L2+McGinley,+Sarah

COLLEGE OF EDUCATION, HEALTH AND REHABILITATION LESSON PLAN FORMAT
 * UNIVERSITY OF MAINE AT FARMINGTON

Teacher’s Name:** Ms. McGinley **Lesson 2:** Apply
 * Grade Level:** Nine **Topic:** Polynomials

__Objectives__
Students will understand that Algebra is made up of symbols, tables, graphs, and verbal rules that need to be chosen for the best representation and they can convert from one to another. Students will know what it means to solve equations, use symbols, use graphs, verbal rules, and use different forms of equations. Students will be able to recognize which representation of a symbol, table, graph, or use verbal rules are being used.

__Maine Learning Results Alignment__
Maine Learning Results: Mathematics - D. Symbols and Expressions Grade 9 - Students understand and use polynomials and expressions with rational exponents.


 * Rationale:** Through the course of this lesson, students will be able to recognize which representation of a symbol, table, graph, or use verbal rules are being used.

__**Assessment**__
When students are doing the Circle the Sage activity, they will have a chance to rethink the Algebraic content. This activity is used by putting students into groups. The teacher will divide the number of students in class by four, as even as possible. One student from each group will be appointed a representation to be an expert on. The students in the group will answer the question where would you use this representation in real life? The expert will be the one to decide whether or not the answers given are correct examples. All the students in the group will need to keep a list as examples are given. Once each group has five or more examples listed, the students will then be divided into different groups where one or more members from each group form a new group. There should be at least one member from each original group. These original members are now the expert on their representation. Each member shares to the rest of the group what the representation is and what are the examples the original group came up with. By the end of this activity, every student should have examples for all four representations. Students will be able to incorporate ideas from the Problem-Solution chart that had students think about the different places where they have seen Algebra. During this activity students were asked to go outside to explore where they see applications of Algebra and skyscrapers or buildings can be included. Once everyone has shared their answers we will discuss it as a class. Both the Problem-Solution and the list of examples of each repesentation will be checked over during the class discussion. Students will be asked to make an image using Geometer's Sketchpad involving all the information gained from the previous activities. The teacher will give constructive feedback about these activities in order to complete a well made Geometer's Sketchpad image. Once the students have produced a rough copy of their Geometer's Sketchpad image, the teacher will conference with the students about the progress of their image. Students will be able to revise and refine the image before the teacher scores the final product using a checklist. Students will be able to rehearse the presentation before the actual presentation time. Students will have a chance to show their knowledge through the Pre and Post student survey.
 * Formative (Assessment for Learning)**

In class, students will be asked produce an image of a shape of a specific polynomial using Geometer's Sketchpad. The polynomial used should be visible on the image. Also, somewhere in the image there should be an explanation of why the polynomial would look like it does using the knowledge learned in the previous lesson. Once it has been completed, students will be asked to post it to the class wiki so the we can refer back to it whenever needed. The Geometer's Sketchpad image will be graded using a checklist.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be asked produce an image of a shape of a specific polynomial using Geometer's Sketchpad. The polynomial used should be visible on the image. Also, somewhere in the image there should be an explanation of why the polynomial would look like it does using the knowledge learned in the previous lesson. Once it has been completed, students will be asked to post it to the class wiki so the we can refer back to it whenever needed.

Art: During the Problem-Solution activity, students will be asked to go outside to explore where they see applications of Algebra and skyscrapers or buildings can be included.

__Groupings__
When students are doing the Circle the Sage activity, they will have a chance to rethink the Algebraic content. This activity is used by putting students into groups. The teacher will divide the number of students in class by four, as evenly as possible using a deck of cards. There are four suits in a deck and there are four representations to consider. Before class begins, the teacher will have put an even amount of each suit in a deck of the amount of students are in the class. Each person, as they walk into class, will recieve a card. Each suit will then form a group. If this is done properly, there should be four groups, each group all the same suit. One student from each group will be appointed a representation to be an expert on. The students in the group will answer the question where would you use this representation in real life? The expert will be the one to decide whether or not the answers given are correct examples. All the students in the group will need to keep a list as examples are given. Once each group has five or more examples listed, the students will then be divided into different groups where one or more members from each group form a new group. There should be at least one member from each original group. These original members are now the expert on their representation. Each member shares to the rest of the group what the representation is and what are the examples the original group came up with. By the end of this activity, every student should have examples for all four representations.

