Blog Post #5

Blog Post #5

This semester, I have been surprised by the literacy levels of my students. They are able to acquire new vocabulary and use it in their speech and writing. Students have learned vocabulary through clear definitions and repeated use in their written and oral explanations of problems that they do. They have resources that they can use to help them demonstrate this knowledge, such as graphic organizers and a word wall with visual and written explanations of vocabulary terms. They are not able to only read this information and be expected to use it. They need to see what they are learning, hear it verbally and then use it. It is not possible to give them a list of vocabulary terms and expect them to use this information to understand concepts and use it on problems.

Journal... Sept. 30, 2013
My literacy rich classroom looks like an environment where students are beginning to use multiple input methods to learn vocabulary in mathematics.
My students are engaged in collaborative group work to practice their use of new vocabulary words before using them in their own practice and writing.
They are reading basic definitions of vocabulary words.

Journal... December 15, 2013
My literacy rich classroom looks like an environment where students are using multiple input methods to learn and master vocabulary in mathematics. Students are using this vocabulary daily to explain their thinking on various problems both in writing and orally.
My students are engaged in a collaborative work environment where they can gather information by listening to others, sharing their thinking orally with members of their group and summarizing their thoughts by applying the vocabulary to explain their thinking.
They are reading definitions of vocabulary words and they are reading word problems that apply their knowledge of vocabulary words and concepts.
They are writing reflections that summarize their thinking about about problems. In these reflections and short descriptions of thinking, they use vocabulary to justify their thoughts and the steps that they took to solve problems.
They are discussing their mathematical thinking with each other during collaborative group work. They use vocabulary to affirm or challenge each other’s ideas and work together to explain their thinking about a problem before applying this knowledge to individual practice.

Journal... May 30, 2013
My literacy rich classroom looks like an environment rich in vocabulary use through multiple pathways. Students read, listen to, write about and speak using new and previously learned vocabulary. Through the repeated use of these words using these different methods, all students have access to this language.
My students are engaged in lessons by interacting with me as well as other students to ask questions, affirm their understanding and explain concepts in small groups or to the whole class. They can then apply this knowledge to their own practice when they individually explain their thinking in writing of a reflection or explanation of the process needed to solve.
They are capable of independent learning in the following areas. Students are able to acquire new knowledge of vocabulary through the repeated use and application of their knowledge. This helps them in reducing the number of errors and assumptions that they make in solving problems.

Unit Plan

UNIT TOPIC:  Constructions/Extension and Application

This unit comes after a chapter on triangles and polygons. The constructions part of the unit will involve constructing various shapes/figures the students have been working with and incorporates using triangle congruence to prove their constructions are valid. The Extension and Application part of the unit provides a review of concepts that have been previously covered in a new and challenging way. My CT developed the plans for the constructions part of the unit and I developed the plans for the Extension/Application part of the unit.

UNIT CONTEXT          

Subject/Content Area Mathematics

Course Geometry

Grade Level 9-12       

Length of Unit: This unit will last one week. There will be four class periods, three that are 55 minutes long and one that is 115 minutes long.

FACTS ABOUT THE LEARNERS        

Whole Class Information

·       Number of students in class: There are 36 students in period 4 and 37 students in period 5.

·       Demographic Information: Period 4: 18 girls, 18 boys. Ethnicity-25 students “Yes, Hispanic or Latino”. English Learners-3 students at the intermediate level, 2 students at the advanced level. 16 students in the class who have been redesignated. Special Education-3 students with IEPs. Period 5: 17 girls, 20 boys. Ethnicity-20 students “Yes, Hispanic or Latino”. English Learners- 2 students at the early advanced level, 8 students who have been redesignated. Special Education- 5 students with IEPs.

·       Developmental Needs: The students enjoy and do well in small groups working on problems at the large whiteboards available for each group. Many of the students play sports or are involved on campus in some way. The students respond well to smaller group activities where they are working together, rather than lecture based or heavy individual practice lessons. There are many visual learners in the classroom and students who respond better to hands-on activities. Creating a safe environment where students feel free to share their perspectives and ask questions without the fear of being laughed at or told they are wrong, is important with these classes.

 

Individual Student Information and Differentiation Strategies

Provide the following information for 5 specific students

·       What is the students’ name? Elena

·      What is the level of your English Learner? Early Intermediate English Learner

·       Elena is a 10^th grader. She is from Mexico and has a large extended family. She moved to the U.S one and half years ago and visits her grandparents and other family members and friends in Mexico during the summer.

·      What are the student’s individual ed. goals? Reading, writing & subject levels? Based on her grades, she is highly motivated to succeed, so her individual goals are to work toward a higher level of English proficiency, as well as continuing to develop her content knowledge.

·      She is literate in Spanish and often reads Spanish literature. Her report cards from school in Mexico indicate above average grades. She is shy but works well in small groups.

