Sumner, Josie

TASK 3

Sumner, JosieMissouri Pre-Service Teacher Assessment (MoPTA)

Missouri State Lesson Plan Form**based on Eric Jensen’s Teaching with the Brain in Mind 2nd Edition, Jensen’s 10 Minute Lesson Plan http://www.10minutelessonplans.com ,

revised: csfairbairn2014

Teacher Candidate: Josie Sumner Date: 9/15/14

Main Subject: Mathematics Grade: 4 If MoPTA, Task # 3

Desired End Point Essential Question (overarching content question) What is the relationship between multiples and factors of a whole number?

Describe the Evidence of Learning CAS and/or GLE CCSS.Math.Content.4.OA.B.4Recognize that a whole number is a multiple of each of its factors.

Learning Goal/s and Objective/s What students will know and what the students will do appropriate for meeting curricular and student needsLG - The student will know that a whole number is a multiple of each of its factors.OBJ- Using the anchor chart and 100s Chart Investigation, the student will be able to identify multiples of the whole numbers 3, 4, and 5 by answering 2 out of 3 answers correctly on a multiple choice quiz.Personal Teaching Goal - My personal teaching goal for this lesson is to manage student behavior, and also to structure the lesson appropriately through guided instruction and scaffolding in order to help students clearly understand related math skills.

Assessment Tools How student learning will be evaluated including a self-assessment

ITEMS COLLECTED CRITERIA FOR MEASUREMENT OBJECTIVE ASSESSMENT IS ALIGNED TO FEEDBACK

100s Chart Investigation Followed directions, answered questions correctly

CCSS.Math.Content.4.OA.B.4 Going over answers to the investigation

Post-Assessment Answered at least 2 out of 3 questions correctly

CCSS.Math.Content.4.OA.B.4 Graded and handed back with comments and suggestions for improvement and practice

Teacher Content Knowledge and Common Student Misunderstandings What the teacher needs to know to instruct the lessonFactors:

- A number you skip count by to reach a certain number- Number or numbers you multiply to get a certain number- Building blocks- Finite (limited)- Ex) Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Multiples:- Skip counting by a number- The product- Doubling, tripling, etc… a number- Building- Infinite (unlimited)- Ex) Multiples of 24: 24, 48, 72, 96, 120

The common multiples of 3 and 4 are: 12, 24, 36, 48, 60, 72, 84, 96The common multiples of 3 and 5 are: 15, 30, 45, 60, 75, 90The common multiples of 4 and 5 are: 20, 40, 60, 80, 100The common multiple of 3, 4, and 5 is: 60The next number after 100 that is a multiple of 3, 4, and 5 is: 120

Prior Knowledge Needed Previous content being built upon and how prior knowledge will be determinedOver the last two weeks, the students have been learning about factors of whole numbers, arrays, along with prime and composite numbers. All of these ideas will be built upon while I teach about multiples, especially in the anchor chart discussion where factors and multiples will be juxtaposed and contrasted.

Resources and Materials Materials needed in the planning and instruction of the lessonPost-its, Chart Paper, SMART Board, 100s Chart & 100s Chart Investigation worksheet, Blue, red, and yellow writing utensils, Pencil, Post-Assessment “Are You a Multiple Master?”

Technology Technology incorporated into the lesson to enhance instruction and student learningSMART Board Interactive Activity

Key Academic Language Language needed for understanding and what students will do with language (words/phrases) to express understandingFactors, Prime, Composite, Multiples, Skip Counting, Product, and Infinite

Levels of Questioning Strategies DOK level and descriptionLevel 1: List the multiples of 3, 4, and 5.Level 2: Compare and contrast the components of factors and multiples.Level 4: Connect multiples of several whole numbers to recognize patterns.

Sumner, JosieClassroom Management and Safety Strategies Student behavior needs to help keep students on task and actively engaged

- Recall Strategies: Teacher- “Yo!” Students- “What’s up?”/Teacher- “Nixa” Students- Eagles- Teacher- “All eyes on me and I’ll know that you’re ready”- For transitions, I plan to give instructions for the next step and then play music on the SMART Board, giving them until the music stops

to get where they need to be. Also, I will make sure that every student is on task and right where they need to be before I continue the lesson plan at any point in time.

- For voice volume control, I will use a scale of 0-5 and explain to the students that their voices should be at a 0 (silent) during the pre- and post-assessments, and a 1 while they work with their partner on the 100s Chart Investigation.

Enrichment Activities for early finishers that extend students’ understanding and thinkingI will have early finishers extend their 100s Chart Investigation, and I will provide them with a list of other whole numbers that they can shade in the multiples of on their 100s chart while they wait for most of the other students to finish up. I would prefer all of the students to have completed the 100s Chart Investigation before we move on to the next piece of the lesson.