**__Differentiated Instructio____n__**

 * Strategies**
 * Verbal:** Students will be asked to discuss the Algebraic content in groups.
 * Visual:** An image is being shown for my hook.
 * Logical:** Students had to think about the different representations of Algebra and how they are used in real life.
 * Naturalist:** While using to Problem-Solution Charts the students will be asked to go outside to find algebra in nature.
 * Kinesthetic:** Students will be asked to change groups during the Circle the Sage activity.
 * Intrapersonal:** Students are working alone when filling out the Pre and Post student survey.
 * Interpersonal:** During the activity Circle the Sage the students are asked to work in groups.

I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.
 * Modifications/Accommodations**

An absent student will be asked to contact me through e-mail: sarah.mcginley@maine.edu, on the day he/she is absent. We will later make arragements to discuss what material was covered that day. Students will need to check what the class did that day on the class wiki or he/she has the option to Skype into class the day he/she is absent. I would like the student to come see me in the morning of the following day to get any handouts that may have been circulated on the absent day. All students will have a folder placed somewhere in the back of the classroom that will hold all handouts for that day. The students also have the option to check the homework hotline through internet of by phone if he/she does not have internet. The students will need to check with his/her classmates for notes if they are not posted to the wiki.

Technology: Students will be asked produce an image of a shape of a specific polynomial using Geometer's Sketchpad. The polynomial used should be visible on the image. Also, somewhere in the image there should be an explanation of why the polynomial would look like it does using the knowledge learned in the previous lesson. Once it has been completed, students will be asked to post it to the class wiki so the we can refer back to it whenever needed.
 * Extensions**

Art: During the Problem-Solution activity, students will be asked to go outside to explore where they see applications of Algebra and skyscrapers or buildings can be included.

__**Materials, Resources and Technology**__
Student laptops Teacher's computer Internet Deck of playing cards Blank Lined paper Projector's screen Check list [|Problem-Solution Graphic Organizer] [|Circle the Sage activity] [|Geometer's Sketchpad tutorial]
 * Materials:**

[|Image] [|Problem-Solution Graphic Organizer] [|Circle the Sage activity] [|Geometer's Sketchpad tutorial]
 * Resources:**

Geometer's Sketchpad Laptops (Student's and Teacher's) Web Link Projector [|Image]
 * Technology:**

__Source for Lesson Plan and Research__
Image: [] This is an image of a skyscraper in the making. Problem-Solution Graphic Organizer: [] This site gives the PDF file for usage. Circle the Sage activity: [] This site shows how to use the Circle the Sage activity. Geometer's Sketchpad tutorial: [] This site gives a video tutorial of how to use Geometer's Sketchpad.

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** Students will be asked to consider the task of recognizing which representation of a symbol, table, graph, or use verbal rules are being used through different approaches throughout this lesson on polynomials. To address the "beach ball learner", students will be introduced to the concept of polynomials through art, brainstorming ideas, peer discussion, and lecture and group discussion. Students will be provided with lectures, notes, peer perspectives, online resources, and feedback in order to absorb all information. This lesson asks students to use new activities to process their thinking when it comes to recognizing which representation of a symbol, table, graph, or use verbal rules are being used. They are able to expand as little or as much knowledge on each of the representations as they feel necessary. To address the "clipboard learner", the lesson has been organized in such a fashion that every assignment given builds on the next. When students begin the lesson, they understand that they are going to be working with four different representations. As the lesson progresses, students will realize that these representations are everywhere. At the end of this lesson, the Geometer's Sketchpad image will provide the students with an artistic representation of what they have accomplished in the lesson. To address the "microscope learner" students will be asked to analyze different representations at the beginning of the lesson. They will have to understand these concepts in order to recognize when these representations are being used. Students will also have to be able to discuss their findings with their peers and absorb more information from the opinions of others. To address the "puppy" learner, students will be asked to work together in groups to answer a question about the representations and where to find them in nature. Throughout the lesson, students are asked to "report out" their findings and share their ideas of where these represenations are found. These groups are designed to get peers to support other peers.
 * //Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development.//