·      What can you do to differentiate each student’s

o      Content. I will provide her with a list of any new vocabulary ahead of time. In our classroom, we have a word wall that includes graphics, so this will help her with using vocabulary when doing problems in class, as well as when she completes exit tickets and reflections.

o      Process. Allow her to work with a bilingual partner.

o      Product. Assess her at the i+1 level and focus on her ability to express her understanding through reflection and answering simple questions. (Readiness)

o      Affect. Give feedback through written and oral comments to allow her to understand and track her progress. (Readiness)

o      Learning Environment. It will be best if Elena can sit next to a bilingual student, so arranging seats in pairs and small groups will help to (Readiness/Learning Profile)

Based on their developmental needs (readiness, interests and learning profile)?

·       In order to obtain evidence of Elena’s learning, I would choose to assess her on the informal formative assessments in which she would have the ability to show me what she is working on, as well as use simple communication to tell me the process she took to get there. This would give her an opportunity to practice her oral English, and I can adjust the way that I assess her based on her CELDT level.

·       Elena is very motivated, so she will work hard to achieve success in the class. The next steps I would take to help Elena progress would be to encourage her to keep practicing her English while working in small groups. She tends to be a shy person, but gets along well with others and since we have created a risk free environment for our class, students will not criticize her if she does not explain things correctly right away. If she starts to practice in the small groups, she can work up the confidence to present her thinking to the class in the future. 

·       What is the students’ name? Larissa

·      What is the level of your English Learner? Intermediate English Learner

·       Larissa is an 11^th grader. She was born in the U.S and grew up speaking Spanish with her family. Her mother speaks more English now, so she speaks English primarily at home now.

·       She would like to do well in school and take as many classes as possible because she would like to be a nurse and knows that she must take and pass certain classes in order to do this.

·       Readiness:  Able to learn and communicate new ideas and vocabulary with images and clear statements/definitions. She has received average grades in past math classes. She has retaken Algebra, but is confident in her ability now. She is motivated and asks many questions for clarification.   

Learning Profile: Visual and auditory preferences. Shy, so prefers individual help or working in a small group, rather than speaking to the class/asking questions. Note-taking has helped keep her organized and allows her to have something to refer back to and understand during group and individual practice.

       Interest: Spending time with friends and family. Fashion.

·      What can you do to differentiate each student’s

o      Content: Allow her to use notes when working on in class as well as exit tickets and reflections. Notes really help her to organize her thoughts and remind her of the vocabulary words used to describe certain mathematical concepts.

o      Process: Larissa works well in groups, but is shy, so allowing her to work in small groups helps her to feel more comfortable.

o      Product: Assess her at the i+1 level.

o      Affect: Larissa asks a lot of questions and seeks feedback often. Giving her frequent oral as well as some written feedback which she can refer back to, will be helpful in moving her toward the learning goals.

o      Learning Environment. She works well with others so placing her near a student who is willing to help her is effective. Her younger sister is in the same class, they do not work particularly well together so keeping them apart is best. (Learning Profile)

Based on their developmental needs (readiness, interests and learning profile)?

·       I would choose the informal formative assessments to assess Larissa’s progress so that she has the time and ability to explain her thinking to me in the best way that she can, in a low-pressure situation.

·       Larissa is giving a lot of effort in this class and would really like to do well, allowing her to use notes and offering assessments other than formal written assessments will help her to feel more comfortable and more successful.

·       What is the students’ name? Alex

·       What category does the student qualify for special education services? Specialized Learning Disability-literacy skill, including the acquisition of sound/symbol relationships and word identification.

·       Alex is a 10^th grader who is

·      Alex would like to improve his use of vocabulary.

·      Alex reads at the 7^th grade level and struggles with decoding words. He has asthma. He is a self-isolating person and does not readily join group-learning situations.

·      What can you do to differentiate each student’s

o      Content: Provide new vocabulary ahead of time and allow Alex to see and use the word wall with graphics for reference. Make a sheet similar to the word wall that he can use at home as well.

o      Process: Since the class is group based, allow Alex to have a more independent role in the group, suggesting he be the recorder of information.

o      Product: Encourage him to speak to you about his understanding, and allow him to turn in his work and assess him, knowing about his learning difficulties.

o      Affect: Written feedback will be best for Alex, as he does not respond well to interaction.

·       I would choose to assess Alex’s exit tickets and reflections since he will not readily share his thinking orally. 

·       Encouraging Alex to take a more active role in groups will help him move forward. We have created a risk free environment where all students should be accepting of others ideas.

·       What is the students’ name? John

·       What category does the student qualify for special education services? Special day class

·       John is an 11^th grader who is involved in a special day class for students with severe learning disabilities. He has a supportive home environment, in which his parents support his learning goals.

·       John would like to improve his understanding of geometry, and use vocabulary to explain what he is saying. He has trouble using the words that he would like to explain the process that he uses to solve problems.

·       Readiness: Algebra skills are sufficient to learn new concepts and apply old knowledge. He is in a special day class.

Learning Profile: Visual preferences. Pictures and organizers are very helpful. Notes/organizers to refer back to help to keep thoughts and new ideas organized and are helpful to refer back to on future assignments. Does not always do well in small group situations.

