School of EducationService – Leadership – Competence –

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Mathematics Lesson Design TemplateTeacher CandidateMentor TeacherUniversity CoordinatorSchoolGrade 2nd EAPSubject MathDate February 25, 20121. Context for Learning – Who are the students you are teaching in this class?1.1 – What is the name of the course [unit] you are documenting?Mathematics- multiplication and division missing factors, inverse operation1.2 – What is the length of the course [unit]?5 days for this unit.1.3 – What is the class schedule?Every day from 8:45am to 10:15am1.4 – Total number of students 24 Male 12 Female 121.5 – Number of students with limited English proficiency N/A1.6 – Number of students identified as gifted and talented 241.7 – Number of students with Individualized Education Plans (IEPs) 11.8 – Number of students with 504 plans 11.9 – Attach a chart that summarizes the required accommodations or modifications for any students that will affect your instruction of this lesson. Consult with your mentor teacher to complete the chart.There are no accommodations needed for the IEP or 504 students per this lesson.1.10 – Describe the range of abilities in the classroom.Everyone is working at a third or fourth grade math level. All are advanced and portray characteristics of picking up the new math material quickly.1.11 – Describe the range of socio-economic backgrounds of the students.The entire class ranges from middle to upper class in socio-economics.1.12 – Describe the racial/ethnic composition of the classroom and how you make your teaching and learning culturally responsive.Very Diverse class, ranges from Caucasian to Chinese, Chinese-American, Indian, and Asian. For this lesson each students opinion and statements are accepted, no student is singled out, and every student has a voice.1.13 – What prior knowledge, skills, and academic background do students bring to the lesson? (Consider previous learning experiences, assessment data, etc.)These students have been working on the unit of missing factors in multiplication and division problems. They have been introduced to inverse operations but not with academic language.1.14 – What do you know about the students’ conversational and academic English? How do you know?All students are proficient in the English language both written and conversational. This is seen

through their reading, speaking, and writing abilities on a daily basis.1.15 – Is there any ability grouping or tracking in the class? If so, please describe how it affects your class.There are two separate math groups. A third grade level consisting of 23 students. In addition there is a fourth grade level group consisting of 1 student. Both groups will be participating in this lesson because it is extra practice and covers academic language.1.16 – What additional needs might students have?Some students require glasses and do not have them, so working on the white board or document camera, images must appear large for everyone to see.1.17 – Describe any district, school, grade-level, and/or cooperating teacher requirements or expectations that might impact your planning or delivery of instruction, such as required curricula, pacing plan, use of specific instructional strategies, or standardized tests, etc.The required curricula are Math Expressions. For this lesson I made a lesson that gives extra practice in learning multiplication and division missing factors using inverse operation to solve. School wide gradual release plan is required by teachers. This is a plan where the teacher teaches the lesson, models how to solve a problem, then as a class with the teacher they solve a problem, then they work with a partner so solve a problem, and then they work individually to solve the problem. This is instruction and concept skills being gradually released to the students.1.18 – Describe any classroom rules, routines and/or classroom management issues that affect the lesson. How might you proactively address those issues in your lesson design?Classroom rules that will affect my lesson are respect and no sharpening pencils during a lesson. These are the only two rules/routines that will affect this lesson. There are no classroom management issues that will pertain to this lesson.1.19 – Identify any textbook or instructional program you primarily use for instruction. If a textbook, please provide the name, publisher, and date of publication.Math Expression By: Karen C. Fuson, Houghton Mifflin Harcourt (2009).2. Lesson Plan Explanation – Why are you teaching this lesson?2.1 – Upon what assessment data or previous lessons are you building?I am building on the previous lesson of finding missing information in addition and subtraction problems, as well as solving simply multiplication and division problems, writing story problems, and solving them.2.2 – What requisite skills do students need in order to access the lesson and participate fully?Students need to know their multiplication and division facts. They need to understand how to eliminate unnecessary information in a problem. They also need to know how to write a story problem with given information (such as an equation).2.3 – How does the content build on what the students already know and are able to do?This content builds on the fact that students know how to multiply and divide, but when is comes to more difficult problems such as missing information, they will be able to use their multiplication and division skills to solve for the missing information through inverse operations. They are taking what they know how to do, and expanding it to solve more complex problems. They are also building on their ability to write a variety of story problems based on the information or equation given.2.4 – How does this lesson fit in the curriculum?