Rationale:** Please refer to my content notes. I used the Maine Learning results for Algebra in Mathematics that states students understand and use polynomials and expressions with rational exponents. In this lesson, students will gain knowledge of how to recognize which representation of a symbol, table, graph, or use verbal rules are being used. At the beginning of the lesson students are familiarizing themselves with the different representations found in Algebra. Once the students gain this knowledge on polynomials, they are going to apply their knowledge in making a Geometer's Sketchpad image. This is a personal representation of their knowledge of recognizing which representation of a symbol, table, graph, or use verbal rules are being used. They will have to apply what they know to create this summative assessment and develop sufficient artifacts that demonstrate their knowledge on the subject matter. Students will have to use what they know in order to create artifacts that will be used later on in the unit.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:**
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * Verbal:** Students will be asked to discuss the Algebraic content in groups.
 * Visual:** An image is being shown for my hook.
 * Logical:** Students had to think about the different representations of Algebra and how they are used in real life.
 * Naturalist:** While using to Problem-Solution Charts the students will be asked to go outside to find algebra in nature.
 * Kinesthetic:** Students will be asked to change groups during the Circle the Sage activity.
 * Intrapersonal:** Students are working alone when filling out the Pre and Post student survey.
 * Interpersonal:** During the activity Circle the Sage the students are asked to work in groups.

Students are going to produce a Geometer's Sketchpad image at the end of this lesson. The image is a Type II technology because students are given the task of creating evidence of their understandings for a variety of representations in Algebra. Students will be asked to create meaningful artifacts that clearly demonstrate their understanding and ability to recognize the material. Students will use the Problem-Solution Graphic Organizer, and the Circle the Sage activity in order to create these artifacts that demonstrate their new knowledge about recognizing which representation of a symbol, table, graph, or use verbal rules are being used. Students will be asked to create their own image of where these representations are found in the real world, so the information becomes embedded in their brains and their product reflects this in a Type II way. Students will use some of their personal references to create these artifacts and use them in an electronical way that best makes sense to them. This allows students to take the information that they have learned throughout this lesson and process it in their own way and create an electronic presence that they will have to reference at later times.

Rationale: Formative (Assessment for Learning)** When students are doing the Circle the Sage activity, they will have a chance to rethink the Algebraic content. This activity is used by putting students into groups. The teacher will divide the number of students in class by four, as even as possible. One student from each group will be appointed a representation to be an expert on. The students in the group will answer the question where would you use this representation in real life? The expert will be the one to decide whether or not the answers given are correct examples. All the students in the group will need to keep a list as examples are given. Once each group has five or more examples listed, the students will then be divided into different groups where one or more members from each group form a new group. There should be at least one member from each original group. These original members are now the expert on their representation. Each member shares to the rest of the group what the representation is and what are the examples the original group came up with. By the end of this activity, every student should have examples for all four representations. Students will be able to incorporate ideas from the Problem-Solution chart that had students think about the different places where they have seen Algebra. During this activity students were asked to go outside to explore where they see applications of Algebra and skyscrapers or buildings can be included. Once everyone has shared their answers we will discuss it as a class. Both the Problem-Solution and the list of examples of each repesentation will be checked over during the class discussion. Students will be asked to make an image using Geometer's Sketchpad involving all the information gained from the previous activities. The teacher will give constructive feedback about these activities in order to complete a well made Geometer's Sketchpad image. Once the students have produced a rough copy of their Geometer's Sketchpad image, the teacher will conference with the students about the progress of their image. Students will be able to revise and refine the image before the teacher scores the final product using a checklist. Students will be able to rehearse the presentation before the actual presentation time. Students will have a chance to show their knowledge through the Pre and Post student survey.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

In class, students will be asked produce an image of a shape of a specific polynomial using Geometer's Sketchpad. The polynomial used should be visible on the image. Also, somewhere in the image there should be an explanation of why the polynomial would look like it does using the knowledge learned in the previous lesson. Once it has been completed, students will be asked to post it to the class wiki so the we can refer back to it whenever needed. The Geometer's Sketchpad image will be graded using a checklist.
 * Summative (Assessment of Learning)**