        Interest: Art, especially drawing, and reading.

·       What can you do to differentiate each student’s

o      Content: Giving organization to notes will help John to make sense of concepts, and allowing him to have access to vocabulary before a lesson, will help him.

o      Process: Allowing him extra time to work on things, so that he can get help in his resources class, will help him feel the support he needs to succeed.

o      John does well on more formal tests, as he is not great at verbalizing his understanding and is better at relating concepts on paper.

o      John has a tendency to speak out in class, so keeping him close to the front of the room, will allow the instructor to speak with him readily.

·       The formal formative assessments will be best to display John’s progress towards learning goals. He does not verbalize his understanding as well as he can write it, so allowing him to display knowledge on the exit tickets and reflection, will be best for him.

·       Making sure that John feels comfortable and welcome in the classroom will be the best way to ensure his success. If he feels that he is not welcome or wanted in the class, then he will not perform. Making sure to continue the environment created where all students have a chance to contribute, will help John feel comfortable.

·       What is the students’ name? McKinley

·       What category does the student qualify for special education services? McKenna has an IEP plan based on her Specialized Learning Disability

·       Describe student’s grade level, culture, language, SES, family, affect. McKenna is an 11^th grader who speaks English only. She comes from a large middle class family where she is always encouraged to read and do her homework, but is rarely checked in on or receives little help with homework. She is a social person, who is very involved on campus through organized activities and ASB.

·      What are the student’s individual ed. goals? Reading, writing & subject levels? McKenna is a very hard worker and is motivated to succeed in all subjects. She enjoys English the most, and feels that she struggles in math because of her past experiences.

·      Describe developmental needs (readiness, interest, & learning profile) for each student. McKenna’s learning profile suggests that multiple modalities will be the most successful for her. She will benefit from directions being clarified.

·      What can you do to differentiate each student’s

o      Content: She has trouble relating concepts, so allowing her to use notes on assignments is necessary.

o      Process: Clarifying directions is necessary for McKinley’s success.

o      Product: Informal assessments are best for her. Allowing her to work on the test in another room or have extended time is necessary.

o      Affect: Both oral and written feedback will be best for her.

Learning Environment: Allowing McKinley to work in groups will help her to feel comfortable with the material.

·       Informal formative assessment will be best to check for McKinley’s understanding. She gets anxiety with more formal tests and often seeks clarification on many problems because she feels she cannot ask questions. Allowing her to verbalize her understanding through these less formal assessments will be best for her.

·      McKinley is highly motivated to succeed and will work very hard to get a good grade in the class. Allowing her to talk through and verbalize her understanding whenever possible and assessing her as much in this way, will help her feel successful.

Unit Rationale: Enduring Understandings & Essential Questions

This unit comes at a great point in the year, as we have just finished a unit on triangle congruence, which incorporated a lot of review from the first two units, which covered angles, segments, properties of parallel lines and polygons. This unit combines constructions with a review of previous concepts in a way that challenges students to apply knowledge to more challenging problems than they have seen before. It is important for the students to truly understand these concepts and how they affect the real world, as they start to pick up on where they see these concepts outside of the classroom. This unit gives use a chance to explicitly link concepts to the student’s lives and challenges them to think about geometry in a new way. Having students think through problems and label their thinking by justifying their answers is a goal of the course that is particularly important in this unit.

 

Enduring Understandings (EU)

At the end of this unit, I hope that students have a better understanding of the core concepts of the class by applying their previous knowledge and thinking to solve complex problems. Students should be able to label the steps that they took to come to the conclusion.

Essential Questions

·       What are the ways we apply old knowledge to new concepts?

·       Is it possible to look at a picture and answer the questions we have by solving mathematically?

·       Where in the real world do we see/notice concepts from class?

·       How can we use real world examples of geometry to model what we have covered in class?

·       How can we construct what we have been learning and prove that we know it is correct?

·       What other shapes can we construct using knowledge of how to construct basic figures?

Reason for the Instructional Strategies & Student Activities

STANDARDS

Content Standards

5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.

12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.

13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.

16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.

 

ELD Standards

Listening and Speaking: Cluster 7- EA. Respond to messages by asking questions, challenging statements, or offering examples that affirm the message. Cluster 9-EA. Prepare and deliver brief oral presentations/reports on historical investigations, a problem and solution, or a cause and effect.

Writing Strategies and Applications: Cluster 5-EA. Write reflective compositions that explore the significance of events.

