mini edTPA Template Name: Sarah BoresTasks 1­3 Name: Kendall CurleyFall 2013 Name: Ryan McCarthy

Task 1: Planning for Instruction and Assessment

1. Lesson Background Teacher’s Name: Ms. Kathryn Powers School: Winton Woods High School Class: Geometry Date: November 12­13th, 2013

2. Standards / Objectives Topic or Essential Question

What angles are formed when a pair of parallel lines are cut by a transversal? What are the resultingproperties? How can these properties be used to find angle measures?

Standard(s) Addressed: CCSS.Math.Content.HSG­CO.C.9: Prove theorems about lines and angles. Theorems include: vertical

angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent andcorresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly thoseequidistant from the segment’s endpoints.

CCSS.Math.Practice.MP7: Look for and make use of structure. Instructional Content Objectives

Students will successfully identify same­side interior, alternate interior, alternate exterior, and correspondingangles and understand the relationships between these angles.

Students will use knowledge of the angle pair properties to identify congruent and supplementary angles andsolve for missing angle measures.

Students will begin to build an understanding of how these angle pair theorems can serve as reasoning ingeometric proofs (i.e. when given that two angles are congruent, students are able to draw upon theirknowledge of the introduced theorems to explain why such congruence exists).

Assessment of content objectives Informal questions throughout the lecture portion of the lesson will be used to gauge students’

understanding of the parallel line properties. In order to assess the students’ ability to identify the various angle pairs, students will work on a class

activity. They are given a diagram of two parallel lines cut by a transversal and asked to mark same­sideinterior, alternate interior, alternate exterior, corresponding angles, and congruent angles.

On the second day, the students will be working on a group activity, which involves them working in groupsof four to five students to create a poster board displaying the definition, characteristics, and visualexamples of a given angle pair.

For the second half of the second day, students will be given a worksheet assessing them on their abilityto identify angle pairs, find missing angle measures, solve algebraic equations, and analyze errors.

3. Language Academic Language Functions and Forms (including key lesson vocabulary)

Alternate Interior Angles: Angles that reside on the inside of two parallel lines, but on opposite sides ofthe transversal line. These angles are non­adjacent. From the diagram below, angle 4 & 5 and 3 & 6 arealternate interior angles. These angles are congruent.

Alternate Exterior Angles: Angles that reside on the outside of two parallel lines, but on opposite sides ofthe transversal line. These angles are non­adjacent. From the diagram below, angle 1 & 8 and 2 & 7 arealternate exterior angles. These angles are congruent.

Same­side Interior Angles: Angles that reside on the inside of two parallel lines, but on the same side of

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the transversal line. From the diagram below, angle 4 & 6 and 3 & 5 are same­side interior angles. Theseangles are supplementary.

Corresponding Angles: When two parallel lines are cut by a transversal line, corresponding angles arelocated in the same position/location of each intersection. From the diagram below, angle 1 & 5 arecorresponding angles, as are angles 2 & 6, 4 & 8, and 3 & 7. These angles are congruent.

Transversal Line: A line that cuts two or more parallel lines. From the diagram below, diagonal line thatintersects the two other lines is the transversal line.

Parallel Lines: Two or more Coplanar lines that never intersect. From the diagram below, the two linesthat run left to right are parallel lines.

Language Objectives Explain why two angles are alternate interior, alternate exterior, corresponding, same­side angles, or neither. Describe the differences between the properties of alternate interior, alternate exterior, corresponding, and

same­side angles. Use knowledge of language terminology to solve and justify the measures of various angles formed by

parallel lines cut by a transversal.

Assessment of language objectivesStudents will be prompted to identify various angle pairs and explain why the two angles are alternate interior,alternate exterior, corresponding or same­side interior throughout the class activity on day one of the lesson.Students should be able to correctly identify the angle pair, justify their identification, and demonstrate theirknowledge of the properties of the various angle pairs.On day two of the lesson, students will work in groups to make posters describing alternate interior, alternateexterior, corresponding, and same­side interior angles. Students must effectively communicate the definition of eachtype of angles and their respective properties to their peers. The worksheet following this activity will prompt studentsto identify congruent angles and justify their answers with the necessary terminology and reasoning. Furthermore,students will be required to explain, in writing, how and why an example problem is incorrect (error analysis).

4. Differentiation (including accommodations and modifications of content, materials, delivery, activity, assignment,assessment, etc.)Assignment/Assessment DifferentiationMany students work after school and have other outside commitments that take priority over homework. Homeworkassignments are not beneficial to this group of students, as many do not even attempt to complete them. To ensure that thestudents receive quality instruction and practice during class time, they will complete homework worksheets in class with aidfrom teachers and peers. No homework outside of class will be assigned, unless students willingly take the assignmenthome to further complete.

Activity DifferentiationThis particular group of students prefers to be active in their learning experience and engage in hands­on activities. To keepstudents involved in the lesson, creative, hands­on activities are incorporated into each day of the lesson. These activitiesinclude: labeling angle pairs personal diagrams and creating posters in groups on different types of angle pairs and their

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properties.

Content DifferentiationSome of the students are taking algebra and geometry simultaneously, therefore, their algebra skills are not at the level ofother geometry students. To ensure that their limited algebra skills do not hinder their performance in geometry, theproperties and definitions within the lesson will be presented and elaborated on prior to application using algebra. Forexample, students will use actual angle measures to demonstrate their knowledge of angle pair properties prior to usingangle measures represented with variable terms (ex. 3x+7).

Materials DifferentiationAll materials and worksheets will be provided to the students. Furthermore, extra copies will be made to accommodate anyloss of items. Students' learning should not and will not be hindered by any lack of materials.

Delivery DifferentiationThe students at Winton Woods are energetic and easily bored. Thus, we will spend a minimal amount of time on formalnotes, with the majority of our focus being on interactive activities which will deliver information and test studentunderstanding in a nontraditional way.

5. Lesson Sequence (Including opening hook and closure ­ include estimated time allotted next to each phase of thelesson)Day oneOpening (5 Min.): Students complete assigned warm­up to review skills learned throughout the semester in preparation forthe semester exam. Once students complete the warm­up, we will go over the answers as a class.

PowerPoint Presentation on Promethean board (15 Min.): Students will complete the guided notes provided on theproperties of parallel lines. The guided notes ask students to write out the properties of each type of angle pair and mark anexample on their provided diagram of two parallel lines cut by a transversal. Students will concentrate on the properties onthis day as they have already taken notes on the definitions of the various angle pair types (alternate interior, alternateexterior, corresponding, same side interior, and same side exterior). Both the PowerPoint presentation and Guided Notesworksheet are attached as additional PDFs.