This lesson fits the curriculum by being the next step in the lesson sequence. It also provides students with more practice on a more difficult subject to grasp. It also continues their mental thinking of writing and solving word problems.2.5 – How does this lesson build on previous lessons or previous learning?This lesson builds on the students’ ability to use their multiplication and division skills to solve problems inversely. They know how to multiply and divide, but it builds on using the inverse operation to solve for a missing piece to either a division or multiplication problem. It also keeps building on their story problem writing skills and solving those story problems.2.6 – How will the learning in this lesson be further developed in subsequent lessons?The learning in this lesson will be further developed in subsequent lessons by the continuous practice with story problems, multiplication, and division. Students will also refer to the inverse operation for solving problems more frequently in subsequent lessons after it is learned. They will also continue to learn about missing information, identifying information that is missing or not needed, and furthering their knowledge around solving complex equations.3. Learning Targets – What are the objectives for the lesson?3.1 – What is the title of your lesson?Solving Problems Backwards3.2 – Summarize the content focus of the lesson. This summary might take the form of a “big idea” or “essential question.”The big idea for this lesson is to take equations with missing information, and use the given information and to determine the missing information. Students will be using the inverse operations to determine the missing information.3.3/3.4 – Cite the PE’s/standards using the numbers and text. Include one or more mathematics content PE and one or more mathematics process PE.P.E. 3.2.C - Determine products, quotients, and missing information factors using the inverse relationship between multiplication and division.P.E. 3.6.C - Identify missing information that is needed to solve a problem.3.5 – Cite the objectives (skills or concepts) for the lesson. What do you want students to think, know and/or be able to do at the end of the lesson? Be concrete and specific. The objectives need to be measurable. They need to be aligned with the PE’s/standards. Use action verbs based on Bloom’s. State whether students will be working at the concrete, pictorial, and/or symbolic-abstract levels. Students will be able to solve for missing factors using the inverse of the operation.

Students will be able to identify the missing information, and solve for it using inverse operation, to solve the problem as a whole.3.6 – Rephrase your learning targets using student-friendly language.I will be able to identify missing information in a math problem and solve for the missing information using the opposite operation.3.7 – How will students demonstrate this? Describe observable actions. – e.g. Given (learning activities or teaching strategies), the students will (assessable behaviors) in order to demonstrate (connection to PE’s/Standards).Give a worksheet consisting of multiplication and division problems with missing information the students will be able to solve the problems using the inverse operation in order to demonstrate the relationship between multiplication and division.

3.8 – What do you as the teacher know about this particular concept/topic etc.?As a teacher I know that this topic can be tricky. I know that you have to fully understand what the equation is asking you to solve for, and then figure out how to use the inverse operation of the initial problem to solve for the missing information. Through the years, I have also become very familiar with solving daily math problems using this method. Such as being at the store. I have 20 dollars, and I want to buy some cookies. Each cookie costs 2 dollars, how many cookies can I buy? Well 2 x __ = 20. So I say 20 ÷ 2 = 10. I can buy 10 cookies.3.9 – Where did you find this information? (List specific resources, using APA style.)I found this information through daily life, and learning this concept back in elementary school. I have also acquired this information through courses at Seattle Pacific University, the teacher’s edition of Math Expressions (Grade 3) Sowder, J., Sowder, L., & Nickerson, S. (2011). Reconceptualizing mathematics. (1 ed.). New York: W H Freeman & Co.3.10 – Academic Language – What are the linguistic demands embedded in the learning targets? (Consider what language and literacy skills students may need to know in order to demonstrate their competency on the learning targets successfully.)The linguistic demands embedded in this learning target, are to know what the words product, quotient, inverse operation, and missing factors mean. It also requires students to know how to write an equation, and write a word problem based on a given equation.3.11 – Academic Language – What key vocabulary (content-specific terms) do you need to teach?Product, quotient, multiplication (review), division (review), inverse operation, missing factors.3.12 – Academic Language Functions – What are students doing with language to express their developing understanding of the content you are teaching?Students are using academic language during class discussion; they are also writing story problems that contain the key vocabulary. They are also using a “KNWS” chart on each problem to state the different parts of the equation they know, what they do not need, what they want to know, and a strategy to find the answer to the problem.3.13 – Academic Language Forms – What words and phrases (implied grammatical features and syntactic structures) do students need in order to express their understanding of the content you are teaching? How will you teach students the relevant grammatical constructions?Students need to know how to form simply sentences to show they can write what they know, do not need, what they want to know, and their strategy for finding it. They also need to know how to form a basic sentence with a capital first letter of the first word, and a period or question mark at the end depending on whether or not it is a question they are asking.3.14 – Academic Language Fluency – What opportunities will you provide for students to practice the new language and develop fluency, both written and oral?Students will have an opportunity to practice the new language during class discussion, and during writing their word problems, and solving equations with a “KNWS” chart.4. Lesson Assessment – How will students demonstrate their learning?Formative Assessment (Process)4.1 – How will you know that the students are learning/working towards the learning targets?I will know students are working/learning towards the learning targets through listening to class discussion and checking in with them to make sure everyone is understanding before moving on to the next item (mainly with examples, and non-examples). If students do not understand I will keep teaching the material in different ways until all students understand the material. I will

