bracelets. Student 1 used 25 beads on her bracelet. Student 2 used 39 beads on his bracelet. How many beads did they use in all?Subtraction:1. Mrs. Moyers had 32 paper clips. She gave 16 of them to Miss. Stultz. How many paper clips does Mrs. Moyers have left?2. Student 1 baked 48 cookies. His dog ate 19 of them. How many are left?3. Student 1 saw 31 birds, 24 of them flew away. How many were left?4. Student 1 had 32 dollars. He spent 14 dollars on a shirt. How much money does he have left?Lesson Implementation ReflectionAs soon as possible after teaching your lesson, think about the experience. Use the questions/prompts below to guide your thinking. Be thorough in your reflection and use specific examples to support your insights.A. Based on your plan for assessing learning and the data you collected, evaluate the success of the lesson. Be thorough in your description. Cite multiple examples of student behavior and language that document your conclusions.Look at the assessment data and identify 2 students who appear to fall into these 3 categories: (1) Gets it; (2) Has some good ideas, but there’s still room for learning and (3) Does not get it. Organize your responses to the following questions in a chart/table form similar to the one below.Gets itHas some good ideas, but…Does not get itStudent AStudent BStudent CStudent DStudent EStudent Fa. Understands…When to regroup when adding and subtracting and the process of using the manipulatives.How to use the manipulatives to regroup when adding and subtracting.This student understands how to do the procedures with the manipulatives and when and why to regroup and “trade” a ten for ten ones.n/aHow do regroup the old-fashioned procedural way.n/ab. Confused about…Using the pictures on the subtraction worksheet to check his answers.Nothing.Taking each problem step by step and following the whole problem through. She gets very distracted and then loses her place in the process.n/aThe purpose of using the maps to solve the problem. She wanted to do the math in her head but kept getting the wrong answer.n/ac. Questions to ask to clarify what I knowI would ask him what the first and last things to do when solving a problem are (Checking the sign and checking your work). On problems 3, 4, 5, and 6 on the addition worksheet and problems 3, 5, and 6 on the subtraction worksheet this student had to change his answers due to careless mistakes.I would also have this student check her work to make sure she got the right answer. Careless mistakes were the only things that kept her from getting the right answers. She was a quick worker and was able to work ahead of her peers.I would work through the problems with this student in order to help her focus, and I would have her explain each step to me as she did it until she got the correct answer.n/aI would have her use the mat to check all her answers, and when she got the right answer using the mat she would begin to realize that the math in her head was incorrect.n/ad. Ideas to work on nextBeing able to solve the problems mentally using the same concepts used with the manipulatives.I worked with this student during indoor recess on three digit addition and subtraction problems, so I think that those type problems with one step regrouping would be good for this student to try on her own.I would perhaps make a step by step guide to help this student stay on track. I think once she learns how to focus she will be able to master this procedure. She knows the steps and how to do it; she just cannot do it herself without guidance, because she gets distracted.n/aThis student really needs to work on having a positive attitude toward the activity and trying to do it rather than just not wanting to. She also needs to focus on checking the signs first and taking her time on the problem.n/aB. How did your actual teaching of the lesson differ from your plans? Describe the changes and explain why you made them. Be thorough and specific in your descriptions.The main difference between my lesson plans and the actual lesson was the size of the groups. When I planned the lesson, my cooperating teacher and I had initially decided that I would work in small groups to do this lesson. When it came time for me to do the lesson, however, she asked that I work one-on-one with the struggling students. My lesson was also pushed to the very end of the day, so I was only able to do a full lesson with one student (student A) and half of the lesson with another student (student C) before they went home for the day. My teacher asked that I work with struggling students the following week as well, so I was able to work with student C again, as well as students B and E. When I worked with these students, she gave me worksheets that the other students in the class were doing, and this is why I do not have record of this work from these students. During this lesson, the three students all worked with me at the same time in a small group. I feel as though this was much less successful than working one-on-one with a student, because they kept looking at the others’ sheets and copying the answers that the others called aloud. They were also very off task, and this is why students C and E had trouble focusing.C. Based on this experience, what changes would you make if you were to present this activity again? Why? Cite at least one way you could incorporate developmentally appropriate practice in a better or more through way.If I were to do this activity again, I would try to plan to do it over a longer period of time and be able to work with all the students individually for a longer period of time. It would be much easier to do this lesson and achieve the results I was looking for if I was in the classroom every day. Spacing it out over a few weeks was very difficult to work with the struggling students and make the difference in their learning how I would have liked. If this was my classroom, and I had more time to do this lesson, I would have loved to include a whole group discussion after I worked with all the struggling students. This whole group discussion would allow all the students to work on the same problem and compare their answers. It would also give those struggling learners a chance to shine and show off that they, too, know how to get the right answers; thus, giving them confidence in their abilities.I also would have loved to work with more students, and for a longer period of time, but this just wasn’t possible with the agenda that my cooperating teacher had for the students. D. What did you learn from this experience about children, teaching, and yourself?Children: I definitely learned that each child learns differently in a different setting. The difference between the first lesson (individually) and the second lesson (small group) was like night and day. I really think that those who struggle with concepts really need that extra attention and in depth explanation. I also learned that it is very important to teach children this method of regrouping, because it is totally different from the “old-fashioned” procedural method. This method shows the students why you have to regroup, and it gives them a constructivist, hands-on example of why we have to regroup. I noticed that children often do not realize that they cannot subtract a large number from a smaller number, and they just mentally reverse the order of which is on top and which is on bottom, and subtract them anyway. This hands-on method with the beans makes them physically see that they cannot take 7 from 2 because they do not have that many to take away unless they regroup.Teaching: I definitely learned that time management is most important. Some children take longer than others to complete the same task, so leaving enough time for students to complete the whole lesson in order to gain full understanding is crucial. I also learned that children learn in many different ways. Some children get very distracted and need that extra attention. This focus and help is crucial for them to gain an understanding of the concepts, and sometimes one-on-one help is the only thing that can help. I did realize, however, that children understand concepts that you do not think they do, they many simply need some extra guidance to get the information out of them.Myself: I learned that I am more capable of helping students than I thought I was. Even though this lesson didn’t really go exactly as planned, I feel as though I made a difference with the students I worked with, and it gave me a lot of confidence in my teaching abilities. I was very afraid that I would not be able to explain this procedure in a way that the students would understand, but I feel as though it went very well. The students definitely seemed to respond well to my lesson. I was also very happy that I could introduce this way of teaching regrouping to my cooperating teacher, because she had never heard of it before and she really liked it. She said that she noticed a difference in the students’ response to regrouping and she really liked this method. ................
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