Class Activity (25 min): Each student is given an enlarged diagram of a set of parallel lines cut by a transversal and chips tomark specific angles (see attached photo titled, “Diagram Activity Example”). As a class, we will discuss the various anglepairs (alternate interior, alternate exterior, corresponding, same­side exterior, and same­ side interior) and their propertieswhile students practice marking the angle pairs on their personal diagram.Students will be prompted with questions like:

Identify a pair of alternate interior angles. If one of the angles in your pair is 65 degrees, what is the angle measure ofthe other angle? How do you know that?

Identify a pair of same­side interior angles. If I know that one of the angles in the angle pair is 30 degrees and theother angle is 2x­35 degrees, how will I go about finding the value of x? (If students do not know how to properly setup the equation as 2x­35+30=180 because same­side interior angles are supplementary, they will be prompted tothink about the property of same­side interior angles and how the two angles are related)

Do you think we could find the angle measure of each angle knowing only one angle measure?

Day TwoOpening (5 Min.): As a class, we will review the various angle pairs and their respective properties. Students will be remindedthat the angle pair properties only hold when the lines are parallel.

Group Activity (20 Min): Students will be divided into groups of 3­4 to create a poster for an assigned angle pair (see attachedphoto titled, “Student Created Poster Example”). In their poster, students must communicate what it means to be alternateinterior, alternate exterior, corresponding, or same­side interior angles, as well as their properties.Their poster must also

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include a diagram of two parallel lines cut by a transversal labeled with an example of their angle pair. They will assign one ofthe angles in their pair an angle measure and the other an algebraic expression. Each group must be able to explain to theclass how to go about solving for x based on the property of their angle pair (congruent or supplementary). Students maychoose to divide up the roles within their group or collaborate on each part of the poster. Once each group has completedtheir poster (10 min), each group will share their poster with the class.

In­Class Worksheet ( 20 min): Students will work individually on the in­class worksheet, which is provided in the SupportingMaterials section and as an attached PDF.

6. Supporting Materials (include no more than 2 pages of additional materials needed to understand what you and thestudents will be doing)

Geometry Worksheet

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Appendix A: Context for Learning Information (No more than 3 pages for the 3 sections)

Directions: Use the Context for Learning Information to supply information about your school/classroom context.

I. About the School Where You Are Teaching

1. In what type of school do you teach?a. Middle school:b. High school:c. Other (please describe):

2. In what type of community is the school located?a. Urbanb. Suburban (with an urban feel)c. Rurald. Other (please describe):

3. List any special features of your school or classroom setting (e.g., charter, co­ teaching, themed magnet, remedialcourse, honors course) that will affect your teaching in this learning segment.

a. Co­teaching/intervention specialist present in the room due to large number of students with IEP’s. Not onlydoes this specialist act as another authority figure, but is better able to assist students struggling withcertain exceptionalities. This specialist spends the class visiting with the students with IEP’s to assistthem with any issues that they are having as well as making sure they stay focused and on track.

b. Many of the students in this Geometry class are also simultaneously in Algebra 1. Unfortunately this meansthat their Algebra skills are not up to par which impacts their understanding of geometry.

4. Describe any district, school, or cooperating teacher requirements or expectations that might affect your planning ordelivery of instruction, such as required curricula, pacing plan, use of specific instructional strategies, orstandardized tests.

a. School/teachers are required to follow the Ohio Common Core standards/curriculum and many teachershave a book (whether tangible or online) to guide their lessons, instruction, and assessment. Thus, ourlesson will have to match up with the appropriate Common Core standards.

b. School uses Response to Intervention (RTI) as both a placing plan and academic/behavioral disciplinarymethod.

II. About the Class Featured in This Assessment

1. What is the name of this course?a. College Prep (CP) Geometry

2. What is the length of the course?a. One semester:b. One year:c. Other (please describe):

3. What is the class schedule (e.g., 50 minutes every day, 90 minutes every other day)?a. 49 minutes every Monday, Tuesday, Thursday, and Friday and 40 minutes on Wednesday (due to an early

dismissal schedule)

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4. Is there any ability grouping or tracking in mathematics? If so, please describe how it affects your class.a. With RTI, teachers are highly encouraged to give pretests for each section to determine a student’s prior

knowledge and level of understanding in that given topic. Based on the pretest scores, students are dividedinto at most 3 groups. The instruction and content is uniform throughout each group, but assignments canbe modified to appropriately meet the needs of a particular student.

b. However, a pretest will not be given on this section so no differentiated instruction or assignment based onacademic level will be implemented.

5. Identify any textbook or instructional program you primarily use for mathematics instruction. If a textbook, pleaseprovide the title, publisher, and date of publication.

a. Geometry by McDougall Littell (students use for homework problems, additional aid)b. Geometry Common Core by Pearson electronic version, (pearsonsuccessnet.com): used to guide

instruction, create lesson plans, includes additional resources such as worksheets and example problems

6. List other resources (e.g., electronic white board, graphing calculators, online resources) you use for mathematicsinstruction in this class.

a. Promethean Board (electronic white board)b. Calculatorsc. Online Common Core Geometry textbook

III. About the Students in the Class Featured in This Assessment

1. Grade level composition (e.g., all seventh grade; 2 sophomores and 30 juniors):

2. Number of students in the class: 26 Males: 16 Females: 10

3. Complete the chart below to summarize required or needed supports, accommodations or modifications for your studentsthat will affect your instruction in this learning segment. As needed, consult with your cooperating teacher to complete thechart. The first two rows have been completed in italics as examples. Use as many rows as you need.

Consider the variety of learners in your class who may require different strategies/supports oraccommodations/modifications to instruction or assessment.

English language learners Gifted students needing greater support or challenge Students with Individualized Education Programs (IEPs) or 504 plans Struggling readers Underperforming students or those with gaps in academic knowledge

Learning Needs Category Number of Students Supports, Accommodations,Modifications, and/or Pertinent IEP

Goals

English Language Learner (ELL) 2 Visual examples, simplified use ofnon­mathematical vocabulary,encouragement of speaking in nativelanguage

IEP ­ Specific Learning Disability 2 Extra time for worksheet assignment ifneeded, individualized assistance

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504 Plan (Struggling Reader) 1 Delivery accommodations ­ visualexamples, verbal notes, simplified usenon­mathematical vocabulary

IEP ­ Not Identified 3 Extra time for worksheet assignment ifneeded, individualized assistance,presence of Intervention Specialist

Gifted ­ Visual Performing Arts 1 Flexibility in requirements forcompletion learning activities allowingfor creativity, multiple opportunities tointeract with tangible materials anddraw

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Appendix B: Planning Commentary

Directions: Respond to the prompts below (no more than 9 single­spaced pages, including prompts).