BEFORE Preparation of Learners: Differentiation/Accommodations/Modifications Learner needs (including low and high), learning differences, cultural and language differences, etc.One way that I will accommodate to different learning abilities is by pairing students together to work on exploring multiples together, because two heads are better than one. Also for students who are at a little bit higher of a learning level will be provided with a longer list of whole numbers to explore the multiples of. Since the 4th grade team at my school rotates students at math time separating out the low, middle, and high level learners among the three teachers, I will be working with the lowest level and will most likely be dealing with a lot of students with the same capabilities.

Opening/Housekeeping - Optimal Environment Teacher approach to helping students achieve the learning objectives and meet their needs including seating arrangement, grouping criteria, lighting, music, supplies etc.The white board and SMART Board are placed at the front of the room, which is where I will have the students sit in front of during the anchor chart and SMART Board activity. The student desks are placed in table teams, which allows students to effectively interact with one another during collaborative activities. During the 100s Chart Investigation, I will allow students to disperse throughout the room and work on the floor with their partner if they choose to do so because they have been able to manage that in the past. DURING

Buy-In and Discovery of Prior Knowledge Pose Essential Question; Engagement – getting learners vested emotionally creating a positive social climate; Frame – the invitation to learn/set-up/background by activating prior knowledge and hooking the learners mentallyFrame – the invitation to learn/set-up/background by activating prior knowledge and hooking the learners mentallyFor my pre-assessment of student prior knowledge, I will hand each student a post-it note and up on the board I will write, “List the first five multiples of 3 (after 3)” and give them a couple minutes to answer the question to the best of their ability. Then I will have them post their answers up on the board and sit quietly at the carpe before the next part of the lesson.

New Content Explored Explore/Explain - Sequence of events of lesson elements and learning activities in order for students to acquire knowledge; include differentiation strategies for focus studentsNext, I will create an anchor T- chart with the class showing the differences between factors and multiples, but also discussing the connection between the two elements. Through this discussion, students will hopefully be able to build upon prior knowledge of what factors are and prepare their minds to explore multiples of given whole numbers. After the T-chart, we will begin the SMART Board activity. Several students will be called up to the board, one at a time. Each page will have a new question that will be: “Which of these whole numbers are multiples of ___?” and about 6-7 whole numbers will be dispersed throughout the page. The correct answers will fade once they are dragged and dropped into the center object of the screen, and incorrect answers will bounce back. This will serve as an activity that will check students’ understanding of what they just learned. Content/Skill Processing Activities Elaboration - Deepen learning through extension of content with active processing/collaborative practice with peers or teacher)The students will then be split off into partners to work on the 100s Chart Investigation. Each student will get their own 100s chart, and each student pair will get 1 copy of the 100s Chart Investigation. The students will be given time to complete this assignment with their partners. After all of the students have completed this assignment, we will go over the answers as a class.

Assessment and Error Correction Evaluation - Trial-and-error time with feedback and more active processing/practice with peers or teacherI will hand out a post-assessment worksheet titled, “Are You a Multiple Master?” which the students will fill out at the end of this lesson. There will be 3 questions total, and they will be expected to get at least 2 of them correct. The assessment questions will directly correlate with the study of multiples of 3, 4, and 5. After collecting the post-assessments, I will grade them and provide feedback with comments and suggestions written on their papers.

AFTER Consolidation - Encoding and Transfer Memory Strengthening through real world connection to other content, processes, self and through rehearsing/incorporating/applying building on the learning to increase understanding

Whenever a person counts groups of things, such as counting by weeks (7 days) or counting egg cartons (12 eggs), they are using multiples. Multiples are also very closely related to factors and using arrays, which will be reinforced throughout the lesson so students will be able to strengthen their memories by making those connections.

Closure Students articulate Essential Question; what was learned and what is coming up nextAt the end of the lesson, I will call upon one student and ask what we learned about multiples during math time, hoping they will state back what we discussed on the anchor T-chart.

Highlight all that apply (addressing learning styles, multiple intelligences, and brain compatible strategies used) Kagan structure graphic organizer technology visuals manipulatives brainstorming/discussion game experiment Blocks strategy problem solving global awareness career seeds music/rhythm/rhyme writing drawing/artwork vocalizations multicultural link movement mnemonic device differentiations

Sumner, Josie

Modification PlanFocus Student 1:

In order to differentiate and accommodate my lesson plan for Focus Student 1, I must first examine his strengths and challenges. By being mindful of these factors, I will be able to support the Focus Student with supplemental instruction where he needs it, and also work with skills he has mastered to help him achieve success.

