Lesson Plan Doubles Subtraction.doc.docx



FRAMEWORK FOR PLANNING A PROBLEM SOLVING LESSON in MATHEMATICS Name: Chelsea Tamietti, Olivia HagertyLesson Title: Using doubles to subtractGrade Level: 1st Big Idea:What strategies can I use to subtract? Subtracting with doubles facts. Instructional Objectives: Relate doubles addition facts to subtraction facts. Students should be able to find the sum of an addition doubles fact to help them find the difference to a subtraction doubles fact. Students will understand the inverse of adding doubles will give you a related subtraction doubles fact. Arizona and Common Core Math Standards Addressed:Common Core Standards:Domain: Operations and Algebraic ThinkingStandard: 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums. The TASK: Choosing TasksThink about what makes a good problem or task, and how well the problem or task will engage students in the important mathematical ideas you want to address in the lesson. For example, for each task, think about numbers, context, and problem structures, and say why you are choosing the numbers, contexts, and problem structures you decide upon. TASK(S):The task if for students to learn how to use doubles in subtraction. Students will use doubles 6-10 for this lesson, so they should have a previous knowledge of these facts. Numbers and problems were all what the book required other than the extension activity. That was focused on the students favorite doubles facts.Teacher will pose the strategy to students and they will get an opportunity to work with doubles on their white boards. Then teacher will then pass out manipulatives (counting cubes) for students to use to work through the doubles facts and doubles subtraction facts. Then students will be turned on their own to work out of their book and work on the doubles subtraction problems.After that, if time is allotted, students will work on other doubles facts on their own and as a class they will discuss how the student solved the fact. WHY:Why these numbers:These numbers are what are given in the curriculum book, but I also have students choose their favorite so they are more interested in the materials. Why this problem context (setting or objects in problem):The setting is where the students usually are for math (carpet then seats) and the objects in the problem were both student interest and also what the book required. Why this problem structure (what mathematical information is given and what is unknown):Students know how to subtract, and they know doubles, but this is another strategy to help them subtract in different/easier ways. ANTICIPATED STUDENT RESPONSES: Students’ ThinkingList many different ideas for how students might respond to your task. For each idea explain why students might think that and how you might respond to challenge or extend their thinking.Students may not understand the strategy so teacher might need to word the problems or pose the problems in a different way. Students might not have a grasp on their doubles facts so teacher might have to help them remember those, maybe have students write them on their paper to refer back to. Students might think it is too easy and become bored, so teacher will need to give them higher level thinking numbers, and allow them to have time to work on bigger numbers. Vocabulary and Language ObjectivesState the key mathematical vocabulary to be used in the lesson, including vocabulary in students’ native language, if appropriate. If an ELD classroom, state the language objective for the lesson.DoublesSubtractionStrategiesAdditionPart, whole Materials & ToolsConsider the following questions about tools (e.g., manipulatives, oganizers): How do the tools I use in the lesson act as learning supports? Do the tools make the topic easier for the students to understand? Do I offer a variety of tools for students to use? Description of the Mathematics Tools you will have available for students:Whiteboards, markers and erasersConnecting cubes (10 ec.)Student math bookCurriculum PowerPoint Public CriteriaConsider and state the key rules and expectations you need to make clear to students before you start the lesson. For example, rules for using materials, for working in groups, etc.When students use whiteboards they are for writing math facts not drawing.When they are asked to stop they need to hold their writing utensil in the air, put it under their shoe, or put their hands on their head.Students need to raise their hand before answering a question.When students are given connecting cubes, they are tools not toys so they should use them to solve the problems not to play with.When they work with a buddy to solve the problem, they need to be respectful of their peers. 3 PART LESSON PLAN 1) BEFORE: IntroductionConsider and State how you will: Transition students into the lesson (Before Before).Introduce the task. You might introduce the problem through a story book, a picture, a question, simply by discussing the context and getting students to talk about it, or something else. Get the students ready. Here you need to find out what students already know about the topic / task, and help get them ‘ready’ to work on the task. You might begin with an easier version of the same task. You might have them brainstorm ways of solving the task. Or something else.Pose the task. Make sure all students understand what the task is asking.Include SPECIFIC QUESTIONS that you will ask students during this part of the lesson. YOUR PLAN for what teacher and students will do and WHY:Introduce the task: Students have been working on different ways to subtract for a few weeks now, so they have previous knowledge of strategies for subtracting. To begin the lesson, teacher will say that they will be working with doubles (like in addition) but they will use them to subtract. Teacher will review the doubles facts with the students to refresh their minds.Get the students ready: Students should already have an understanding for subtraction because we have been doing it for a while and they should have an understanding for doubles facts because we worked with them many times with addition.Pose the task: “Today we will be working on how to subtract using doubles facts. We have already worked with doubles using addition, but today we will be working on how to subtract using those same doubles facts. How can you rearrange the numbers in an addition doubles fact to make a subtraction sentence?” 