I. Central Focus

1. Describe the central focus and purpose for the content you will teach in this learning segment.The central focus of this lesson will be to build both a procedural and conceptual understanding of the angleproperties of parallel lines. Since a foundational knowledge of the angle properties and methods of identification isneeded, our first day of instructional will be focused on building procedural knowledge ­ vocabulary, definitions,properties, diagrams, etc. Thus, our first day activity will be purposeful and meaningful for creating this necessarybasic knowledge.

The second day will be focused on developing deeper understanding and the realization that the definitions andproperties are to be used for more specific problems. The posters and worksheet will be implemented to fulfill thepurpose of strengthening problem solving skills and conceptual understanding. The content that will be coveredcombines the new material as well as algebra skills, such as setting up and solving equations. The purpose of thismulti­faceted content is to reinforce new and old ideas and demonstrate the vital and prominent relationship betweenvarious mathematical concepts.

2. Given the central focus, describe how the standards and learning objectives within your learning segment address

a. conceptual understandingi. The main standard to be addressed in this unit is "to prove theorems about lines and angles".

Geometric proofs are arguably the greatest example of conceptual knowledge. Students not onlyhave to understand the basic language terminology and solve problems, but work backwards injustifying each step of a proof.

ii. While our two day lesson will not directly address proofs, the learning objectives begin to build thenecessary conceptual understanding. The students will be expected to justify why various anglesare congruent as well as describe angle relationships.

b. procedural fluencyi. Procedural fluency is addressed in the lesson as we will expect the students to effectively describe,

label, and identify the various angle pairs formed by parallel lines cut by a transversal.ii. Furthermore, they will be expected to use their past algebra knowledge to solve algebraic equations

to later find missing angle measures.c. mathematical reasoning and/or problem solving skills

i. The biggest example of mathematical reasoning and problem solving skills will accompany theproblems asking students to solve for missing angle measures. One of our learning objectives isthat students will be able to complete these problems using their knowledge of angle pair propertiesand setting up and solving equations.

ii. Students will first have to read and understand what the problem is asking and then shuffle throughthe various methods of solving it. Identifying the angle pair relationships and setting up an algebraicequations from those properties is a major learning objective and the strongest case for thedemonstration of students' problem solving skills.

3. Explain how your plan builds on lessons that came before to help students make connections between facts,concepts, and procedures, and to develop their reasoning and/or problem solving skills to deepen their learning ofmathematics.

a. The lesson that will precede ours introduced the students to the various angle pairs that are formed by twolines cut by a transversal. Our lesson will dig deeper and build on that knowledge by discussing the variousproperties (such as congruence and supplements) that occur when the two lines cut by a transversal are

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parallel. The previous lesson will also go over the formal definitions of parallel lines and a transversal, termsthat will be frequently used in our lesson.

b. Earlier in the semester, the students were taught about other kinds of angle pairs (such as vertical andsupplementary angles). Our lesson builds on that knowledge as the term "supplementary" will be frequentlyused and the presence of vertical angles can be used to justify angle congruence. By instructing students toutilize past knowledge, we will be improving their problem solving skills and ability to reason mathematically.

c. Finally, students will be expected to utilize their algebraic skills to set up and solve equations for missingangle measures. These types of problems will require students to draw upon previous knowledge as well asthe new material from our lesson to solve problems and visualize and identify relationships. It is our goal thatthis lesson will deepen the students' understanding of the strong connections between various mathdisciplines and thus, stress the importance of continually practicing "old" material.

II. Knowledge of Students to Inform TeachingFor each of the prompts below (II.1–3), describe what you know about your students with respect to the central focus of thelearning segment.

1. Prior academic learning and prerequisite skills related to the central focus—What do students know, what can theydo, and what are they learning to do?

Prior to teaching this lesson, students can identify, communicate, and apply angles in a mathematical context.Students have also been introduced to various pairs of angles involving intersecting lines and the properties that areassociated with them. These pairs of angles include complementary, vertical, linear pairs, supplementary, andadjacent. Majority of students have successfully completed Algebra I and have been taught how to create and solvemulti­variable equations.

However, just because the students have been presented with such content does not indicate mastery. They are stillgrappling with connecting particular past topics such as algebra with current topics. Thus, they are learning to usetheir prior knowledge to aid in any and all problem solving. For example, in a question asking a student to solve formissing angle measures that are labeled with algebra expressions, he or she will be expected to practice drawing onknowledge of setting up equations, identifying angle pairs, and utilizing known properties.

2. Personal/cultural/community assets related to the central focus—What do you know about your students’ everydayexperiences, cultural backgrounds and practices, and interests?

a. The central focus of the lesson will be directed at the procedural and conceptual understanding of theproperties of parallel lines. Because of our observations on the students, we will narrow our focus andpersonalize our lesson to involve the culture of the school.

b. Students at Winton Woods are active, spirited, and opinionated. They are not comfortable with or interestedin daily lectures and note­taking and using these types of instruction often results in a poor managedclassroom. Therefore our focus and learning objectives will be achieved largely through in­class, hands­onactivities. Our students also enjoy using technology in their everyday lives, so we will be leveraging thePromethean board during instruction. The students will be actively involved in their learning and will engagein opportunities to create their own artifacts and sharing their newfound knowledge with peers.

c. Furthermore, we have observed that the students' retention and motivation to complete homework is poor.Unfortunately, this is not ideal to building student understanding of the concepts. Therefore, our lesson'sfocus and activities will need to reflect this. It is our plan to integrate student culture and preferences inallotting class time to complete practice problems ­ an assignment that would traditionally be viewed ashomework material.

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3. Mathematical dispositions—What do you know about the extent to which your studentsa. perceive mathematics as “sensible, useful, and worthwhile”

i. Very few, even those students who easily grasp new mathematical knowledge and theories have apositive disposition toward mathematics. Several students in the class do not write notes evenwhen they are prompted to write the information down because that particular information will be onthe test. These same students do not copy down examples that were discussed in class even onhomework that was to be turned in for a grade.

b. persist in applying mathematics to solve problemsi. Again, very few. If a student does not know how to start a problem or even what the problem is

asking, he or she does not even try or consult his or her notes. Many students in the class do nottry problems unless a teacher stands over them to make sure they were doing their work, especiallywith the warm up problems that are given each day. Several students in the class get frustratedwith a problem and ask for help, and then get even more frustrated when they are not given theanswer, and tend to give up without being pushed.

c. believe in their ability to learn mathematicsi. As mentioned earlier, students tend to give up easily and have the belief that the math is too difficult

for them to understand or to learn. When students are “tutored” and they figure out the solution,they believe that they can do it, but many students do not feel that they are able to figure outmathematics on their own ­ scaffolding is necessary to foster motivation.