One of Focus Student 1’s strengths is that he rarely guesses an answer, but works hard through all of the strategies he has been taught in order to find the best possible answer for math problems. Another one of his strengths is that he always shows his work and his thinking down on paper whenever being presented with a math equation, which is helpful for him and the teacher to see exactly what areas he may need more assistance in, or the areas that he has mastered. Focus Student 1 also excels when working with others on math equations, because he is given the chance to explain and justify his thinking process. Focus Student 1’s last strength is that he is one of the better students in the class at his multiplication times tables, which will play a significant role in understanding multiples and factors.

One of Focus Student 1’s weaknesses is that he was placed in the lowest level math class of the 4th grade, showing some frustration in this area overall. Another one of Focus Student 1’s weaknesses is that he has shown difficulty while skip-counting, which would come in handy while learning about multiples.

My lesson will be modified in order to accommodate some of Focus Student 1’s learning needs. For example, I will be teaching several methods or strategies in finding certain multiples and allow the students to decide which one suits them best. Another way I will cater my lesson to Focus Student 1 is by providing him with more opportunities to skip count numbers. While practicing with a 100s chart, I will go beyond the given numbers to skip-count by (3, 4, and 5) and instruct him to continue with 6, 8 and 10 in order to give him a visual representation of any patterns he may come across that will help strengthen his memory and number sense. One last way I will differentiate my lesson plan will be by allowing the students time to work with partners during the independent practice, which will support his learning by giving him the chance to explain his thinking to others and reaching a common consensus on an answer before moving on.

Sumner, Josie

Modification PlanFocus Student 2:

In order to differentiate and accommodate my lesson plan for Focus Student 2, I must first examine his strengths and challenges. By being mindful of these factors, I will be able to support the Focus Student with supplemental instruction where he needs it, and also work with skills he has mastered to help him achieve success.

One of Focus Student 2’s strengths is that he is great at making connections when it comes to math, which is related to the learning goal because he will need to understand how multiples and factors go hand in hand. Another one of Focus Student 2’s strengths is that he has shown to be a very hard-worker, and even though he is pulled out for several IEPs throughout the day, he still manages to jump into whole class instruction and hold himself accountable to the work we do while he is present. This is an important strength for the lesson because teaching multiples will be a new concept for most of the students and may be hard to understand, so it will take a little extra brain power to succeed by the end of the lesson and demonstrate progress.

One of Focus Student 2’s weaknesses is that he also was placed in the lowest level math class of the 4th grade, showing some of the same frustration as Focus Student 1 in this area overall. Another one of the Focus Student’s weaknesses is that he often continues onto the next problem while working independently, without checking whether his last answer was correct or not. Focus Student 2’s last weakness is that he is one of the more struggling students in the class when it comes to his multiplication facts, which will be very important when finding some of the larger multiples.

I plan to differentiate my lesson plan to support Focus Student 2 by having him work with a partner during the independent practice piece in order to hold him accountable to obtaining the best possible answers. I will also be visiting him frequently during this time, checking for understanding and asking probing questions in order to get him going in the right direction if he seems to be having trouble. Since one of his strengths is in making connections, I think it will be important to have conversations with him about the multiples he finds and any patterns he may put together. Also, since he seems to have a little more trouble with his multiplication facts, I plan to engage him in the guided discussion at the beginning of the lesson, asking him about how factors can produce multiples, using specific examples to make sure he is following along.

Sumner, Josie

Teacher Instructional Artifact:

Sumner, Josie

Student Work Sample from the Instruction:

Sumner, Josie

Student Work Sample for Focus Student 1:

Sumner, Josie

Student Work Sample for Focus Student 2:

Sumner, Josie

MISSOURI PRE-SERVICE TEACHER ASSESSMENT

TASK THREE (25,500 characters max – no more than 8 pages)The content focus must be Mathematics if an Elementary Teacher Candidate.

Please note that I have added “objectives” to those prompts that ask about learning goals, so that teacher candidates get more specific instead of global in responses.

Directions: Type answers under each prompt and undo the “bold” print on the answer.

Textbox 3.0: Contextual Information

Guiding Promptsa) Describe your classroom. Include the grade level, content area, subject matter, and number of students. Provide relevant information about any of your students with special needs.My student teaching takes place in a 4th grade classroom, the content area will be mathematics, the subject matter will be factoring, and there are 23 students. The 4th grade team all got together at the beginning of the school year, created a math test, and gave it to all of the 4th graders in all 3 of the classrooms in order to gather data on the students’ math comprehension. After collecting and analyzing the data, they separated all of the students into a high level math class, a mid-level math class, and a low level math class, each taught by a different teacher. Although my teacher is in charge of the mid-level math class, I go to the teacher who teaches the low level learners because they need the most attention, and I will learn the most by working with them every day. Some of these students are pulled out for IEPs at different points of math instruction, so there are times that only 17-20 students are in attendance.