2) DURING: ExploringConsider and State how you will:Find out about students’ thinking. What will you be listening and looking for, what strategies do you expect to see?Support students’ thinking when needed – hints, suggestions, questions to get students moving on the task, or to help students who are struggling.Encourage students to test out their own ideas.Support diverse groups of learners.Pose questions that help students extend their thinking by looking for patterns, considering multiple solutions, explaining their reasoning and thinking, etc.Include SPECIFIC QUESTIONS that you will ask students during this part of the lesson. YOUR PLAN for what teacher and students will do and WHY:Find out about students’ thinking. Are students using proper vocabulary; part, part, whole, doubles, subtraction. Are they using the strategy (doubles) to subtract or are they using a different strategy. Do students understand that the task is to take an addition double fact such as 7+7=14 and simply rearrange the numbers to get the subtraction problem. The whole first minus a part equals the other part,14-7=7. I expect to see this strategy, but also counting down with fingers and using cubes to subtract as well.Support students’ thinking Teacher will provide students with white boards to help them work through the problems, she will also allow them to use cubes in order to help them work through the problems. Teacher will phrase the problems in many ways so that it is easily understood, so part plus part equals whole, whole minus a part equals the last part, bigger number always going first (all for doubles). If students are understanding how to work through the problems, ask them how they know, or what they did to get the answer so that their peers can hear it from other peers and continue their learning. Teacher will allow time for students to work on numbers that they prefer whether larger or smaller than 6-10 doubles. Allow for students to work though problems in the way they understand, even if it isn’t this exact strategy, students need to have a grasp on subtraction and doubles before this strategy would be beneficial. 3) AFTER: SummarizingConsider how you will:Facilitate a class discussion and a sharing of students’ strategies. Think about how and where students will share, how many will share, and how you will choose those students.Encourage dialogue and debate among students. Think about how the class will determine whether a solution is correct or incorrect. Think about how to extend the children’s thinking.Summarize the important mathematical ideas. Consider how you will draw students’ attention to the big mathematical concepts. Make sure you define here what those important mathematical ideas are.Include SPECIFIC QUESTIONS that you will ask students during this part of the lesson.Transition students from the lesson to the next activity (After After). YOUR PLAN for what teacher and students will do and WHY:Facilitate a class discussion and a sharing of students’ strategies. Students will be able to share with their peers how to work through the work book problems while at their desks if they are having trouble. In Chelsea’s class students worked together on the carpet to come up with other doubles subtraction facts, then talk about how they solved them and how they knew how to solve them. In Olivia’s class the students were given white boards, markers, and unifix cubes to help solve the problems. The students wrote as many doubles facts as they could without solving them and then switched boards with their partner for the partner to solve. The students also came up to the Smartboard to solve other problems and if there were incorrect answers we discussed as a class and let the student come back up to the board and correct his/her answer. Encourage dialogue and debate To decide whether the problem is correct or not students will show thumbs up if they agree or thumbs down if they disagree with the student after answering the question. If students say yes, have them explain why and how they figured it out, and if students say no, ask them to explain why and how they figured it out.Summarize the important mathematical ideas. Doubles subtraction facts are the same as doubles addition facts they are just written in a different order (bigger number first). Doubles facts are where the two parts are the same number so for example 7+7=14. This strategy can be used with any doubles facts. Why do you put the bigger number first? If you start with the whole and take a part away, what is left? How do you know that 14-7=7? How did you figure it out? ASSESSMENTHow will you assess what students learned?Students have a math work book that they have worksheets that correlate with the lesson of the day. Teacher will check as the students go for understanding. If students are able to solely use doubles to subtract, and aren’t using another strategy such as fingers or counting down, then they understand the concept. Chelsea also had students come up with other doubles facts at the end of the lesson and asked students how they solved them and how they knew how to