III. Supporting Students’ Mathematics LearningDirections: Respond to prompts below (III. 1–3). As needed, refer to the instructional materials and the lesson plan you haveincluded to support your explanations. Use principles from research and/or theory to support your explanations, whereappropriate.

1. Explain how your understanding of your students’ prior academic learning, personal/cultural/community assets, andmathematical dispositions (from prompts II. 1–3 above) guided your choice or adaptation of learning tasks andmaterials.

Our understanding of the students’ prior academic learning, cultural and community assets, and mathematicaldispositions will be used to guide every aspect of our lesson.

We will use students’ prior academic learning as a basis and foundation to expand student growth. We willcapitalize on the students’ prior knowledge of learning several types of angle pairs and how to solve an equation tobuild connections to more angle pairs and properties of parallel lines. By using these connections, we will be able tobuild more concrete conceptual understanding.

We will use our knowledge of the students’ cultural and community assets to gear on how to effectively use activitiesand instruction to expand student growth. The students at Winton Woods High School prefer instruction to beinteractive, varied, and meaningful. We will utilize this understanding of the school’s culture to gear our lesson to beinteractive with various styles of instruction. We will incorporate former instruction, hands­on models, artifactcreation, and worksheet practice to gain deeper understand of the content material and learning tasks.

We will use our understanding of the students’ mathematical dispositions to incorporate powerful, meaningful, andeffective real­world examples in the instruction. The students at Winton Woods High School select to understandand master only skills necessary for post­graduate life. Students constantly ask, “When will I use this in real life?”With this knowledge, we will be able to incorporate meaningful examples of how this information is important andapplicable to the students’ personal lives. Without these meaningful examples, students will become disengagedand the lesson will not be effective.

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2. Describe and justify why your instructional strategies and planned supports are appropriate for the whole class andstudents with similar or specific learning needs.

One instructional strategy we will utilize to insure knowledge retention with all of ourstudents is Bruner’s Stages of Representations. Concepts will be represented in allthree stages of Bruner’s model. For the first level, hands­on/enactive stage, eachstudent will be provided a diagram of parallel lines cut by a transversal and twotokens. Directly following formal instruction, students will be given several tasks toidentify a particular pair of angles. The picture to the right is an example of theactivity.

For the second stage of Bruner’s model, iconic/drawings, we will have students formgroups to create a poster of a particular property. The students are to draw a parallellines cut by a transversal, label the angles of the property they will be given, provide ageneric algebraic equation to find the angle measurement, and write the characteristics of those angles (i.e.

congruent, supplementary). The groups will then share their posters to theclass. The picture to the left is an example of what is expected from thestudents during this exercise.

For the third stage, symbolic writing and mathematical symbolism, we will havestudents complete a working testing their ability to solve math problems usingthe knowledge from this lesson and previous lessons. Such symbolic andmathematics writing will take place as students will be required to set up andsolve algebraic equations as well as identify and justify angle congruence. (Tosee copy of worksheet, return to learning materials section after the lessonsequence and/or Task 3­ examples of student work.)

We will also be utilizing Vygotsky’s Zone of Proximal Development (ZPD).Zygotsky’s ZPD model is the theory that student learning can be expanded byusing the student’s prior knowledge and setting the goals within reach of thestudents development. This strategy allows students to use their prior

knowledge and build connections to more advanced mathematical content. The lesson prior consisted of learningcomplementary, supplementary, vertical, linear pair, and adjacent angles and reviewing how to solve equations.With this prior knowledge, students will be able to expand their learning growth to incorporate more pairs of anglesand properties of parallel lines.

3. Describe common mathematical preconceptions, errors, or misunderstandings within your content focus and howyou will address them.

The biggest area for misconception and error is with the terminology of the properties. Students will commonly useterminology interchangeably. For example, when trying to identify corresponding angles, students might state themas same­side interior or another property. Knowing that this is a common error among our students, we will providesimplified definitions for students during formal instruction. By eliminating confusing and advanced mathematicallanguage, we will allow students to understand the properties of parallel lines in their own language. Another way wewill address this common error is to post the student­created posters (as described in III.2) on the wall for thestudents to reference when needed.

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IV. Supporting Mathematics Development Through Language

1. Language Demand: Language Function. Identify one language function essential for students to learn themathematics within your central focus (e.g., compare/contrast, conjecture, describe, explain, prove). You maychoose one of these or another more appropriate for your learning segment.

The ability to explain how to find various angle measures is key within this lesson as adeep understanding of the definition of various angle pairs, as well as their properties, isnecessary to find other angle measures. Students will need to explain their thinkingorally during the class activity on day one, in creating their posters with group memberson day two, and in writing on the in­class worksheet on day two.

2. Identify a key learning task from your plan that provides students with opportunities topractice using the language function.

The class activity on day one of the lesson asks students to find an angle measuregiven the angle measure of the other angle in the angle pair. For example, if studentsare given the angle measure of the one of the chips pictured below is 115 degrees andasked to find the angle measure of the second chip, they should respond with 115 degrees. Students will beprompted to explain how they know that the second angle is 115 degrees using correct terminology and properties.They will need to explain that the angles are alternate exterior angles and alternate exterior angles arecongruent.They will also need to explain that they can use the fact that alternate exterior angles are congruentbecause the two lines on their diagram are parallel.