UNIT OBJECTIVES

Constructions:

1. After seeing an example modeled, while following along, students will be able to individually construct an equilateral triangle, copy of a segment, copy of an angle, an angle bisector, the midpoint, a perpendicular bisector (through any point, a point on a line, or a point not on the line) using a straight edge and compass, and will be assessed on their ability to construct these through both formative and summative assessments. (Standard 16.0, L&S Cluster 7) (Cognitive)

2. After the previous unit on triangle congruence, and following along with instructor led “labeling of thinking” students will be able to write a proof of various constructions including, angle bisector, copying an angle and perpendicular bisector and will be assessed on their ability to understand and apply their knowledge to complete the proof on their own. (Standards 5.0,16.0) (Cognitive)

Extension/Application:

3. Using previous knowledge of theorems and properties of lines, triangles and polygons, students will discuss with group members, and label the steps taken to solve for missing parts in complex figures and all group members will be asked to explain their thinking to group members or to the class, in order to assess their deeper understanding. (Standards 7.0, 12.0, L&S Cluster 7 and 9) (Cognitive)

4. After working together in small groups to come to conclusions about missing information using a “pass the pen” method to allow all students to give input, students will individually display their knowledge on a smaller version of these types of problems, indicating the vocabulary and knowledge they needed to solve. (Standards 7.0, 12.0, 13.0, L&S Cluster 7 and WS&A Cluster 5)

ASSESSMENT PLAN

·       Name of Assessment: Constructions Understanding (Objectives 1 and 2)

·       Formality: Informal

·       Type: Formative

·       Purpose: To assess student understanding and ability to explain process. Instructors will walk around checking for understanding by looking at student work and asking students to explain the steps they took.

·       Implementation Method: Written (Constructions) and verbal (Explanations)

·       Communication of Expectations: Modeling by instructor to show expectation of steps, student samples to show expectations of results.

·       Evaluation Criteria: Correct markings indicate steps taken to get result, formal proof indicates understanding of thinking by whole class.

·       Feedback Strategies: Oral feedback and supplemental instruction individually

·       Student Self-Assessments: Students will check their construction with the student sample provided.

·       Name of Assessment: Constructions Quiz

·       Formality: Formal (30 points)

·       Type: Formative

·       Purpose: To check for student’s understanding when doing constructions individually, and how well they can apply knowledge of proofs to prove their construction is valid.

·       Implementation Method: Written (Constructions)

·       Communication of Expectations: Modeling and practice in class.

·       Evaluation Criteria: Correct markings indicate steps taken to get result, formal proof indicates understanding of applying previous knowledge to constructions.

·       Feedback Strategies: Written feedback on quiz to be returned to students.

·       Name of Assessment: Extension/Application Understanding

·       Formality: Informal

·       Type: Formative

·       Purpose: Assess students on ability to provide correct answers for missing parts as well as justifications for their answers. Instructors will walk around to groups or individuals to check for correctness and ask students to explain and write their thinking. If appropriate, have students present to the class or in smaller groups to have them practice using vocabulary.

·       Implementation Method: Written and verbal.

·       Communication of Expectations: Examples of student work shown to model the methods of “labeling thinking”.

·       Evaluation Criteria: Rubric provided in resources.

·       Feedback Strategies: Oral feedback

·       Student Self-Assessments: Rubric provided in resources.

·       Name of Assessment: Extension/Application Exit Ticket

·       Formality: Formal (Credit is given on the rubric scale)

·       Type: Formative

·       Purpose: Check for student’s use and understanding of labeling thinking in order to justify their answers for missing parts.

·       Implementation Method: Written

·       Communication of Expectations: Group work done in class provides expectations, as well as the rubric created for the extension/application portion of the unit.

·       Evaluation Criteria: Rubric is provided in resources.

·       Feedback Strategies: Written feedback on exit ticket to be returned to students.

·       Student Self-Assessments: Rubric is provided in resources.

STEPS OF INSTRUCTION

Into: (Monday, 10/15)

Objectives/Standards

Students will use prior knowledge to look at a complicated figure and record things that they notice and things that they wonder to get oriented with the picture and contribute to class discussion about what students recorded, then students will work in groups to talk through and label their thinking, providing reasons for the conclusions they make. (Standards 7.0, 13.0, L&S Cluster 7)

Student Activity

·       Hook: Challenge students to think about the figure (provided in resources) mathematically, asking them to record what they notice and what they wonder.

·       This activity will be directly related to things that they have seen in the past. There are many connections to previous concepts that students will notice. The notice/wonder introduction activates this prior knowledge by giving them the freedom to recall what they want to.

·       To begin the overall into lesson, students will record what they notice/wonder. Then, the instructor will provide numbers for five of the angles and students will work in groups to fill in the rest of the angles. They will “pass the pen” between group members filling in one angle at a time and writing in their justifications in the order in which they solve.

·       The room is arranged with white boards around the room that groups of four to six are assigned to work at for group work. Seating is changed every two weeks, so groups are switched up regularly.

·       Transitions have been practiced, so students know that they have only a certain amount of time before they will be expected to be at their boards starting the problem. If student behavior becomes an issue, I will address it in the small groups, so that the behavior issues do not distract other groups. If it will help, I will rotate groups or switch members to create a more productive environment.

·       Questions to prompt learning: What specifically are you struggling with? What is the next step you should take? How do you know that (point to something specific)? Justify your thinking, how can you explain what you have done so far, and how can you use this information to continue.

·       Unit Preview: A short discussion about using mathematics to prove things that we notice about figures or things in the real world will be conducted as a short conclusion before students are told to complete this for homework so that we can come to final conclusions about what students were wondering from the picture.