solve them to check for understanding. Olivia also walked around the room while the students were working on their white boards to see if they were writing and solving the doubles facts correctly. Olivia had the students show their answers by holding up their white boards and by holding up their unifix cubes. ACCOMMODATIONSSelect TWO groups of students (e.g., English Language Learners, inclusion students) and describe how you will adapt the lesson, as appropriate, to meet their needs. For students with an IEP in Chelsea’s class, teacher will limit the number of problems from the worksheet and also provided them with lower doubles facts to work with such as 1+1 or 2+2, etc. They will also be encouraged to use the unifix cubes for extra help. For ELL students Olivia will encourage working with the unifix cubes while working in the workbook for a visual representation of the numbers. For the English language learners, there are pictures on the PowerPoint, there is a short video that describes the task, and they will be provided with counting cubes and white boards to work though the problems. EXTENSIONS UP AND DOWNDescribe how you could adapt the task (i.e., task structure, context, and/or numbers) for students who struggle with the mathematics (extensions down) and for students who are ready for an additional challenge (extensions up).For students who are above the task, allow them to use higher doubles numbers, and allow them to explore and come up with those numbers themselves. Say if a student wanted to do 500+500 allow them the time to explore those higher doubles facts. For students who are struggling or for extensions down, provide lower numbers other than 6+6, maybe do 3+3. Also, help them to use the blocks to help them work through the problems. For the students struggling another option would be to make sure that they are using their unifix cubes to visual represent the problem so that they can see easier what is happening when they do the addition and subtraction. Summary of Lesson This lesson of subtraction using doubles was about using a different strategy in order to subtract. Students have already worked with doubles using addition, so they have a previous knowledge of doubles. They have also worked with the terminology of part, part, whole. Students will be given both addition and subtraction problems all revolved around doubles 6-10. They will also be given the addition doubles fact and the subtraction doubles fact so it creates a visual and may help them work through the problems. For example, 4+4 is given, students solve, then next to it is 8-4 and students solve.We added some tools to help the students, and we also took a lot of the content out of the lesson that was provided in the book’s lesson that we didn’t think was necessary. The program that our school follows includes a PowerPoint for each lesson. We decided to take out a lot of the parts that were review or activities that seemed confusing. We did this so we could focus on helping them learn the new strategy. We added the use of slates, markers and counting cubes to help the visual learners work though the problems with physical materials. Chelsea also did an activity to extend the students learning, that wasn’t part of the lesson. Chelsea and Olivia had both planned it to give the higher thinkers and even the lower thinkers an opportunity to use higher doubles facts or lower doubles facts that were easier to understand. Chelsea had students come up with their favorite doubles fact and she wrote it on the board. When all the students were done with their book work, the class came together and talked about how the students solved the problem, and how they knew how to solve the problem.Reflection of Lesson- ChelseaOverall, I felt that my lesson went pretty well. After watching it several of times though, I noticed a lot that I didn’t do well or that I would have liked to do differently. I think that I should have started with the doubles video to get the students ready for the lesson instead of just starting. It was fine the way I did it and the students did well, and we did review all the doubles facts, but I think it would have made in more entertaining for the students. The students are used to coming in from recess and getting started right away though, so I did what they were used to, but it wasn’t the most fun way to transition. Also I was extremely nervous because it was my first time teaching a formal lesson in the class, and I was being videotaped, so it made the process a little more nerve racking. Thankfully though, I prepared plenty before doing the lesson. I went over it with Olivia then with my mentor teacher, then I made note cards and went over it multiple times by myself, I was ready, but once the camera started I got nervous.Once we got started, I became a little less nervous, and the students responded to me very well. Most of them were focused and on task and were following along, but there were some that were very lost. This was what I struggled with the most because I didn’t know how to address their behavior while teaching and being recorded. I felt terrible putting them on the back burner, but I have never seen my mentor teacher address it, so I didn’t know what she usually does either. I also struggled because this lesson was very boring. I was bored learning it and there is only so many ways to make a lesson exciting if you have to follow what the curriculum book says. I tried to have different components for the students to use and different materials, and I think that helped, but unfortunately I don’t feel like that was enough. Thankfully my students still did amazing, and a lot of them understood and could do the task very quickly.I think that the good parts of my lesson were that the students