also periodically ask if anyone has questions, and answer those questions. During work time students can freely ask questions to myself or their peers.4.2 – How will students demonstrate their understanding?During discussion it will be thumbs up or down after I ask if everyone understands the material. Also I will answer and re-teach material until I receive all thumbs up before moving on. The worksheet will show the students work, using the inverse operation taught to solve for the missing information. The “KNWS” chart for each problem which demonstrate student’s ability to identify with the missing factor is in the “what they want to know (W)” section.4.3 – Describe the ways in which you will use these assessments to inform your teaching decisions during the lesson.If a student shows a thumb down, I will ask them what they do not understand, once that is identified, I will re-teach the material in different ways until the student understands the material, and can tell me they understand. If someone has a question I will explain and demonstrate the material again, and answer their question before moving on in the lesson.Summative Assessment (Product) THERE IS NO SUMMATIVE ASSESSMENT FOR THIS LESSON. IT IS PART OF A UNIT, BUT NOT THE END OF A UNIT! 4.4 – In what ways will the evidence document student achievement?

4.5 – How might you modify your assessment(s) for the students with whom you are working?

4.6 – How will students be able to reflect upon and self-assess their learning?

4.7 – To what extent are your assessments aligned with your objectives?

4.8 – Complete the following table to highlight what the students will do to demonstrate competence specific to learning for this lesson. Consider the following questions:

Formative Assessment In what ways will you monitor student learning during the lesson and how might this guide your

instruction? What specific actions do you expect to observe? How will you record what you see and hear? What feedback will you provide? How will your feedback support students in meeting the learning targets?

Summative Assessment What evidence of student learning will you collect? What criteria will you use to judge whether or not your students are meeting the learning targets? What are your evaluative criteria (or rubric) and how do they measure student proficiency for your

learning targets?

Description of formative assessment

activityEvaluative criteria What the assessment is

designed to assess Feedback to students

Oral assessment Student’s ability to Students’ ability to Verbal feedback. Tell

during class discussion about examples, and non-examples, and why they do or do not work.

Observation of students working with one another on first three of worksheet correctly.

Completion of worksheet with correctly solving the problems using the new concept.

identify and explain why an example is either a true example or a non example.

Visually observe their work on their worksheet, and what they are saying to solve the problems together.

Review of worksheet, and check it with answer key to assess whether they understand and using the new concept correctly.

see the correct way to solve problems using inverse operations, and their ability to explain why something is right or wrong.

Their ability to take the new concept and apply it to their worksheet correctly.

Ability to solve the problems on the worksheet using the new concept in the correct manner, while covering all parts and showing their work.

them they did a nice job explaining it; revoice it back to make sure it is what they said. If it is an explanation that doesn’t fit, pose a question to get them thinking on the right track.

Verbal good job, or simply asking them to explain why they did something on the worksheet (if incorrect), and discussing the situation one on one from there to get them on the right track.