Assessment

The homework will be to finish this star problem, labeling and solving, and it will be checked for completeness the next class. Also, a discussion about what students had wondered will be debriefed, using the answers that they found on their homework.

Through:

	Day 1: M (10/15)	Day 2/3: T/W (10/16 and 10/17)	Day 4: Th (10/18)	Day 5: F (10/19)
Content Standards	Geo 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. Geo 13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. Geo 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Listening and Speaking: Cluster 7- EA. Respond to messages by asking questions, challenging statements, or offering examples that affirm the message.	Geo 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. Geo 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Listening and Speaking: Cluster 7- EA. Respond to messages by asking questions, challenging statements, or offering examples that affirm the message.	Geo 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. Geo 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Listening and Speaking: Cluster 7- EA. Respond to messages by asking questions, challenging statements, or offering examples that affirm the message.	Geometry 12.0  Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. Geo 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Listening and Speaking: Cluster 7- EA. Respond to messages by asking questions, challenging statements, or offering examples that affirm the message. Cluster  9- EA. Prepare and deliver brief oral presentations/reports on historical investigations, a problem and solution, or a cause and effect.
Learning Objectives	After following along with instructor led examples, students will be able to use a straight edge and compass to construct an equilateral triangle and copy a segment, using notes taken during example. Students will use prior knowledge to look at a complicated figure and record things that they notice and things that they wonder to get oriented with the picture and contribute to class discussion about what students recorded, then students will work in groups to talk through and label their thinking, providing reasons for the conclusions they make.	After following along with instructor led examples, students will be able to use a straight edge and compass to copy and angle, construct an angle bisector and determine the location of a midpoint, using notes taken during example. Students will also follow along while instructor labels thinking on a proof of how we know the methods of construction for copying an angle and constructing an angle bisector are valid, then students will be able to individually write up their formal proofs for this to include in their notes. Students will use prior knowledge of parallel lines and properties of a triangle to record their observations about a complicated figure and solve for certain missing pieces while providing justifications on their individual whiteboards while the instructor monitors for correct answers and reasoning.	After following along with instructor led examples, students will be able to use a straight edge and compass to construct a perpendicular line and perpendicular bisector, in order to prove that their constructions are right, they will use the thinking labeled on their board and create their own proof. After working in groups to complete a problem that requires finding values of missing angles and justifying thinking, students will be able to individually complete a similar task as an exit ticket.	After a week of taking notes on and practicing constructions, students will be able to complete a quiz covering three topics they have seen previous days. After learning about properties of polygons and having some time to think about and note important aspects of the figure presented, students will be able to answer the question ”How many sides does the polygon that is cut off have?” using discussion with peers, direct questioning and a step-by-step approach to solving.
Student Activity	Students will use the straight edge and compass to follow along while the instructor models how to copy a segment and construct an equilateral triangle. Then students will try these constructions on their own. Students will record what they notice/wonder about the figure. Then, the instructor will provide numbers for five of the angles and students will work in groups to fill in the rest of the angles. They will “pass the pen” between group members filling in one angle at a time and writing in their justifications in the order in which they solve.	Students will use the straight edge and compass to follow along while the instructor models how to copy an angle and construct a angle bisector, and determine the location of a midpoint. Then students will try these constructions on their own. Students will briefly write down what they notice and wonder about the figure on the board. Then, the instructor will indicate which angle they should give the value for. Students will write the value of this angle and how they know that the answer they have written is true, based on information given in the figure.	Students will use the straight edge and compass to construct a perpendicular line after seeing an example from the instructor. Students will split up into groups to find the missing angles of a figure given by the instructor. They will discuss and “pass the pen” so that all members of the group have a chance to contribute to the solution. One group will be asked to present their findings and justify them in order to allow the whole class to assess their knowledge as a group. Then, students will copy down a sketch of the homework and will be told to write three mathematical facts that they know about the shape in the picture. Finally, students will complete an exit ticket as an assessment.	Students will write on the board the ideas that they came up with for homework, investigation of the pentagon. Then students will complete a short quiz on constructions. Students will write on their papers the things that they notice and wonder about the figure that is presented. Then, they will share some of the things that they came up with to contribute to the class discussion. Then students will split up into groups to answer the question, “How many sides does the cut off polygon have?” Once students have come to a conclusion in groups, one groups will present the way that they solved the problem.
Assess-ment	The homework will be to finish this star problem, labeling and solving, and it will be checked for completeness the next class. Also, a discussion about what students had wondered will be debriefed, using the answers that they found on their homework. (Student samples of this homework are provided in the resources, graded with rubric)	Whiteboard answers will be assessed for correctness through an informal formative assessment. Instructor will be informed of overall understanding and misconceptions and students will be able to self assess when correct answer is presented. Also, students will complete an exit ticket that is a simpler version of the parallel lines problem, in which they will solve for missing angles and “label their thinking” using vocabulary. (graded with rubric)	Students will complete an exit ticket in which they must solve for missing angles and justify how they got their answer by “labeling their thinking”, using vocabulary. (graded with rubric)	Students will reflect on the concepts and knowledge that they needed in order to answer this question. Students will use vocabulary words in their reflections. (Student samples are provided in resources.)