b) Describe any physical, social, behavioral, and developmental factors that may impact the instruction that occurs in your classroom. Mention any linguistic, cultural, and health considerations that may also impact teaching and learning.Since these students are lower level learners, I have noticed that the majority of them are a little behind in social and developmental aspects as well. For example, when working in groups or pairs, there is sometimes conflict and distraction. Also, behavior problems tend to occur more often in this classroom than the others for many reasons, but mainly because these students get the most frustrated with the material and it causes them to find ways to get off task. The school year is still new, so the teachers are still learning where specifically all the students are academically and how to accommodate to them best, so everything is trial and error and subject to change.

c) Describe any factors related to the school and surrounding community that may impact the teaching and learning that occurs in your classroom.One factor related to the school that may impact the teaching and learning that occurs in my classroom is the fact that the students are pretty fluent in the use of iPads because they have had a year of experience with it in the 3rd grade, so the teachers utilize them quite often for teaching lessons and providing educational activities. Also, since the school is a magnet school, there are still students from all different learning levels, capabilities, and socioeconomic statuses, but the parents or guardians had to fill out an application for them to attend the school and the parents must also volunteer at least 20 hours each to the school, so you automatically know that the parents have to care somewhat about the education of their students. This factor has been found to directly correlate to student success in the classroom.

Sumner, Josie

STEP 1: Planning the Lesson

Textbox 3.1.1: Standards and Learning Goals and Student Background Information(Refer to the representative two pages of your lesson plan in these prompts.)

Guiding Promptsa) What learning theory/method will guide your planning process? Provide a brief description of the theory/method. How will you make use of it?I believe that the Constructivist Theory guides my planning process because it places emphasis on learning as an active, constructive process, and the learner is an information constructor. New information is linked to prior knowledge, which is exactly why learning about the use of multiples relates to this theory. In order to understand how to use and identify multiples, students must first have solid prior knowledge on factors. Learning during this lesson will take place in a constructive process because students will be given guided instruction, and then left on their own to explore where certain multiples come from and how patterns are formed. They will do this by making connections as they actively participate in the 100s Chart Investigation, which is part of the Explore phase of my lesson plan format.

b) What learning goals, objectives, and standards, both Missouri and national standards, did you identify for the lesson (provide the number and title of each standard that you list)? How will they guide the planned learning activities?CCSS.Math.Content.4.OA.B.4Recognize that a whole number is a multiple of each of its factors. LG- The student will know that a whole number is a multiple of each of its factors.OBJ- Using the anchor chart and 100s Chart Investigation, the student will be able to identify multiples of the whole numbers 3, 4, and 5 by answering 2 out of 3 answers correctly on a multiple choice quiz.

The standard, learning goal, and objective will all guide the planned learning activities because they will all work cohesively to develop understanding in the students about the multiples of 3, 4, and 5 specifically, allowing them to recognize any patterns that may exist and also to have the skills allowing them to correctly answer the questions on the post-test.

c) What is the content focus of the lesson? What related content that the students have previously encountered will support the learning in this lesson?The content focus of the lesson is in identifying the multiples of 3, 4, and 5. The related content that the students have previously encountered which will support the learning in this lesson is their knowledge of factors and arrays, along with prime and composite numbers.

d) What are some difficulties students might encounter with the content, and how do you plan to address these difficulties?Some difficulties the students might encounter with learning this content will be in noticing common multiples among different whole numbers. Students might first think to skip a multiple if it is already being used by a different whole number. I plan to address this difficulty during the 100s Chart Investigation by instructing students to use different methods of noting the multiples they come across so they will get a clear visual of the common multiples they skip count to using 3s, 4s, and 5s.

Sumner, Josie

Textbox 3.1.2: Instructional Strategies

Guiding Promptsa) What different instructional strategies do you plan to use to engage students in the lesson and to enhance their learning? Provide a rationale for your choice of each strategy.One instructional strategy I plan to use to engage students in my lesson is through the use of technology. By using 21st century skills to practice with new content, students are more drawn to participate in the learning that takes place. Another instructional strategy I plan to use to engage students in my lesson is through collaboration. I will allow students the opportunity to work together, which will force them to hold each other accountable. An instructional strategy I plan to use to enhance student learning is through guided discussion. Guided discussion will play an important role at the beginning of this lesson in order to engage students while teaching and discussing new content. Another instructional strategy I plan to use in my lesson to enhance student learning is a Think-Pair-Share during the guided discussion at the beginning. A Think-Pair-Share strategy will enhance student learning because it instructs all students to partake in the discussion, rather than whoever gets called on by the teacher.

b) How do the instructional strategies connect to the learning goals and objectives to facilitate student learning?The instructional strategies I chose connect to the learning goals and objectives that facilitate student learning because it is very important to incorporate a lot of guided instruction when introducing a new topic and expecting students to comprehend it. The guided discussion paired with the T-chart explaining the components of factors and multiples connects to the learning goals and objectives because it facilitates student learning by helping them understand how the two build off of each other and go hand in hand.