3. Additional Language Demands. Given the language function and task identified above, describe the followingassociated language demands (written or oral) students need to understand and/or use.

a. Vocabulary and/or symbols

When explaining how they know the measure of an unknown angle, students will need to have a good graspon the angle pair terminology such as: alternate interior, alternate exterior, same­side interior, same­sideexterior, and corresponding. They should understand that alternate or same­side refers to the angles’location with respect to the transversal (same side or different sides) and interior or exterior refers to theangles’ location with respect to the parallel lines (inside or outside of). They will use this terminology toidentify how the two angles, both known and unknown, are related so they can identify the correct propertybased on the angle pair. Once they identify the angle pair and its respective property, they will also need tounderstand the meaning of “congruent” and “supplementary.” They should be able to explain thatcongruent means to have the same angle measure and supplementary means that the two angle measuressum to 180 degrees. Students must also recognize that in order to argue that the various angle pairproperties are true, the lines must be parallel. Students

b. Mathematical precision (e.g., using clear definitions, labeling axes, specifying units of measure, statingmeaning of symbols), appropriate to your students’ mathematical and language development

It is extremely important that students can easily distinguish between the various angle pairs and theirproperties. In order to identify the angle pair, students must be able to recognize lines as parallel cut by atransversal. Parallel lines will be indicated by the small parallel marks on each of the lines or the fact thatthe lines are parallel will be clearly stated. Students must then be able to accurately identify alternateinterior, same­side interior, alternate exterior, same­side exterior, and corresponding angles. After correctlyidentifying the angle pair, students should be able to clearly articulate the angle pair’s respective property aseither supplementary or congruent.

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c. Plus syntax or discourse.To spark a conversation about the relationships between the various angle pairs, we will prompt the classwith the following questions:

Can we determine the measure of all angles in the diagram given only one angle measure? Once a student provides an answer and an explanation, Does anyone agree or disagree with their

response? Why? Are their multiple ways to justify why an angle measure is that particular degree measure? I.e. Are

their multiple ways to justify congruence?We want students to be able to articulate their justifications for why angles are supplementary or congruent.Engaging in class discussion will allow students to explain their thinking and collaborate with peers.

4. Language Supports. Refer to your lesson plan and instructional materials as needed in your response to theprompt. Describe the instructional supports (during and/or prior to the learning task) that help students understandand successfully use the language function and additional language identified in prompts IV 1–3.

Prior to this lesson, students will learn the definitions of the various angle pairs (alternate interior, same­side interior,alternate exterior, same­side exterior, and corresponding). The guided notes taken during the PowerPointpresentation will reinforce identifying angle pairs by their location with respect to the parallel lines and thetransversal. Starting with the diagram activity and class discussion on day one of the lesson, students will be askedto identify specific angle pairs and use their properties to explain relationships to other angles in the diagram.Throughout the task and discussion, students will need to correctly utilize the key vocabulary, alternate interior,same­side interior, alternate exterior, same­side exterior, corresponding, parallel, transversal, supplementary andcongruent, in an effort to explain their responses. On day two, students, in groups, will manipulate the necessarylanguage to communicate the definition and property of their assigned angle pair. The poster activity also asksstudents to explain to the class how they would set up and solve an algebraic expression using their angle pair’sgiven property. Following the poster activity, students will complete an in­class worksheet that assess theirunderstanding of the angle pairs and their properties. Questions 1­7 on the worksheet ask students to identify allangles congruent to a given angle or find a measure of a specific angle. For each question, students must use thekey vocabulary to explain why an angle is congruent to the given angle or why an angle measure is a certainmeasure. Question 11, an error analysis question, allows students to once again use the terminology stressedthroughout the lesson to explain why a provided solution is correct or incorrect.

V. Monitoring Student Learning. Refer to the assessments you will submit as part of the materials for Task 1.

1. Describe how your planned formal and informal assessments will provide direct evidence of students’ conceptualunderstanding, procedural fluency, and mathematical reasoning and/or problem solving skills throughout the learningsegment.

Formal Assessment: The worksheet activity will be our main form of formal assessment. The questions that will beasked on the worksheet will assess the students’ conceptual understanding, procedural fluency, and problemsolving. Questions 1­7 will assess the students’ procedural fluency. These questions are geared for students toshow their fluency and knowledge of the step­by­step procedures to solve the problems. Questions 8­10 will assessthe students’ problem solving skills. These questions are geared to assess the students’ skills to interpret, set­up,and solve a problem. The final question, number 11, will assess the students’ conceptual understanding. The erroranalysis problem is designed for students to show their ability to identify the incorrect “solution” and justify why it isincorrect by using their understanding of the concepts discussed during the prior two days of lesson. The questionscan be found by referencing Part 6: Supporting Material Geometry Worksheet (pg. 4­5).

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Informal Assessment: There are multiple assessments we will utilize during instruction to assess the students’conceptual understanding, procedural fluency, and problem solving. We will assess conceptual understanding byprompting students to use justification and reasoning to explain their chosen answers. We will also assessconceptual understanding by prompting students to agree or disagree with another student’s answer and providejustification. We will assess procedural fluency through the in­class diagram activity. We will propose severalproblems involving angle pairs during this activity and students will use their diagram to show direct evidence of howfluent they are at understanding the procedures of identification. We will assess problem­solving skills through theactivity of setting up equations to find angle measurements using algebraic equations. Students will need to identifywhether or not the angles are supplementary or congruent, set­up the algebraic equation and then solve for the givenvariable.

2. Explain how the design or adaptation of your planned assessments allows students with specific needs todemonstrate their learning.

In our classroom, we will have the presence of English Language Learners (ELL), students with learning disabilities,gifted students, and various other students on Individualized Education Programs (IEP).

Our lesson plan will address each of these specific needs in particular, yet subtle ways. Those students whose firstlanguage is not English are placed on a pass/fail scale for all content courses. Thus, mastery of the material will notbe the main focus, but instead it will be giving opportunities for the ELL students to practice the English languageand use math terminology. Our diagram and poster activities will allow such students to explain their thinkingprocesses aloud to their peers. Furthermore, we recognized the importance of maintaining one’s native culture, thuswe will provide and allow opportunities for these students to interact in their first language. Group work andinteraction with peers will also be a major component in the lesson aiding the English language learners’’ classroomexperience.

In terms of accommodations, our lesson plan, instruction, and planned assessments will be composed of simplifiednon­math language so as to direct the focus to the pertinent content vocabulary. Visual examples will also beimportant in communicating the new content to ELL students as well as to any struggling readers.

Furthermore, with struggling readers and those individuals on IEPs, additional assistance (in the form of either acooperating teacher, classmate, or intervention specialist) will be readily available as needed. Deadlines for theassigned worksheet can and will be extended if necessary to accommodate those students with exceptionalities.

Lastly, our lesson plan consists of three major learning activities that will act as planned assessments ­ diagramangle identification, creation of posters, and the worksheet. Each activity will stress the content in a different andimportant way, allowing students with any disabilities or learning style preferences to have ample opportunities tograsp the new material. This variety of assessment will also provide the visual­artistically gifted student chances toexpress and understand the content through drawings and tactile activities.