Closure/Beyond:

The lesson plan provided below is the closure/beyond lesson.

The objectives, standards, activities and assessment are presented just above here in the unit calendar, and in more detail in the lesson plan below.

·       In this lesson students will make meaning of the concepts that have been covered in the unit by developing their own questions about a figure, through a notice and wonder activity, and then they will use mathematics to answer the question that they developed. Throughout the unit students have been using vocabulary and including this in their exit tickets, as well as throughout the lesson by “labeling their thinking”. The quiz on constructions will also allow students to summarize what they have learned so far and they must include a proof in order to incorporate their prior knowledge.

·       The “product” that I will collect from students as evidence of their learning is the reflection that they write at the end of the class that summarizes what they needed to know in order to solve the problem that they worked on in class. For constructions, the quiz is collected, graded and returned in order to get an idea of where students are in understanding constructions and give them feedback about how they are meeting the expectations of the course.

·       The next unit will be on quadrilaterals. Students have been using their knowledge and vocabulary to find the values of missing angles and label the process that they took to get those answers by including justification. This will carry over into the next unit, as students will be finding missing angles and sides of quadrilaterals and will be using a similar approach.

 MATERIALS/RESOURCES

All materials that are needed for the unit are included. It is also necessary to have a class set of compasses as well as rulers or some kind of straight edge. 

Lesson Plan:

1. TITLE OF THE LESSON Assessment of constructions and polygon extension as a part of a unit on constructions, and extension and application of previously covered topics.	2. CURRICULUM AREA & GRADE LEVEL Geometry, grades 9-12
3A. STUDENT INFORMATION: English Language Learners Lupe         1.) Readiness Level: Intermediate level. 11th grader. Able to learn and communicate new ideas and vocabulary with images and clear statements/definitions.               2.) Learning Profile: Visual and auditory preferences. Shy, so prefers individual help or working in a small group, rather than speaking to the class/asking questions. Note-taking has helped keep her organized and allows her to have something to refer back to and understand during group and individual practice.              3.) Interest: Spending time with friends, fashion. Wants to be a nurse when she is older. Ana         1.) Readiness Level: Intermediate level. 12th grader. She speaks Spanish at home with her family. She has previously taken SEI classes. In 10th grade she took SEI Algebra 1 and failed both semesters. In 11th grade she took Algebra 1 and passed one semester and failed the other. She has the skills necessary to pass this class, she need to focus and not get worked up when it comes time to take a test.         2.) Learning Profile: She is a visual/auditory learner and works well in groups.         3.) Interest: She spends a lot of time with her friends and family and she would like to get a job after she graduates so that she can pay for college. Melissa         1.) Readiness Level: Intermediate level. 11th grader. She speaks both English and Spanish at home. In 10th grade she took Algebra 1 and passed the first semester and failed the second semester. This class is a challenge for her because she doesn’t have a very strong background in Algebra, which is necessary to apply the concepts in geometry. She will benefit from some extra Algebra help.         2.) Learning Profile: She is a Kinesthetic learner and prefers to have problems explained slowly while she follows along and then trying one on her own.         3.) Interest: She likes spending time at the beach with her friends and she would like to go to college for 8 years to become a dentist. Martin         1.) Readiness Level: Early Advanced level. 11th grader. He speaks Spanish with his family. He passed two semesters of Algebra 1 in 8th grade, failed two semesters of Geometry in 9th grade, and then took Algebra 1 again in 10th grade and passed one semester and failed the other. Since this class is a repeat of what he has seen, he will benefit from clear definitions to reach his prior knowledge and clear explanation of expectations so that he can be successful.         2.) Learning Profile: Visual/auditory learner. He will benefit from clear visuals of figures and their properties.         3.) Interest: In his free time he enjoys drawing and lifting weights. He would like to be a firefighter or go into the military when he graduates from high school. Eduardo         1.) Readiness Level: Early Advanced level. 12th grader. Starting learning English in preschool. Continues to speak both Spanish and English at home. In 9th grade he took SEI Algebra and did not pass either semester. In 10th grade he continued on to Geometry, but failed both semesters, so in 11th grade he took Transitional/Basic math and passed both semesters. He is passing the class so far this year, but will need to work hard to keep his grade.         2.) Learning Profile: He is a visual learner, and he is motivated to do well. He works well individually, and benefits from being able to ask clarifying questions.         3.) Interest: After school, he enjoys playing soccer and boxing. He is close with his family and enjoys spending time with them. Christian         1.) Readiness Level: Advanced level. 12th grader. He speaks Spanish at home with his family. In 9th grade he took SEI Algebra and failed both semesters. In 10th and 11th grade he took Algebra 1 and he passed one out of four semesters. He seems to have developed a good understanding of Algebra through taking those classes, and he is determined to pass this class in order to graduate.         2.) Learning Profile: He is a visual learner. He works well in groups and is a good leader.         3.) Interest: He enjoys hanging out with his friends and is working hard to graduate at the end of this year. Daniela         1.) Readiness Level: Advanced level.  11th grader. She speaks Spanish at home with her family. In 9th and 10th grade she took Algebra 1 and failed all four semesters. She has trouble with the Algebra concepts that are needed for this class, so she will benefit from extra help on making sure she keeps her process of solving organized.         2.) Learning Profile: She is a visual learner and benefits from pictures and clear, repeated explanations.         3.) Interest: She likes to play soccer and draw in her free time and she would like to join the Navy after high school.	3B. STUDENT INFORMATION: Students w/ Special Needs Victor         1.) Readiness Level: Algebra skills are sufficient to learn new concepts and apply old knowledge. He is in a special day class.         2.) Learning Profile: Visual preferences. Pictures and organizers are very helpful. Notes/organizers to refer back to help to keep thoughts and new ideas organized and are helpful to refer back to on future assignments. Does not always do well in small group situations.         3.) Interest: Art, especially drawing, and reading. Ernesto         1.) Readiness Level: He has a bleeding heart problem in which he takes medicine for. He has trouble focusing on the tasks that he is assigned and can often be a distraction to himself and the other people around him.         2.) Learning Profile: He has visual and auditory preferences, with an emphasis on auditory, as he does better when there is constant prompts about new vocabulary and the use of new vocabulary in context.         3.) Interest: He enjoys playing baseball and hanging out with his friends. He would like to continue school in order to become a mechanic. Sydney         1.) Readiness Level:         2.) Learning Profile: She is a visual learner as well as has a preference for hands on activities in which she can make connections to the real world.         3.) Interest: She is very interested in baking and would like to go to culinary school in order to own and run her own bakery which she would like to travel with. She enjoys hanging out with her friends and she is also involved in the drama department as a behind the scenes technical manager. Chyanne         1.) Readiness Level: 10th grader. Has severe vision problems, instead of 20/20 she has 4/4 and easily gets dizzy when she must concentrate to read or understand something that she cannot easily see. She will need larger print documents and may need assistance seeing certain aspects of the lesson.         2.) Learning Profile: She is a kinesthetic learner and learns best when she is able to use manipulatives and participate in hands on activities.         3.) Interest: She enjoys making origami and art in general. She also loves animals, especially horses. Javier         1.) Readiness Level:         2.) Learning Profile: He is a visual and auditory learner and benefits from clear, repeated explanation.         3.) Interest: In his free time, he wrestles, runs and plays football. Isaac         1.) Readiness Level: He is .  He has behavior issues in other classes, so it will be best to make sure that he continues to be an exemplary student in this class.         2.) Learning Profile: He is an auditory learner. He benefits from listening to others use vocabulary in order to master it himself. He will also do well when using the vocabulary in group situations, as he is a social person who likes to talk, but knows how to stay on task.         3.) Interest: He would like to own his own shoe company and he likes to play football and basketball in his free time.
4. RATIONALE      A. Enduring Understanding: Students will make connections to previous knowledge and concepts covered in class by applying it to a more abstract problem. Students will understand that using a step-by-step approach, which they have used for proofs, they will be able to solve even more challenging problems.      B. Essential Questions: How can we apply our old knowledge to new concepts? Is it possible to look at a picture and answer the burning questions that we have by solving mathematically? How can we use real world examples to model concepts we have covered in class?      C. Reason for Instructional Strategies and Student Activities: The unit created on constructions was only meant to last half of each class period, so that students don’t get too overwhelmed. The other half of each class was planned to cover previous topics. It was decided that these “minilessons” would be a good opportunity to use some more challenging extension problems that involve many topics we have covered, but also get students to step back and really think about what they have learned. By allowing the students to think about the problem during the notice and wonder activity of this day’s lesson, students will gather their own thoughts and ideas before splitting up in groups to work on the problem. Having them work in groups to discuss and challenge each other’s ideas as well as encouraging students to ask very specific questions of the instructors and their peers, will help them to think about the challenging task.