c) What informed your decisions to use individual, small group, and/or whole group instruction to facilitate student learning?Whole group instruction will facilitate student learning while comparing and contrasting factors and multiples because the students need direct and guided instruction, and to all be paying attention at the same time while the teacher introduces new content to the class. Small group (partner) instruction will facilitate student learning during the 100s Chart Investigation (Explore phase) because it is important that the students work together in helping each other understand the new material, while the teacher moves from group to group and offers guidance as needed. This style of learning supports the Constructivist Theory because it places emphasis on learning as an active, constructive process, and the learner is an information constructor.

Textbox 3.1.3: Learning Activities

Guiding Promptsa) What learning activities do you plan to implement in this lesson?Provide a rationale for your choices.One learning activity I plan to implement in this lesson with be a T-chart on chart paper, where the class generates a list of characteristics of both factors and multiples. The T-chart will enhance student learning because it allows the class as a whole to develop a list of their own when it comes to finding the differences between factors and multiples. The next learning activity I plan to implement in this lesson is a SMART Board interactive activity, because it will

Sumner, Josieget some of the students up and moving, and serve as a simple follow-up to the discussion introducing multiples. Another learning activity I plan to implement in this lesson will be a 100s Chart Investigation, where students will partner up and use the instructions on the worksheet guide to color code multiples of given whole numbers. This learning activity will be very useful because not only will it show students what the multiples are of the numbers 3, 4, and 5, but it also serves as a visual aid for any patterns that take place from 1-100 and common multiples of the given numbers as well.

b) How will these learning activities address student strengths and needs?These learning activities will address student strengths because they are for the most part, very productive with their schoolwork when it comes to working in pairs. However, since these students are the lowest level math learners in the 4th grade, they can become easily frustrated with new material and look for distractions if the frustration level is too high. The learning activities will address student needs because there are several different transitions and opportunities to succeed within the lesson, giving them the chance to gain some intrinsic motivation that will help them continue and stay focused.

c) How did your class demographics inform the design of the learning activities you chose?Class demographics will inform the design of the learning activities I chose because the students are pretty fluent in the use of the SMART Board and other technology, and I want to give them the chance to practice and demonstrate their knowledge in a way they are excited about and familiar with. Also, class demographics will inform the design of the learning activities I chose because keeping in mind that this is the lowest level math class in the 4th grade, I wanted to offer them a visual aid (100s chart) to illustrate factors and multiples, guiding them to make connections on their own.

Textbox 3.1.4: Technology

Guiding Promptsa) What materials and resources will you use to support your instruction?Provide a rationale to support those choices.The students will have red, blue, and yellow writing utensils to use on their 100s Chart Investigation, which also comes with a 100s chart. These materials will support my instruction because each color will be used to represent the multiples of different whole numbers, which will provide students with a clear visual of which numbers are common multiples of several different factors. Another material I will use in my lesson will be an anchor T-chart, which will support my instruction because it will create a graphic organizer in the students’ minds, helping them with the introduction of new topics by building off of prior knowledge. Post-its and a post-assessment, “Are You a Multiple Master” will be administered at the beginning and at the end of the lesson, respectively. The post-its will support my instruction by engaging students with a Think-Write, and the post-assessment will show if any progress exists by the end of the lesson. A resource I used to guide some of my ideas was the Investigations book that the teachers of 4th grade follow with math curriculum. This resource was very helpful and important because it showed me certain concepts and strategies about multiples that the students would understand.

b) What types of technology do you plan to use for this lesson?I plan to use a SMART Board interactive activity for my lesson in order to check student understanding of new concepts. Several students will be called up to the board, one at a time. Each page will have a new question that will be: “Which of these whole numbers are multiples

Sumner, Josieof ___?” and about 6-7 whole numbers will be dispersed throughout the page. The correct answers will fade once they are dragged and dropped into the center object of the screen, and incorrect answers will bounce back and not accepted.

c) How will your chosen technology enhance your instruction and student learning in this lesson?My chosen technology will enhance my instruction because it will incorporate 21st century skills to teach basic content in a new light. The SMART Board activity will enhance student learning in this lesson because it encourages them to participate and learn in a more interactive and enjoyable way.