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Task 2: Instructing and Engaging Students in Learning

I. VideoDirections: Include link to 1 or 2 YouTube videos HERE. Total time of all video should not exceed 2 minutes. Provide thelink(s) to the video directly within this Google Document. The sharing settings of the video should be set to “unlisted” toprotect student privacy. Use the “blur all faces” feature (under enhancements) to further protect identities of participants.

Video Link:

Students Identifying Alternate Exterior Angles on Board http://www.youtube.com/watch?v=0GG_pDTpRNk

Student Completes Error Analysis http://www.youtube.com/watch?v=9mH3y1iCqK4

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II. Instruction CommentaryDirections: Write the Instruction Commentary (no more than 3 single­spaced pages, including prompts) by providing yourresponse to each of the prompts below.

1. Promoting a Positive Learning EnvironmentRefer to scenes in the video clip where you provided a positive learning environment (include reference to exact timeswithin the video).

a. How did you demonstrate mutual respect for, rapport with, and responsiveness to students with varied needsand backgrounds, and challenge students to engage in learning?We demonstrated mutual respect and rapport with our students in several moments during the video clips.In the video title, “Students Identifying Alternate Exterior Angles on Board”, between the 14­19 and 35­41second mark, Ms. Curley builds our rapport and demonstrates respect for the students by politely callingstudents who volunteered to answer the in­class activity answers.

We were also responsive to students with various needs and backgrounds. In the video titled, StudentCompletes Error Analysis, at the 13, 35, and 47 second mark, Ms. Bores is responding to a student’sanalysis of a worksheet problem. The student in the video is identified as a gifted student. Gifted studentsrequire additional tasks that stretch their level of understanding. Ms. Bores is providing open questionsduring this interaction to push the student to think deeper about the problem in front of her.

We challenged students to engage in learning by provided students with in­class tasks. At the ## secondmark of the Alternate Exterior Angle video, Ms. Curley challenges students to use their diagram and chipsto identify a pair of alternate exterior angles. Also during the Error Analysis video, at the 35 and 47 secondmark, Ms. Bores challenges the student with follow­up questions to engage the student to think deeperconceptually.

2. Engaging Students in LearningRefer to examples from the clip in your explanations (include reference to exact times within the video).

a. Explain how your instruction engaged students in developingi. conceptual understanding

The video clip titled “Student Completes Error Analysis” consists of a student interacting and explaining herthought process for Question #11 on the worksheet assignment. Throughout the clip, the student madecomments about why one answer was correct and the other was not. At the 6 second timestamp, thestudent states that the first choice is correct, because she recognizes that the angles identified withalgebraic expressions are congruent. At the 19 second mark, the student identifies the second expressionto be incorrect. She states that second answer sets up answer in the context that the two angles aresupplementary. She states later, between the 11­19 second mark, the angles are congruent, because theyare alternate interior angles. At the end of the video, 49 second mark, she states that she can say alternateinterior angles are congruent, because the lines are parallel. She knows the lines are parallel, because thediagram shows the parallel markers on the two lines.

This shows conceptual understanding, because she is given an abstract question involving severalmathematical concepts from this lesson and prior lessons. She used her formal mathematicalunderstandings from the lesson about the properties of parallel lines and prior lessons about solvingequations algebraic to analyze the options, describe what is happening with both of the selections, andexplain what occurred. The explanation shows direct evidence that the student understands themathematical concept, because she uses the lesson’s mathematical terminology and properties andcharacteristics of parallel lines and their angles.

ii. procedural fluencyOur instruction engaged students in procedural fluency through repetition of identifying angle pairs of parallel

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lines when cut by a transversal. In the video titled, “Students Identifying Alternate Exterior Angles onBoard,” at the 5 second mark, the student is using the diagram to identify a pair of alternate exterior angles.During this exercise, Ms. Curley tasked the students to identify each angle pair at least once. Afteridentifying the angle pair, Ms. Curley then tasked students to identify the angle pair on the Prometheanboard. At the 44 and 57 second mark, two students approach the board to identify a pair of alternateexterior angles. Once again, through repetition and practice, the students became fluent in identifyingvarious angle pairs.

iii. mathematical reasoning and/or problem solving skillsOur instruction engaged students in mathematical reasoning and problem solving through various problemson the activity worksheet. Specifically, between the 3 and 12 second mark in the Error Analysis video, thestudent is using her problem solving skills and mathematical reasoning when describing that the two anglesin questioned are congruent and not supplementary. At the 19 second mark, she says, “This one is wrong,because it says 4x­2 +3x­6 = 180 and these two angles don’t equal 180; they are congruent.” She is usingthe reasoning and skills she acquired through our instruction and prior instructions to dissect the erroranalysis the problem.

b. Describe how your instruction linked students’ prior academic learning and personal, cultural, andcommunity assets with new learning.The video clip titled, “Students Identifying Alternate Exterior Angles on Board” consists of students usinghands­on diagrams and the Promethean board to identify alternate exterior angles. As stated earlier, inSection II.2, the culture of our classroom at Winton Woods High School appreciates various teachingmethods with minimum formal note taking. The video opens with Ms. Curley giving the students with thetask of identifying a pair of alternate exterior angles. Students are prompted to describe the location ofalternate exterior angles in relation to the transversal and the parallel lines. Such knowledge was learned inthe lesson prior, but was touched upon again because retention is a growing problem for this group ofstudents. At 5 second mark, the student is shown to use the tokens to mark a pair of alternate exteriorangles. At the 44 and 57 second mark, Ms. Curley incorporates student participation by having studentsidentify multiple pairs of alternate exterior angles.

3. Deepening Student Learning during InstructionRefer to examples from the clip in your explanations (provide references to specific times within the video in yourresponses).

a. Explain how you elicited and responded to student responses to promote thinking and develop conceptualunderstanding, procedural fluency, and mathematical reasoning and/or problem solving skills.We elicited student responses to promote conceptual understanding and mathematical reasoning throughasking open­ended questions. As stated in Task 2 Section II Question 1, Ms. Bores elicited a student toexplain her mathematical reasoning and conceptual understanding. In the video titled, Student CompletesError Analysis, at the 13, 35, and 47 second mark, Ms. Bores is providing open questions during thisinteraction to push the student to think deeper about the problem in front of her.