were paying attention and were focused and engaged for the most part. I also think it was good that we included multiple aspects to the lesson, slates, counting cubes, a video, group work and individual work, because I think all of these helped the students in one way or another. I think I did okay with the lesson delivery, it wasn’t as strong as it good have been, but it also wasn’t terrible. I think that I could have responded better to the students responses and answers to my questions. The students also learned the strategy very quickly which was nice on my part. I was very impressed with them because even though I’m not their full time teacher, the treated me with respect and gave me their attention as if it was my mentor teacher teaching. This made my job a lot easier.As far as the modifications that we made went, I felt that my students did well with the ones I provided, but I would have liked to provide more for them. Olivia and I wanted to do another extension that would be using the students’ interests in one way or another, but unfortunately there wasn’t enough time for that. Also, some of the modifications we made were already being used by our mentor teachers, so we maybe should have veered away from using similar teaching tools to using something different to see how the students would do.Reflection of Lesson- OliviaAt first I was very nervous to teach this math lesson, but it went much better than I thought it would. Before sitting down with Chelsea to plan I was worried about the lesson being boring for the students and I wanted to think of a way to change the lesson to make it less boring. Everyday the students learn math the same way, in front of the Smartboard. The students usually do not get to use manipulatives, so I thought it would be a good idea to bring manipulatives into the lesson. Chelsea and I agreed that we wanted the children to use unifix cubes and white boards to help them with their understanding of the lesson. We also wanted the children to use these manipulatives so that we could see their learning better.After watching the video over and over again I definitely have some critiques for myself and for the lesson in general. I look and sound bored teaching the lesson which means that if I am bored then the students must be bored. The amount of the lesson that involved the Smartboard is something that I should have modified more. If I could have done this lesson in a completely different way I would have. I think that the unifix cube work and the work on the white boards was really good and that children were working together and collaborating. I wish that I had done more of this, but that is a lesson learned!It was very cool to see children working on the white boards with their partners and totally getting the concept. It was also great to see the children working with the unifix cubes and putting them together and taking them apart based on the number sentence. I wish that I had given more time for the children to work on the subtraction part of the lesson, but it seemed as though they needed more work with addition doubles facts before they could move on. They had some unifix cube work with subtraction and then workbook work and this is something I definitely would have changed. I used a lot of the lesson up with whiteboards initially so if I had more time I would have had the students come back together and work with their partners to write subtraction facts and solve them together. Overall I think the lesson went well but it was definitely a learning experience and I know what I can do better next time! Children’s Mathematical ThinkingThe students learned and practiced more of their addition doubles facts and began the process of learning that those double facts can be related to subtraction. We know that the students learned this information because we were able to see them writing the problems on whiteboards, holding up their unifix cubes, and later working in their workbooks. We also know that the students learned the information from their responses to the questions that we asked as a whole group or by the responses they wrote on the smart board. The data that we have to prove that the students learned what we hoped they would is the video recording its self, but more importantly the children’s work on the whiteboard with partners, the unifix cube work with the whole class, and the workbook work later. Choosing to use visuals and manipulatives is also supported in our textbook with the quote, “Many children find doubles easier to grasp than other facts. However all children, and especially children with disabilities, can benefit from using and creating picture cards for each of the doubles” (Van de Walle 162). If we had children in our classes that would have required picture cards then we would have used them as another manipulative. We think what helped the students understand the subtraction using doubles facts was the review of doubles facts. In addition to the review we think that using the unifix cubes was very helpful for the students. We also watched the students interactions with each other and with the manipulatives and this was the best way to see how the students were doing. As our textbook states, “As a teacher watches and/or listens to a child explain a solution, what the child is doing with the tool increases the teacher’s knowledge of what is going on in the child’s head” (Carpenter 91), and if the tool is working for the students or not. Also, to be able to see the physical representation of the number sentences helped a lot of the students. We supported students thinking by reviewing the addition facts and by scaffolding the work with the unifix cubes. When we asked the children to work with the unifix cubes we did an example in