__Teaching and Learning Sequence__
Lesson two's primary focus is on recognizing which representation of a symbol, table, graph, or use verbal rules are being used that will be later used throughout the unit. In this lesson, students will be asked to work individually and in groups, so the classroom arrangement that is best suits this lesson is the "U's" arrangement. This arrangement is functional because students will not have to rearrange desks in order to do the Problem-Solution Graphic Organizer and it allows the class to have a discussion of what representations they have discovered outside, which is encouraged. Students will all still be facing the front of the room, which is also an important component because they are being introduced to new ideas. On the second day students will be asked to participate in the Circle the Sage activity and therefore, the desks will be in the "clusters" arrangement. This arrangement is functional because students will not have to rearrange desks in order to work in groups. The agenda appears as follows:

· Students will view the [|Image] about skyscrapers. (5 min) · Students will have a chance to fill in the Pre part of their Pre and Post student survey before the rest of the lesson begins. (10 min) · Students will receive [|Problem-Solution Graphic Organizer]. (2 min) · Students will fill in the [|Problem-Solution Graphic Organizer] with the titles and they will receive instuctions. (8 min) · Students will go outside to fill in their [|Problem-Solution Graphic Organizer] (30 min) · Students will be asked to participate in a class discussion about their observations from outside. During this time I will walk around the room and check every student's work. (20 min) · Students will be assigned to go outside around their home to add more examples to their graphic organizers. (5 min)
 * __Day 1:__**

· Stu​dents will be handed a playing card as they walk into the classroom and a copy of the [|Circle the Sage activity]. (5 min) · Students will receive instruction on how to get into their groups. (5 min) · Students will receive instruction about the [|Circle the Sage activity] and what their roles are. (5 min) · Students will receive instruction about the question. (5 min) · Students will share their answers to the questions in their groups and record all answers. (10 min) · Students will be assigned to add to their answers through the use of their graphic organizer. (5 min) · Students will be asked to change groups to gather new information about the other presentations from the other tables. Approximately 5 minutes to share each of the four representations. (20 min) · Students will be asked to participate in a class discussion about the different examples of the four different represenations. During this time I will walk around the room and check every student's work. (15 min) · Students will have a chance to fill in the Post part of their Pre and Post student survey. (10 min)
 * __Day 2:__**

__**Day 3:**__ · Students will be introduced to the Geometer's Sketchpad image project through a [|Geometer's Sketchpad tutorial] in video form. (30 min) · Students will receive instruction for the Geometer's Sketchpad image. (10 min) · Students will work on the Geometer's Sketchpad image project and have a chance to ask questions before completing it for homework. (40 min)

Throughout this lesson, students will understand that Algebra is made up of symbols, tables, graphs, and verbal rules that need to be chosen for the best representation and they can convert from one to another. This lesson is focused around the Maine Learning Result that **students will understand and use polynomials and expressions with rational exponents**. In this lesson particularly, students will be asked to recognize which representation of a symbol, table, graph, or use verbal rules are being used by going outside to find examples. They will learn this in order to design and build a skyscraper one must use Algebraic methods. The hook that I will show is an [|Image]. It shows This is an image of a skyscraper in the making.
 * Where, Why, What, Hook Tailor: Visual, Logical**

Students need to become familiar with the different representations of a symbol, table, graph, or use verbal rules used in Algebra. The [|Problem-Solution Graphic Organizer] will be used to map out examples of the different representations by going outside to find the different represenations in nature. Then, when students are using the [|Circle the Sage activity], they will have a chance to rethink the Algebraic content by answering the question that will later incorporate more examples. The teacher will divide the number of students in class by four, as evenly as possible using a deck of cards. Each person, as they walk into class, will recieve a card. Each suit will then form a group. If this is done properly, there should be four groups, each group all the same suit. One student from each group will be appointed a representation to be an expert on. The students in the group will answer the question where would you use this representation in real life? The expert will be the one to decide whether or not the answers given are correct examples. All the students in the group will need to keep a list as examples are given. Once each group has five or more examples listed, the students will then be divided into different groups where one or more members from each group form a new group. There should be at least one member from each original group. These original members are now the expert on their representation. Each member shares to the rest of the group what the representation is and what are the examples the original group came up with. By the end of this activity, every student should have examples for all four representations. The students will have a chance to incorporate any examples recorded from the [|Problem-Solution Graphic Organizer]. Once everyone has shared their answers we will discuss it as a class. Both the [|Problem-Solution Graphic Organizer] and the answer to the question will be checked over during the class discussion. The students will have a chance to finish the Pre and Post student survey for assessment of their understanding after the class discussion.
 * Equip, Explore, Rethink, Tailors: Verbal, Logical, Naturalist, Kinesthetic, Intrapersonal, Interpersonal**