Students, who missed a problem or their work shows the problem solved in a different manner, will be re-taught the concept in a small group or one on one. If students understand and completed the worksheet correctly they get their paper returned with a star.

Description of summative assessment

activityEvaluative criteria What the assessment is

designed to assess Feedback to students

4.8 – Academic Language – Identify the linguistic demands in your assessments and how they might be

modified.My assessment requires students to use academic language in their “KNWS” chart, and to be able to write a word problem with a given equation.4.9 – Academic Language – How is the understanding of academic language being assessed?By observing them using the academic language in oral discussion correctly, and correcting them when needed. Also by observing them using the language in writing correctly on their worksheet.5. Instructing and Engaging Students in Learning – What will happen in the lesson?5.1 – What co-teaching strategy will be used during this lesson? (if applicable, check appropriate method)One Teach, One Observe (lead) X One Teach, One Drift (lead) Station TeachingOne Teach, One Observe (observe) One Teach, One Drift (drift) Supplemental TeachingParallel Teaching Team Teaching Alternative TeachingIf not applicable, is this lesson during your solo time in the classroom? Yes No X5.2 – What learning activities do you have planned for the students? (This describes what the students do.)Students will listen to a part of a story book Big Truck and Car Word Problems Starring Multiplication and Division by: Rebecca Wingard-Nelson. Students will also participate in class discussion about examples and non examples. Class as a whole solves a problem with the teacher, then they solve three problems on their worksheet with a partner and manipulatives, then they solve the rest of the worksheet on their own with manipulatives.5.3 – What instructional strategies will you use? (This describes what the teacher does.)Teacher explicitly states learning targets and objectives. Teacher also leads discussion and engages student thinking my implementing the five talk moves, teacher also models the concept to the students, and then has them work with a partner. Then the students’ work independently. Teacher circulates classroom answering questions and checking in on students while they complete their worksheet.5.4 – What opportunities will the students have to articulate the learning target(s), monitor their own progress, and identify support needed to achieve the learning target(s)?Students will be able to articulate the learning targets during class discussion, partner work, and independent work. They will monitor their own progress as they work independently on the last part of the worksheet, and they will also be able to identify support needed at any time they don’t understand by raising their hand to ask a question or state they are confused.5.5 – Describe the sequence of steps in the lesson in the following table. General lesson sequences may be more directive (e.g., ITIP) or open (constructivist). Whatever design is used, the lesson needs to be explicitly outlined.

For example, an ITIP lesson sequence would include the following sequence: Objective & Purpose Anticipatory Set Input/Activity Modeling Check for Understanding

Guided Practice Independent PracticeFor a constructivist lesson: Objective & Purpose Explore/Experiment Hypothesize/Explain Report/Assess

Sufficient detail is needed to see intention of the learning experiences. Consider the following questions:

How will you communicate the learning targets to the students? How will you communicate your expectations to the students? How will you connect to your students’ previous experiences? How will you link the lesson to their lives as students? What are the key teacher questions or prompts? What are the procedural directions for students to follow? How will you explicitly teach/model or demonstrate the skill/strategy/concept? How will you adapt the instructional procedures to meet the needs of the students whom you are

teaching? What learning activities make up the lesson? What kind of examples/samples will you provide for your students? How will students know where the work is going and what is expected of them? What opportunities will you provide for students to practice this new skill/strategy? What questions might you pose to push student thinking and check for understanding? What feedback do you plan to provide? How might you correct student misunderstandings? What kind of opportunities will you provide students to apply this new learning and demonstrate

mastery? How might students evaluate their work and its implications?

It should be clear that the learning experiences are aligned with the learning targets and assessment tasks. The sequence of lesson steps should reflect: Multiple approaches to learning that are responsive to the description of students provided in the

Context for Learning. Research and principles of effective practice. A transformative multicultural perspective. Attempts to stimulate problem solving and critical thinking.

Complete the following table: Provide an estimate of time. List the sequence of the various learning experiences in the lesson. Articulate a purpose for your selection of each significant learning activity. Focus on the choice of

instructional strategies and on why significant learning experiences are chosen for student engagement. Your purpose statements can help identify evidence of effectiveness in your teaching.