front of the class for the students to see how the addition doubles facts could be related to subtraction. We also reminded the students of our work with part-part-whole. This work let them see that when we use the addition doubles facts to help with subtraction we are using the same numbers just in a different order. Olivia’s class had a hard time understanding the concept of subtracting using doubles. After reading the quote in our textbook, “Subtraction facts prove to be more difficult than addition. This is especially true when children have been taught subtraction through a ‘count-count-count’ approach; for 13-5, count 13, count off 5, count whats left” (Van de Walle 163), Olivia was put at ease that her students had a harder time with the subtraction part of the lesson. The students definitely needed more than this one lesson to understand the relationship between addition doubles and subtraction. Olivia thought that this concept was hard because it was getting the students to extend their thinking to relate a concept they had just learned to a brand new concept. Olivia also thinks that it was hard because subtraction often is a harder concept for the students to understand. For Chelsea’s class, they had a bit of an easier time. Many of the students right away understood that when using the doubles to subtract all you really are doing is rearranging the numbers. Like Olivia’s class they have previous knowledge of subtraction, but what helped Chelsea’s class was that the students were able to make the connection that the bigger number comes first, like in subtraction. They also then saw, that if you take the whole and take away a part, the second of the part is left (doubles facts such as 6+6=12). Some of Chelsea’s students had a difficult time, but most of them could implement the strategy right after they learned it.The children gained a better understanding of what addition doubles facts are as well. The children also deepened their understanding for subtracting (bigger number first). The children were beginning to see the connection between addition doubles facts and using that knowledge to subtract. The children also learned that unifix cubes can be a great resource for helping them solve subtraction and see the relationship between doubles facts addition and subtraction. These are the examples that we have to show what the children learned. Support Children’s ThinkingWe supported students learning by giving them manipulatives to express their learning in a more hands on way. We also supported students learning by asking questions and leading discussions. The unifix cubes were very helpful for some children and the white boards were helpful for others. Most of the children liked the white boards better than the unfix cubes but I think that is because they are not used to using white boards during math so it was new and exciting for them. The white boards were a little distracting for some of the students after we had finished writing and solving the addition doubles facts on them. During the other parts of the lesson that were focused on the smart board and the unfix cubes some children were still playing and writing on the white boards.The students that were the most engaged were the students that were using all the manipulatives, answering the questions on the Smartboard, and were able to vocalize an understanding of what doubles facts were and vocalize the number sentences presented with their appropriate answers. The students who were not engaged were the students who are normally not as engaged as others during the lessons. The students who were not using the manipulatives as much as the other students were not as vocal about answering questions. I think that these children were not engaged because they were distracted by the new manipulatives and because they are the students that normally have a harder time focusing. For the most part though all of the students were pretty engaged. The students all worked really well together when they were in their partner groups and we think that they were having good discussion. Extent Your ThinkingThere were a lot of features from our lesson that we weren’t very pleased with. First off, there was only so many modifications that we could make. With our program you have to stick to what the book says so you are meeting the targets. You can do adjusting within the lesson, but there was only so much “extra” time that we had to do more interesting math activities. This lesson was pretty boring as well. When looking back at our videos, it felt so unnatural teaching because it was how the book wanted the lesson to go. This was disappointing, but the students overall did very well. Some seemed to pick up the concept pretty quickly, and some struggled, but those students in particular have a hard time in general with how fast the math program moves. We tried to add in fun activities for the students, and we wish we could have done more if time allotted, but unfortunately we weren’t able to expand the lesson.If we were to do this lesson again, we would have had an activity that was fun for the students, so for example doing like a matching game with doubles, or using dominoes to work with the doubles. The students did well with the lesson, but I think it could have been more interesting and maybe helped the students who were struggling more if we gave them an opportunity to informally work with the doubles. We also would have provided more opportunities for the more advanced students to work with bigger numbers, and a lower extension activity for the students who were struggling. We would do this to make it more exciting and interesting, but also more developmentally appropriate. ................
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