STEP 2: The Focus StudentsRefer to these students as Focus Student 1 and Focus Student 2

Textbox 3.2.1: Understanding the Two Focus Students

Guiding PromptsFocus Student 1:a) Identify Focus Student 1’s learning strengths and challenges related to the learning goal(s) of the lesson.One of Focus Student 1’s learning strengths related to the learning goal is that he uses strategies taught in class in order to find a certain answer to a math problem, rather than just guessing it. One of Focus Student 1’s challenges related to the learning goal is that he has shown trouble with understanding how to find factors and does not know how to check his work to make sure he has found the right ones, which coincides with the learning goal because students must understand factors before understanding multiples. Another strength of Focus Student 1 is that he always shows his work and is an overall hard-worker, which relates to the learning goal because it is important for the teacher to see student work when finding multiples because it shows a student’s understanding. Another challenge of Focus Student 1 is that he has exhibited difficulty in skip-counting, which is a very crucial piece when it comes to finding multiples of a given whole number. Another one of Focus Student 1’s strengths related to the learning goal is that he has shown during teacher-student interactions that he is great at making connections when it comes to math, which is related to the learning goal because he will need to understand how multiples and factors go hand in hand.

b) What evidence will you collect to show the progress Focus Student 1 makes toward the learning goal(s)?The evidence I will collect to show the progress of Focus Student 1 when it comes to the learning goal includes a Post-it note pre-assessment asking the student to list the first five multiples of 3 (after 3). The next piece I will collect will be the 100s Chart Investigation, where the student will use skip-counting to color in the multiples of 3, 4, and 5, along with picking out common multiples. The last piece of evidence I will collect is a mini-post-assessment, where the student will answer 3 questions about understanding the relationship between multiples and factors.

Focus Student 2:a) Identify Focus Student 2’s learning strengths and challenges related to the learning goal(s) of the lesson.One of Focus Student 2’s strengths related to the learning goal is that he has shown during teacher-student interactions that he is great at making connections when it comes to math, which is related to the learning goal because he will need to understand how multiples and

Sumner, Josiefactors go hand in hand. One of Focus Student 2’s challenges is that he is one of the more struggling students in the class when it comes to his multiplication facts, which will be very important when finding some of the larger multiples. Another challenge related to the learning goal of the lesson is that Focus Student 2 often continues onto the next problem while working on his own, without checking whether his last answer was correct or not. This challenge is related to the learning goal because his answers, when it comes to understanding multiples, will automatically show whether he understands factors, which is where checking his own work would become crucial.

b) What evidence will you collect to show the progress Focus Student 2 makes toward the learning goal(s)?The evidence I will collect to show the progress of Focus Student 2 when it comes to the learning goal includes a Post-it note pre-assessment asking the student to list the first five multiples of 3 (after 3). The next piece I will collect will be the 100s Chart Investigation, where the student will use skip-counting to color in the multiples of 3, 4, and 5, along with picking out common multiples. The last piece of evidence I will collect is a mini-post-assessment, where the student will answer 3 questions about understanding the relationship between multiples and factors.

Textbox 3.2.2: Differentiating Instruction for the Two Focus Students(Refer to the one page modification/adaptation plan for each of the two Focus Students in these prompts.)

Guiding Promptsa) How will you adapt the learning goal(s) and objectives to engage each of the two Focus Students and facilitate their learning?Provide a rationale.Since the students of this math class represent the lowest level in the 4th grade, both of the Focus Students are generally at the same frustration level. However, Focus Student 1 has proven to excel more with his multiplication facts, so I would expect him to do better on the post-assessment. I would adapt the objective degree to facilitate Focus Student 1’s learning by expecting him to get all of the questions (instead of 2 out of 3) correct. To help facilitate the learning of Focus Student 2, I may decrease the amount of multiples we examine during the lesson in order to focus more time on one or two of them, really focusing on any patterns or connections we may find. In order to engage the two Focus Students more, I may change the objective condition by including a little more independent practice, because both of them generally prefer working on their own.

b) Describe how you will differentiate your instructional strategies and learning activities to engage each of the two Focus Students and facilitate their learning?Provide a rationale.I will differentiate my instructional strategies and learning activities to engage both of the two Focus Students by giving them the opportunity to participate in guided discussion at the beginning of the lesson in order to get them actively engaged in the learning process by making connections, which is a strength I have noticed from both of them. I will differentiate my instructional strategies and learning activities to facilitate the learning of both of the Focus Students by allowing them to work with partners when it comes to the 100s Chart Investigation, in order to hold them accountable to checking their answers, since they both have shown they need a little extra support.

Sumner, Josiec) What materials, resources, and technology will you add or adapt to engage each of the two Focus Students and facilitate their learning?Provide a rationale.In order to engage each of the Focus Students, I will adapt my technology by making my SMART Board activity fall-themed because both of them are really excited for the season and Halloween. In order to facilitate the learning of each other Focus Students, I will visit with both of them while they are working in partners on their 100s Chart Investigation (in different partner pairs) and ask/take notes about any connections they have made personally about the multiples they have found while participating in the activity, either justifying or guiding them towards the desired answers. This is an adaptation I will make to the 100s Chart Investigation, because it will not only include showing their work, but also orally explaining their thought process, which is a strength of both Focus Students.

d) How will you and each Focus Student know that you and he/she achieved the learning goals and objectives for the lesson?I will know that each of the Focus Students have achieved the learning goal and objective for the lesson because they will have gotten at least 2 out of the 3 questions correct on the given post-assessment. Each Focus Student will know that he achieved the learning goal and objective for the lesson because I will provide feedback written on their post-assessments including correct answers and any comments or encouragement I can offer. The post-assessments will be handed back the following class period.