5. CONTENT STANDARD(S) Geometry 12.0  Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. Geo 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.	6. ELD STANDARD(S) Listening and Speaking: Cluster 7- EA. Respond to messages by asking questions, challenging statements, or offering examples that affirm the message. Cluster  9- EA. Prepare and deliver brief oral presentations/reports on historical investigations, a problem and solution, or a cause and effect.
7. LEARNING GOAL(S) - OBJECTIVE(S)      A. Cognitive After learning about properties of polygons and having some time to think about and note important aspects of the figure presented, students will be able to answer the question ”How many sides does the polygon that is cut off have?” using discussion with peers, direct questioning and a step-by-step approach to solving.	8. ASSESSMENT(S)      A. Diagnostic/Entry Level: A class discussion/debrief about the homework assigned for the previous night, an investigation of what is known about the pentagon, will give a good idea of what students were able to recall about polygons and the measures of their angles.      B. Formative-Progress Monitoring: As students are working on the problem, we will monitor their conversations and the questions they are asking in order to get an idea of what they understand and what they still need work on.      C. Summative: A final class discussion will determine if students were able to solve the problem. Also, individual reflections on what was needed to solve this problem will be collected. These will both give a good idea of the understanding of the whole class.
9A. EXPLANATION OF DIFFERENTIATION FOR ENGLISH LANGUAGE LEARNERS 1.)  Content/Based on Readiness, Learning Profile or Interest This student works well in groups. She is shy, but she benefits from hearing what others have to say and asking questions in order to clarify concepts. Having the students work in groups to solve this difficult problem, will be a helpful differentiation strategy for her.	9B. EXPLANATION OF DIFFERENTIATION FOR STUDENTS WITH SPECIAL NEEDS 1.)    Content/Based on Readiness, Learning Profile or Interest This student tends to want to do his own thing when he is in a group setting. He will have difficulty with the complexity of this problem. By encouraging all students to record what they know about the figure beforehand and then suggesting they focus on one aspect at a time, will help him to focus energy and knowledge. I will also keep a close eye on his group during this activity in order to make sure he is on task and not getting too overwhelmed. I will have hints to give him when he is able to tell me what he is stuck on, or I will allow him to quickly “spy” on another group.
10. INSTRUCTIONAL STRATEGIES Constructions: A.     Anticipatory Set/Into As students are walking in, ask them to write some of the mathematical things that they noticed about the pentagon investigation that they did for homework the previous night. (included in the resources) Pass out materials needed for constructions while students are putting their work on the boards. (3-5 minutes) B.      Independent Practice/Through Instruct students to use the straight edge and compass to complete the quiz. (included in the resources) Tell students who finish early to write down more things that they know about pentagons on the back of their quiz. (10 minutes) Extension and Application:        A.     Anticipatory Set/Into a. As a class, debrief the information that students have put up on the board. Specifically focus on the mathematical things that were noticed by students. Lead this short discussion to offer a short background relating to the next problem. (3-5 minutes) b. Put up the problem (provided in the resources) on the document camera for students to make sense of. Say nothing except “What do you notice? What do you wonder?” Allow them a short time to write down these things (3 minutes)                                 B. Instruction/Through Conduct a short discussion to highlight some of the main points that were noticed about the figure. Also, allow students to share what they are wondering about the picture. If the discussion does not naturally progress to students talking about how many sides the cut-off polygon has, then prompt this discussion. The goal is to end with directing them to work in groups to find the answer to the question “How many sides does the cut off polygon have” and provide concrete justification for their conclusion. (5 minutes)                                            C. Guided Practice/Through Before allowing them to start, emphasize the importance of following the step-by-step approach that we have been using in order to keep track of thinking and make the problem more manageable. Tell them to start with what they know, or noticed in the figure. Monitor groups while they are working on this question, making sure they “pass the pen” and encouraging them to ask specific questions when they get stuck. If students feel that they don’t know how to proceed with the problem, they can send a “spy” to one of the other groups to just take a look and see if they can add anything that might help them. These “spies” cannot bring a paper or pencil and they must be able to justify any information that they gather. Tell students about this option only if they seem that they need it. (10-15 minutes)                                     D. Closure Debrief the polygon problem as a whole class in order to develop certainty as a group about the number of sides that the cut-off polygon has. (8 minutes)        E. Beyond                 Have students write a reflection including three things that they needed to know to answer the question that was posed today. Collect these responses to get an idea of the concepts students connected to the problem. (3 minutes)	11. STUDENT ACTIVITIES Constructions: A.     Anticipatory Set/Into Students will put their findings from the previous night’s homework on the board as they come into class. (3-5 minutes) B.     Independent Practice/Through Students will use straight edge and compass to complete the quiz. When they are finished they will write down more things that they know about pentagons on the back of their paper. (10 minutes) Extension and Application:        A. Anticipatory Set/Into a. Students will listen and contribute to a conversation about what they wrote about the pentagon picture. (3-5 minutes) b. Students will write down things that they notice and things that they wonder about the figure that is put up on the document camera. (3 minutes)                                       B. Instruction/Through Students will contribute to the class discussion about things that they noticed about the figure that was presented. They will also share what they are wondering about the picture as well. (5 minutes)                                             C. Guided Practice/Through Students will work in groups by discussing and “passing the pen” to answer the question of the day that is a result of the class discussion. If they are stuck, they will need to ask their peers or the instructors, very specific questions. The students may send a “spy” from their group if prompted to get more information. The spy must not bring a pencil or paper. Students must have justification for all claims made to get their final answer. (10-15 minutes)                                               D. Closure Students in each group will share what they got for their final answer with a short justification of how they know it is true. The class will agree on a conclusion for the number of sides that the cut off polygon has. (8 minutes)                                            F. Beyond Students will write a reflection in which they write three things that they needed to know in order to answer the question that was investigated in class. (3 minutes)
12. RESOURCES Constructions: Compass, Ruler, Plain Paper Extension and Application: Previous night’s homework- Pentagon investigation (First picture below), Polygon Problem (Second picture below)