After the students have completed the [|Problem-Solution Graphic Organizer], students will use the [|Circle the Sage activity] in order to rethink the Algebraic content. This activity is used by putting students into groups. The teacher will divide the number of students in class by four, as evenly as possible using a deck of cards. Each person, as they walk into class, will recieve a card. Each suit will then form a group. If this is done properly, there should be four groups, each group all the same suit. One student from each group will be appointed a representation to be an expert on. The students in the group will answer the question where would you use this representation in real life? The expert will be the one to decide whether or not the answers given are correct examples. All the students in the group will need to keep a list as examples are given. Once each group has five or more examples listed, the students will then be divided into different groups where one or more members from each group form a new group. There should be at least one member from each original group. These original members are now the expert on their representation. Each member shares to the rest of the group what the representation is and what are the examples the original group came up with. By the end of this activity, every student should have examples for all four representations. The students will have a chance to incorporate any examples recorded from the [|Problem-Solution Graphic Organizer]. Once everyone has shared their answers we will discuss it as a class. Both the [|Problem-Solution Graphic Organizer] and the answer to the question will be checked over during the class discussion. Now that the students have been able to recognize which representation of a symbol, table, graph, or use verbal rules are being used through the use of the [|Problem-Solution Graphic Organizer], and they have answered the question during the [|Circle the Sage activity], they are ready to start working on their Geometer's Sketchpad Summative Assessment image project. Students will be able to show and apply the different represenations using the Geometer's Sketchpad program. I will start by introducing them to the Geometer's Sketchpad program through the use of a video tutorial. Students will make a Geometer's Sketchpad image and after I give feedback, they will be able to revise it. Students will refine the image before I score the final product. Students will be able to rehearse the presentation before the actual presentation time.
 * Explore, Experience, Rethink, Rehearse, Revise, Tailors: Verbal, Visual, Logical, Naturalist, Kinesthetic, Intrapersonal, Interpersonal**

Students will be able to self-asses their progress through a Pre and Post student survey of understandings as well as through the feedback that I provide in the class discussion. I will provide timely feedback through verbal comments and through addressing questions that I receive from students. When they complete the Pre and Post student survey and are working on their Geometer's Sketchpad image project, I will give students an opportunity to come up and resolve any issues that arise. I will provide times where I will be available for helping students with their Geometer's Sketchpad image project and with any questions that they still do not understand through the use of my office hours. I will have students upload their Geometer's Sketchpad image project to the class wiki artifacts page so that anyone can reference it at any time. I will give them timely feedback by assessing their product with a Checklist in which students will earn their points for completing the Geometer's Sketchpad image project. Creating the image and having students upload it to the class wiki means they will be able to go back and refer to these for future assignments. The more details that the students are in their Geometer's Sketchpad image, the more reference material they are going to have for the Performance Task. The next lesson works more with symbols, tables, graphs, and the use of the verbal rules. If students do well on the next lesson and the next project, they will be able to use this to reference for the Performance Task as well.
 * Evaluate, Tailors: Visual, Logical, Intrapersonal**

__Content Notes__
The question to the [|Circle the Sage activity]. · Question: Where would you use this representation in real life?
 * __Day 2:__**

Geometer's Sketchpad image project Instructions: In class, students will be asked produce an image of a shape of a specific polynomial using Geometer's Sketchpad. The polynomial used should be visible on the image. Also, somewhere in the image there should be an explanation of why the polynomial would look like it does using the knowledge learned in the previous lesson. Once it has been completed, students will be asked to post it to the class wiki so the we can refer back to it whenever needed. The Geometer's Sketchpad image will be graded using a checklist.
 * __Day 3:__**

__Handouts__
Check List [|Problem-Solution Graphic Organizer] [|Circle the Sage activity] Question