STEP 3: Analyzing the Lesson

Textbox 3.3.1: Analyzing the Lesson for the Whole Class(Refer to the one page teacher instructional artifact and one page student work sample from your instruction in these prompts.)

Guiding Promptsa) To what extent did the lesson, including instructional strategies, learning activities, materials, resources, and technology help to facilitate student learning? How does the evidence you collected support this finding?The instructional strategies, learning activities, materials, resources, and technology all help to facilitate student learning because they provide a multitude of strategies of how to understand the math and concept of multiples. All of these things also provide the students with many opportunities to demonstrate their knowledge and experience the content in different settings. Based on the evidence I collected, I did not have to rely on one summative assessment in order to find out whether the students met the learning goal or not, I had multiple tangible examples throughout the lesson to show me they either had it from the beginning, or they were progressing towards the goal. For example, by using the SMART Board activity with a class discussion, I was able to watch the students’ thought processes and acknowledge or correct them as they went. This form of technology, along with the other materials and resources I used throughout the lesson served as the “ME-WE-YOU” model that my CT has been teaching me over the last few weeks.

b) How did the students demonstrate their understanding of the content presented?Provide specific examples from the lesson and student work to support your analysis.One way that the students demonstrated their understanding of the content presented was during the SMART Board activity, which took place after the guided discussion. Three students were chosen to come up individually to the board and choose which whole numbers were multiples of given numbers. One of the students was completely right, and the other students

Sumner, Josiegot two out of three possible answers correct, which was a teaching opportunity for me to step in and ask probing questions until they got the complete right answer. Another way that students demonstrated their understanding was through the 100s Chart Investigation. The worksheet asked students to predict what the next common multiple of 3, 4, and 5 would be after 100, and no one got the correct answer right away. This was a teaching opportunity for me to step in and explain the pattern within the 100s chart in order to lead them to the correct answer (120).

c) While you were teaching, what adjustments to the lesson did you implement to better support student engagement and learning?Provide examples to support your decisions.While I was teaching, one adjustment I made to the lesson in order to better support student engagement was by sitting with different partner pairs and modeling with them how to complete the 100s Chart Investigation. I noticed that several pairs had difficulty getting started with the directions, so I stopped the whole class at one point and explained the instructions more in-depth so they were able to participate. One adjustment I made to the lesson in order to better support student learning was including an extension activity for the 100s Chart Investigation. As a few of the students completed the main part of the 100s chart, I asked them to shade in the multiples of a few other given numbers, and also look for more connections and patterns between them, preparing to share with the class.

d) What steps did you take to foster teacher-to-student and student-to-student interactions? How did they impact student engagement and learning?In order to foster teacher-to-student interactions, I led a guided discussion at the beginning of the lesson with the students while introducing the concept of multiples and relating it to factors and other prior knowledge. This impacted student engagement because they were called on to participate in the discussion and help me develop ideas on T-chart. This interaction impacted student learning because I was able to guide the discussion where it needed go to stay on topic and incorporate the necessary components. In order to foster student to-student interactions, I provided the 100s Chart Investigation for the students to partner up and work on together. This activity impacts student engagement because the students must hold each other accountable in completing it. This activity impacts student learning because it allows them to explore and discover patterns of common multiples on their own without teacher guidance, which gives them more autonomy.

e) What feedback did you provide during the lesson to facilitate student learning? What impact did the feedback have on student learning?Provide specific examples.One way that I provided feedback during the lesson in order to facilitate student learning was by guiding the students during the whole class SMART Board activity. This was a great opportunity for me to see their thought process of picking out multiples, and to offer positive feedback to correct answers along with asking the students how they got them right. I could tell that this had an impact on student learning because other students that were following along were able to make connections to the correct answers when I called on them to get involved. Another form of feedback I used during the lesson was during the 100s Chart Investigation, I would walk from pair to pair, and offer positive feedback, ask students how they got what they got, and provide strategies on how they could obtain correct answers. This made an impact on student learning because I would visit the same pair a second time and see that they were doing it correctly after a little further instruction.

Sumner, Josie

Textbox 3.3.2: Analyzing the Differentiation for the Two Focus Students(Refer to the one page student work sample for each of the two Focus Students in these prompts.)