Time Learning experiences Purpose10-15 min

Teacher reads pages 12-19 of Big Truck and Car Word Problems Starring Multiplication and Division By: Rebecca Wingard-Nelson.Teacher says: Think about key points in these pages being read.After story is read, Teacher says: pair share the three key points they noticed in the story.Teacher says: Think of your three key points, Teacher calls on three random students. Teacher waits for response. After student responds

Engages students into concept lesson being taught.

5 min

20 min

5 min

Teacher says: Does anyone have anything to add to that. Teacher waits for responses.

Teacher explicitly says: Students will be able to solve for missing factors using the inverse of the operation. Students will be able to identify the missing information, and solve for it using inverse operation, to solve the problem as a whole (Teacher also writes the lesson’s objectives on the board.) Underneath, teacher writes student friendly objective [I will be able to identify missing information in a math problem and solve for the missing information using the opposite operation.]

Teacher shows students 2 examples (one multiplication, one division), and two non-examples (one multiplication, one division).Teacher says: analyze and compare and contrast the examples to the non- examples. Think about why the example is an example (how it shows inverse operation to solve the problem) and why the non-example is not an example(does not show an inverse operation to solve the problem) (students apply their own reasoning to this question). *See attached for examples.

Teacher chooses a popsicle stick name.Teacher says: share why the example is an example and why. Teacher waits for response.Teacher says: *student response (revoices) Teacher says: Does anyone has anything to add on to it. Teacher waits for responses. Teacher has another student repeat what the student says in response to adding on. Teacher waits for students to process information. *this process repeats itself until all students are clear as to why the examples are example and the non-examples are non-examples.

Teacher says: Students will be able to solve for missing factors using the inverse of the operation. Students will be able to identify the missing information, and solve for it using

To inform students what they are expected to achieve from this lesson.

Engages student thinking and reasoning to why this concept lesson works with the example and not the non-example. Talk moves keeps the discussion going and allows for student voice.

Reminding students of objectives and learning targets.

5 min

15-20 min

inverse operation, to solve the problem as a whole *see section 3.5 and 3.6

Teacher says: we are going to solve an equation together over the document camera. Teacher writes the equation 7 x __= 21 and “KNWS” vertically below it on a piece of white paper, and places 21 M&M’s on the document camera.

Teacher says: write this on a piece of paper and work alongside to solve this problem.Teacher says: we will use a “KNWS” chart for each problem. A “KNWS” chart tells us what we know and what we don’t need to know, what we want to know, and the strategy used to solve the problem. Teacher chooses a popsicle stick at random.Teacher says: tell me what we know for this problem. Teacher writes this information under the K letter.Teacher says: explain your reasoning for how we know this information. Teacher chooses a popsicle stick at random.Teacher says: tell me what we do not need to know for this problem. Teacher writes this information under the N letter.Teacher says: explain your reasoning for how we know this information. Teacher chooses a popsicle stick at random.Teacher says: tell me what we want to know for this problem. Teacher writes this information under the W letter.Teacher says: explain your reasoning for how we know this information. Teacher chooses a popsicle stick at random.Teacher says: tell me what strategy (this should be something to do with the inverse operation) we can use to solve this problem. Teacher writes this information under the S letter.Teacher says: explain your reasoning for this. Teacher says: Does anyone agrees or disagree, why? Teacher uses talk moves to work through discrepancies until everyone agrees on a strategy. Teacher then solves the problem using

Beginning of gradual release. This is the modeling phase.

Continuation of modeling phase. With more talk moves to get students mind thinking and engaging in the lesson.

5 min

20 min

5-10 min

5 min

the strategy showing her steps in writing, and how she uses the M&M’s as manipulatives to solve 21 ÷ 7 (the inverse operation) to solve the problem on the document camera.

Teacher says: I am going to pass out a worksheet that they will need to complete before silent reading.Teacher says: you can work on the first three problems with manipulatives with their elbow partner. After they complete for first three with their partner, they can finish the worksheet independently with manipulatives. Once they are done with the worksheet they can turn it in, eat their M&M’s and silent read or attempt the challenge question that will be on the board (challenge equation is (30 ÷ __)= 3 x 5.

Teacher gives students time to work while teacher circulates and answers questions that may come up.