We responded to student responses to promote procedural fluency through formal instruction and clarifyingstudent responses. In the Alternate Exterior Angles video, between the 19­35 second mark, Ms. Curleyclarifies the student responses about alternate exterior angles through formal instruction and asked follow­upquestions to cement the students’ ability to fluently identify alternate exterior angles.

b. Explain how you used representations to support students’ understanding and use of mathematicalconcepts and procedures.We used visual representations through the usage of hands­on diagrams, interacting with the digitalrepresentation on the Promethean board, creating “properties of parallel lines” posters, and diagrams viaworksheet problems to support students’ understanding of mathematical concept and procedures. During

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the Alternate Exterior Angle video, at the 5 second mark, the student is interacting with the hands­ondiagrams. At the 44 and 57 second mark of the same video, two students are interacting with therepresentation of the Promethean board. Throughout the whole Error Analysis video, the student is workingon the worksheet assignment with numerous visual representations. Although the posters aren’t in the videoclips, you can see the final product of the poster on page 13.

4. Analyzing Teachinga. How did your instruction support learning for the whole class and students who need greater support or

challenge?Our instruction supported learning for the whole class by utilizing the three stages of Bruner’s model andVygotsky’s Zone of Proximal Development (ZPD), as discussed in Section III.2 in Task 1. By using priorknowledge and three various methods of instruction, we were able to support the numerous cognitive skilllevels and preferred learning styles that composed our classroom.

For students that needed greater support, our instruction provided individualized assistance during theworksheet portion. We assisted students who were having troubles comprehending what the question wasasking. For students who were struggling readers or ELL, numerous methods (student­created posters,worksheet problems, diagram activity) were geared towards visual learners.

For students that needed greater challenge, our instruction provided numerous problems that involved higherlevels of cognitive skills. We also took time to meet with the gifted students individually to ask challengingquestions follow­up questions that pushed their conceptual, procedural, and problem solving skills.

Consider the variety of learners in your class who may require different strategies/support (e.g., students with IEPs,English language learners, struggling readers, underperforming students or those with gaps in academic knowledge,and/or gifted students).

b. What changes would you make to your instruction to better support student learning of the central focus(e.g., missed opportunities)?One aspect of our instruction that we would change would be to provide more modeled and guided practicefor problems consistent with the design of #7 on the worksheet. Students struggled with the ability toconceptualize and problem solve that the trapezoid shape can be viewed as parallel lines cut by twoseparate transversal lines instead of only one. Also the trapezoid consisted of segments and rays insteadof the traditional representation of the lines.

Another aspect of our instruction that we would like to incorporate to better support student learning is tohave more specific feedback delivered on a more individualized level during formal instruction and activities.Feedback is a powerful tool to help guide students towards correct conceptual understanding, proceduralfluency, and mathematical reasoning.

c. Why do you think these changes would improve student learning? Support your explanation with evidence ofstudent learning and principles from theory and/or research as appropriate.These changes would improve student learning, because it would increase their conceptual understanding,procedural fluency, and mathematical reasoning. We want out students to become more abstract thinkersand to be able to break down a problem in more manageable parts. These changes will be incorporatedusing the scaffolding model. We will use modeling, guided practice, feedback, and individual practice to leadto student subject mastery. Furthermore, we do not want to to challenge the students too early. Afterreflecting on the lesson, we realized that some of the problems on the worksheet were out of the students’zone of proximal development. Thus these changes would address suit student needs and academic levelsto best foster student learning.

Task 3: Assessing Student Learning

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I. Student Work Samples with Feedback You Provided (3 samples inserted as images directly within this Google Doc)

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II. Assessment Commentary (no more than 3 single­spaced pages)Directions: Write the Assessment Commentary by providing your response to each of the prompts below.

1. Analyzing Student Learninga. Identify the specific standards/objectives from the lesson plan measured by the assessment chosen for

analysis. Standard(s) Addressed:

CCSS.Math.Content.HSG­CO.C.9: Prove theorems about lines and angles. Theorems include: verticalangles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent andcorresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly thoseequidistant from the segment’s endpoints.

CCSS.Math.Practice.MP7: Look for and make use of structure. Instructional Content Objectives:

Students will successfully identify same­side interior, alternate interior, alternate exterior, and correspondingangles and understand the relationships between these angles.

Students will use knowledge of the angle pair properties to identify congruent and supplementary angles andsolve for missing angle measures.

Students will begin to build an understanding of how these angle pair theorems can serve as reasoning ingeometric proofs (i.e. when given that two angles are congruent, students are able to draw upon theirknowledge of the introduced theorems to explain why such congruence exists).

The questions from the worksheet were provided by the Pearson textbook. The textbook was written using theCommon Core State Standards for each lesson. This allows for a direct connection between the state standardsand the students’ understanding.

b. Provide the evaluation criteria you are using to analyze the student learning (insert scoring guidelines here).The actual assessment (worksheet) was graded based on completion because of the student's tendency to ignoreany assigned work. However, when looking over the student work and providing feedback, we used three evaluativecriteria to reflect on the effectiveness of our instruction and the depth of student learning.

Mathematical Precision1. One third of the criteria used to analyze student learning was based on a correct and complete answer. For

example, the first part of the worksheet was often not performed to completion, i.e., only three congruentangles were identified when there were six.

Evidence of Justification1. Just as important is the evidence of student reasoning and conceptual understanding through written

justification. I.e., why are said angles congruent?2. Students must provide correct justification when prompted.

Use of Mathematical Language1. Do students use the mathematical language of the lesson in their explanations? I.e., instead of saying two

angles are the "same" , are they using the term "congruent" and justify the congruence using knowledge ofangle pairs.

c. Provide a graphic (table or chart) or narrative summary of student learning for your whole class. Be sure tosummarize student learning for all evaluation criteria described above.

MathematicalPrecision

­The majority of students were not complete in their answers when prompted to list congruent angles.­Furthermore, the precision of students’ algebra skills is severely lacking and their inability to set up andsolve basic algebraic equations is stunning.­On the other hand, students did demonstrate mathematical precision when asked to find missing anglemeasures (where algebraic expressions were not involved). They could, for the most part, successfullymatch up congruent angles measures and assign them identical values.

Evidence ofJustification

­The majority of students provided a sufficient justification for their answers when prompted.­Occasionally we would have to remind them to write this justification (which has to do more withcompletion of the problem), but having to explain that two angles are congruent because they arealternate interior was not a prominent struggle among the class.

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Use ofMathematicalLanguage

­The use of mathematical language somewhat goes hand in hand with justification and mathematicalprecision. In order to give the most precise and complete answer, a student should be able to correctlyanswer the problem and provide an appropriate justification using mathematical language from thelesson.­Unfortunately, the students’ use of such language did not meet our expectations. Instead of using theterm “congruent”, many students would just say “the same” either in writing or answering questions inclass. Similarly, students would have a difficult time recalling the necessary terms from the section tobuild their justification.­Even though we attempted to continually use the important mathematical terminology throughout thelesson and prompted students to do the same, a greater focus on such language could be implementedin order to ensure better understanding of the material.

d. Use evidence found in the 3 student work samples and the whole class summary to analyze the patterns oflearning for the whole class and differences for groups or individual learners relative to conceptualunderstanding, procedural fluency, and problem solving.