Guiding Promptsa) To what extent did each of the two Focus Students achieve the learning goals and objectives of the lesson?Cite evidence to support your analysis.Based on their perfect scores from both post-assessments, both Focus Students were able to achieve the learning goal and objective of the lesson. However, it is difficult to truly see the understanding of a math concept such as multiples over the span of one lesson plan, so it would help to gather further evidence over the following few days to decide whether the students were able to make the connection that a given whole number is a multiple of its factors. One reason I said this was because after reading through their 100s Chart Investigations, I noticed a little difficulty with identifying patterns among common multiples (example: predict what the next common multiple of 3, 4, and 5 would be after 100- Focus Student 1 answered “140” and Focus Student 2 answered “160”). If given the chance, I would examine these skills even further over the next few days and use supplement instruction to help the students achieve the learning goal of the lesson.

b) How did your differentiation of specific parts of the lesson help each Focus Student meet the learning goals and objectives?Cite evidence to support your analysis.By having the students work in pairs during the 100s Chart Investigation, I helped the Focus Students achieve the learning goal and objective because they were held accountable to checking their answers and making sure they were on the same page as their partner before moving on. For example, while interacting with Focus Student 1 and his partner, I noticed that his partner was jumping ahead a little, so I made sure to instruct him to go back and help Focus Student 1 through the problems and explaining any thinking behind them. By walking between each of the Focus Students during the investigation, I was able to help them meet the learning goal and objective because I was able to provide more focused instruction based on individual needs and challenges. I was also able to ask each of the students probing questions in order to guide them to correct answers, such as, “What do you notice about common multiples of 3 and 5? What answer do you get when multiplying the two numbers together?”

STEP 4: Reflection

Textbox 3.4.1: Reflecting on the Lesson for the Whole Class

Guiding Promptsa) What specific instructional strategies, learning activities, materials, resources, and technology will you use to help students who did not achieve the learning goals and objectives?Provide specific examples.Out of the whole class, there ended up being three students who were not able to meet the objective I set for them (answering at least 2 out of the 3 questions correctly on the post-test). If given the opportunity to supplement my instruction with more time to teach these students, I would use more time to reflect on the answers of the 100s Chart Investigation, and I would use technology to display an example up on the SMART Board in order to model correct answers for them. I would also give these students the chance to work with Mathtappers: Multiples, an app for their iPads which goes further in-depth about the relationship between multiples and

Sumner, Josiefactors, allowing these students to have a lot more practice. I would also use more ideas from the teacher resource book Investigations, because the 4th grade teachers at this school including my CT pull a lot of activities and instruction ideas from it because it’s set-up is very structured and teachable. One example of a learning activity from Investigations is called “Multiple Turn-Over,” where students partner up and compete against one another to eliminate their list of multiples the quickest by finding common factors among them.

b) How will you use your analysis of this lesson and the evidence of student learning to guide your planning for future lessons for the whole class?When it comes to planning future lessons for the whole class, I will provide a little more scaffolding overall when it comes to modeling. While doing my lesson, I noticed that because I had not modeled the 100s Chart Investigation, I spent a lot more time on answering questions about the instructions rather than teaching patterns and connections of common multiples. I noticed that this specific class, being the lowest level on math in the 4th grade, will need more assistance in the future. I will also plan for technology ‘hiccups’ in the future when it comes to my lesson plans. My SMART Board activity did not transfer to this computer the way that it was saved, so it didn’t work the way I expected it to and some of the students got anxious and lost focus while I was scrambling to figure it out/find a second option.

Textbox 3.4.2: Reflecting on the Differentiated Instruction for the Two Focus Students

Guiding Promptsa) How will you use your analysis of this lesson and the evidence of student learning to guide your planning for future lessons for each of the two Focus Students?Consider specific instructional strategies, learning activities, materials, resources, and technology you will use. Provide specific examples. (Resources: Use a conference with topic, speaker, place, and date and/or a book resource with title and author.)When it comes to planning for future lesson for each of the Focus Students, I would like to learn more about how I can use differentiation in the classroom. Staff Development for Educators is putting on an upcoming conference in Missouri that will focus on improving ALL learners' number sense, mental math skills, and problem-solving skills, called “Singapore Math: Strategies that Work in Every Classroom!” presented by Char Forsten. All three of these areas are extremely important when it comes to learning the relationship between factors and multiples, especially number and mental math (multiplication facts). Also, this sounds like it will be a great seminar I can take away a lot from because strategies will be taught that can help learners all across the board, from 1st to 5th grade. Learning different strategies to teach my Focus Students would be beneficial because I could give them more options for solving the same problems, allowing them to choose which one they prefer or can make better sense of in their heads. For example, there are many different strategies a student can use to find the multiples of a factor, or the factors of a multiple, so it would be important to teach all of the strategies, but pinpoint which strategy may work best for each Focus Student.