After all the worksheets are turned in, teacher says: to come back to desks and together as a class.Teacher says: write down the three main ideas from the lesson on a sheet of paper.Teacher Says: Does anyone want to share of their key points. Teacher writes these on the whiteboard in a list form.

Teacher Says: Students will be able to solve for missing factors using the inverse of the operation. Students will be able to identify the missing information, and solve for it using inverse operation, to solve the problem as a whole.Teacher says: Show me thumbs up or down whether they think they achieved the objective. Then teacher Says: write down any questions they are still thinking about on their paper and turn it in and go to recess.

This is the “we do it” phase. Working with partners.

This leads into the “I do it” independent phase.

Extension and challenge.

Independent work time.

Wrap up of lesson, and checking in to see if the students grasped the main point to the lesson.

Making sure the learning targets/objectives are known, and seeing if the students know if they have achieved the target. Plus any remaining questions can be asked, and be addressed at the next math lesson, so all students are ready to move on.

5.6 – Closure – How will the key points of the lesson be articulated? The targets will be explicitly stated at the end of the lesson. Students will be asked to pair share a key point of the lesson with a peer. Then teacher will ask three students at random to share a different key point of the lesson. Teacher continues to call on students until three different key points are collected by class.5.7 – Closure – What questions or prompts will you use to elicit student articulation of their progress towards the attaining the learning target(s)?Students will be asked at the end of the lesson (by show of hands) if they think they need more practice on this lesson. If anyone thinks more practice is needed, more practice or teaching will be elicited to those students.5.8 – Closure – How will students rethink and revise their understanding and work?Once worksheets are checked, students who need to check some problems or need more teaching on the concept, the students will be able to retry the problems and ensure their understanding with the teacher in small groups or one on one.5.9 – Materials – What materials, including community resources and educational technology, will you need in order to teach this lesson?Class set of worksheets, document camera, M&M’s, Big Truck and Car Word Problems Starring Multiplication and Division by: Rebecca Wingard-Nelson.5.10 – Materials – What materials will students need for this lesson?Desks, pencil, eraser, worksheet5.11 – Grouping of students for learning – How will student learning groups be formed?These learning groups will be their desk pods.5.12 – Management and Safety Issues – Are there management and/or safety issues (physical and/or emotional) that need to be considered when teaching this lesson? If so, list them. What will you do to prepare your students for these issues?N/A5.13 – Family involvement – Describe any family involvement that accompanies this lesson. If the lesson does not explicitly require family involvement, then describe how the lesson fits in with the family involvement plan for the unit. Letting parents know how the student is doing in the course may also be part of the planEach week students receive a progress check sheet home, it states how they are doing in math and items they are struggling with. Depending on how students do with this lesson their progress report will reflect it.6. Analysis of Student Work – What was the positive impact of your teaching?Choose three samples of student work representing the full range of student performance. To the extent possible, at least one of these must be from an English language learner and one from a student who represents a particular teaching challenge related to your expectations for this lesson. The third is a sample of your choice.6.1 – What kind(s) of feedback did you give the students?Students received verbal and written feedback on their work sheets. Students who had questions during work time also received verbal feedback.6.2 – How did your feedback encourage students to monitor their own progress and identify support needed to achieve the learning targets?My feedback was positive, and suggested that they themselves recheck problems. I did not mark any points off of this worksheet, as this is a formative assessment and I want students to

continue to learn and work forward from mistakes. Students have a special ability to recognize things when they double check them, which is why I drew attention to mistakes and stated to re-check it instead of saying it was wrong and writing the correct answer. I want students to think and analyze their work to recognize a mistake and fix it themselves.6.3 – For each work sample, discuss what it illustrates about the students’ developing skills and understandings of the academic content as well as growth in academic language. Consider the following questions: To what extent did each student learn what you had intended them to learn? Did he/she meet the learning targets? How? Why? Cite specific evidence from the sample

collected. What do these samples tell you about each of the students in relationship to the PE/Standard of

focus for this lesson? In what areas did each of the students have difficultly? Why? Were the adaptations/accommodations to the lesson appropriate for each of the students? How?