Conceptual Understanding: The students clearly demonstrated their conceptual understanding of properties ofparallel lines on the error analysis portion of the assessment worksheet. Each of the three focus students accuratelyidentified the incorrect solution. Students A and C both reasoned that solution b was incorrect because the givenangles are congruent and not supplementary. Student C gave further reasoning that the angles are congruentbecause they are alternate interior angles. Each of the focus students, as well as, many other students in the classrecognized that the angles are congruent, therefore, the algebraic expressions should be set equal to each other tofind the value of x. A common problem was justifying why a pair of angles are congruent or supplementary. As aclass, the majority of students grasped the concepts presented fairly easily and were able to easily identify theangles and use their properties to solve problems.Procedural Fluency: In questions 1­4 of the worksheet, students were often unable to identify all of the anglescongruent to the given angle. In each of the student work samples, the student correctly identifies at least onecongruent angle, but fails to recognize that there are several angles that are congruent to the given angle for variousreasons. As a whole, the class lacked perseverance in mathematics and problem solving, which was demonstratedwhen students gave up within a each problem after finding one congruent angle. Once a congruent angle wasidentified, students were able to provide an accurate justification for the congruency based upon properties of thevarious angle pairs described in the lesson. Students A and C provided explanations for the angles they identified ascongruent, but either did not connect the angle to its respective property or failed to provide a justification for eachangle identified. For example, Student A listed three congruent angles and two justifications, vertical and alternateinterior. The student is not specific when providing an angle pair with its proper justification. It is unclear as to whichangle is vertical or alternate interior to which angle and no justification is given for the third angle listed. As a class,the students demonstrated a strong grasp on angle pair identification and their respective properties, butexperienced difficulty when providing clear, organized explanations.Problem Solving: The students demonstrated their problem­solving techniques and strategies on questions 9, 10,and 11 of the worksheet. Question 10 pushed students to recognize parallel lines cut by a transversal in othergeometric shapes. Students A and C, as well as many other students in the class, struggled when multiple variableswere introduced. They wanted to immediately relate two of the expressions and solve for each variable instead ofnoticing the multiple relationships that exist between the expressions. Student A recognized the multiplerelationships and set up the proper equations, but only found the value of one variable. Question 11, the erroranalysis problem, challenged students ability to identify the angle pair and recognize the correct procedure forsolving for the unknown variable. Students had to use their knowledge that alternate interior angles are congruent torecognize that the solution where the expressions were summed and set equal to 180 is incorrect. The class had asolid grasp on setting up equations to solve for unknown variables based upon the angle pairs being congruent orsupplementary. Most of the students in the class, like the focus students, were able to articulate using propermathematical language why one problem solving strategy was correct or incorrect.

2. Feedback to Guide Further LearningExplain how feedback provided to the three focus students addresses their individual strengths and needs relative to

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the standards/objectives measured.Each of the three focus students received comments throughout their worksheet acknowledging correct thoughtsand explanations, and prompting them to think about questions where they answered incorrectly or needed furtherjustification. All three of the focus students demonstrated a quality understanding of naming the various angle pairsand using their respective properties to solve problems, but were sometimes lacking clarity within key aspects oftheir justification. The feedback outlined where additional justification or explanation is required for a completeresponse in an effort to prepare them for the next lesson involving geometric proofs. The goal of this lesson was toexpose students to using properties of various angle pairs to justify a claim. The feedback on the assessmentworksheet will help to strengthen their ability to reason with properties of parallel lines.

3. Evidence of Language Understanding and UseExplain the extent to which your students were able to use language (targeted function, vocabulary, and additionalidentified demands) to develop content understandings.

Throughout the lesson, the students were continually prompted to use the important language of the unit.During in­class discussions, we required that students justify their proclamation of congruence of certain angles withthe terminology and properties.Thus when prompted, students would correctly verbally use the language to developan understanding of the content. Ideally, the students would justify their conclusions about angles without scaffoldingbecause that would show a deep understanding of the topic.

Nevertheless, there was evidence in both the video and worksheet that students had a basic understandingof the applications of angles formed by parallel lines cut by a transversal. For example, the first problems on theworksheet ask the student to identify angles congruent to the given angle and justify. This requires that studentsemploy the required language functions: Use knowledge of language terminology to solve and justify the measures ofvarious angles formed by parallel lines cut by a transversal.

4. Using Assessment to Inform Instructiona. Based on your analysis of student learning presented in prompts 1c–d, describe next steps for instruction

for the whole class and for the 3 focus students and other individuals/groups with specific needs.Based on the analysis discussed in prompts 1c­d, the next steps for instruction in regards to the whole

class would to provide further modeling and guided practice in regards to the overall themes of the instruction thatstudents struggled with. These themes students struggled with were how to justify their answers through the use ofcorrect mathematical terminology and language and setting up and solving algebraic equations. Individualizedpractice (i.e. homework) regarding these themes will also be given to allow students to reach stated standards andcontent objectives.

Since the feedback and overall themes from the 3 focus students aligned with those of the whole class, thenext steps for instruction for these 3 students would equivalent to the instruction that the whole class will receive.

Student groups with specific needs will be provided the similar instruction the whole class will receive aswell as additional individualized instructional assistance and time. Since there will be 5 teachers available during theclass period, achieving individualized assistance for all students will be less challenging.

Once students have mastered the content standards and objectives for this lesson, they will begin usingtheir knowledge of angle pair properties and reasoning to begin writing geometric proofs in the next planned lesson.

b. Explain how these next steps follow from your analysis of student learning. Support your explanation withprinciples from research and/or theory.

Based upon the overall themes we gather from the students’ work and using the theory of scaffolding, we believe thatthe steps of modeling, guided practice, feedback, and individual practice will provide the additional instructionalexperiences to build the necessary cognitive skills that lead to student mastery. The scaffolding theory will allow us,as the teachers, to initially start with the ownership of performing the conceptual understanding, procedural fluency,and mathematical reasoning of the themes discussed. Through modeling, guided practice, feedback, andindividualized practice, the ownership of performing conceptual understanding, procedural fluency, and mathematicalreasoning with shift to the students, which will lead to student mastery.

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