Why? Was the assessment appropriate for these students? How? Why? Are there aspects of the student’s learning that you observed that are not well represented in the

samples? Explain.For each student, they all understood the concept and were able to show that through their work. However, each student did not learn how to use the “KNWS” chart I talked about previously. The learning targets were mostly achieved by each student. For this particular lesson we ran out of time. I plan to have students finish the worksheets this week, thus I will be able to better assess their achievement of the learning targets. Most students had difficulty with the “KNWS” chart. The simplicity of the equations made it difficult to use the chart. However, each student recognized what items needed to be placed under each letter; there just was not enough information to use the chart. I feel as though the “KNWS” chart would be better illustrated with long word problems. Towards the end of the lesson, I told to students not to worry about the “KNWS” chart and that we would go over it later with better problems. This made the students feel better about the worksheet, and stress seemed to be lifted from everyone. This “KNWS” chart really confused the students and made them stressed out because they want to excel and achieve all goals, and this “KNWS” chart was just not applicable to these equations after we got started on solving them. Again, the “KNWS” chart for literacy is not well represented through this worksheet assessment. However, this will be a continuing solving strategy that will be re-taught at a later date.7. Retrospective Reflection – What did you learn about your teaching and student

learning during this lesson?7.1 – Was the lesson taught as planned? If not, what changes were made to the lesson and why?Yes, for the most part. After the students got working on the worksheet, and were demonstrating confusion in the “KNWS” chart, I told them to ignore it and finish the worksheet showing their work. This alleviated stress for the students and allowed them to show their achievement in the objectives of solving problems using the inverse operation and identifying the missing factor.7.2 – To what extent did the whole class or group learn what you intended them to learn? Cite specific examples and/or evidence. This could include student work, mentor teacher observation notes, video, etc.

As shown through student work, the whole class learned the intended items of solving inversely and pin pointing the missing factor. However, the students got confused with a strategy called the “KNWS” chart which was removed part way through the worksheet and will be tended to at a later date.7.3 – What did you learn about your students as learners?These students learn thing so quickly, and retain information. It took them one attempt with my guidance to understand the concept. After I turned them over to work with a partner they were able to solve these problems at a quick pace. The only thing that held them back and was time consuming was the “KNWS” chart.7.4 – What other forms of feedback could you have used? Why?I could have used a method of thumbs up or down during my modeling to make sure the students’ were agreeing with my steps to solve the problem. If someone showed a thumbs down a discussion with talk moves could have started to better their understanding of the lesson.7.5 – What will be your next steps instructionally? Why?The next instructional step would be having them solve more complex or multistep problems that included inverse operations and missing factors. This would include more word problems where they would have to set the equations up and then solve. The “KNWS” chart would a nice addition to the next lesson with better instruction for how to use it. The word problems would be a better way to illustrate its use as well.7.6 – Do you have data to supports these next steps? Explain.Yes. The students’ ability to quickly solve these simple equations tells me that they are ready for the next step. Thus multi-step complex equations and word problems will get their minds thinking deeper into the mathematic world of solving inversely and how to set up equations to do so.7.7 – The next time that you teach this material to a similar group of students, what changes, if any, might you make in planning, instruction and assessment?The only thing I would change in this lesson is removing the “KNWS” chart, which confused these students, and adding it in later on in the unit where it would be most beneficial. The students will better understand and apply it using word problems that have extra information.7.8 – How would the changes improve the learning of students with different needs and characteristics?The changes would allow students to focus on the objective of solving inversely and identifying the missing factor without fretting about making sure the “KNWS” chart was filled in correctly. This would take focus off of a strategy to make sure they understand the problem, and actually practice using the concept of the lesson in full and not distract them from it.7.9 – What have you learned about yourself as a teacher?I have learned that I can adapt and change lessons as I am teaching them to better fit my students. When something is not working I have the amazing ability to catch it right away and adjust my lesson to better suit my students needs. This includes removing confusing material from a lesson and covering that particular material at a later date when it is more appropriate.7.10 – What goals do you have for yourself as you plan future lessons?I plan on collaborating with my mentor teacher to ensure that the problems and material at hand are challenging enough for the students so that they are able to get their minds working and having to think mathematically to solve them. I find too often they complete a lesson

quickly because the material is not challenging enough (for example some equations given to use the new math concepts on are too easy.)