L3+McGinley,+Sarah

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

Teacher’s Name:** Ms. McGinley **Lesson 3:** Interpret
 * Grade Level:** Nine **Topic:** Polynomials

__Objectives__
Students will understand that Algebra is made up of equations that need to be simplified. Students will know expression, equation, exponentials, solve, simplify, symbols, verbal rules, factoring, and inequalities mean. Students will be able to do demonstrate how to simplify equations.

__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 judge which representation of a symbol, table, graph, or use verbal rules.

__**Assessment**__
When students are doing the Numbered Heads Together activity, they will have a chance to rethink the Algebraic content. For this activity students are asked to split into groups of four. The students will be able to share their ideas with the rest of the group. Within the groups each member has a number and as a group the team must answer questions. The questions the groups will be asked to answer are, What formulas should you know in order to graph an equation? When is it easier to use verbal rules to explain specific examples? Is it possible to estimate information from a graph or table in order to make an equation? If yes, then how? How can you represent an equation in a table? Why is it good to use different representations of the same data? Where would you use the different representations in real life? Students will be asked to answer all questions during share time in the group. The Spider Map will have students think about each representation and how another class used that representation to explain some type of data. The students will have a chance to incorporate any information recorded from the Spider Map Graphic Organizer. When the teacher says a number of a student then that numbered person from each group gives the answer that they discussed in their group. Once everyone has shared their answers we will discuss it as a class. Both the Spider Map Graphic Organizer and the answers to the questions will be checked over during the class discussion. Students will be asked to write a Blog involving all the information gained from the previous activities. The teacher will give constructive feedback about these activities in order to complete a well written Blog. Once the students have written a rough copy of their Blog, the teacher will conference with the student about the progress of the Blog. Students will be able to revise and refine their Blog before the teacher scores the final posted Blog entry 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 their journal entries before and after the lesson.
 * Formative (Assessment for Learning)**

Students will be asked to write a blog entry in which they create a symbol, table, or graph from a word problem or equation. The students will post the blog for his or her peers to comment on. Do they understand the graphic you posted? In the blog entry explain the process that created the image and discuss which representation is better to use in what kind of situation. You should have a situation for each representation. All students will comment at least once about the blog and the student who posted the blog will make one comment back to his or her peers. This Blog will be graded using a checklist.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be asked to write a Blog that shows example of each type of representation. The students will post the blog for his or her peers to comment on. Do they understand the graphic you posted? In the blog entry explain the process that created the image and discuss which representation is better to use in what kind of situation. You should have a situation for each representation. All students will comment at least once about the blog and the student who posted the blog will make one comment back to his or her peers.

English: During the Formative Assessment, students are asked to write a journal entry before and after the lesson about the different representations. Writing these journal entries will show what the students already know about the different representations and what they have learned after the lesson. During the Summative Assessment, students are asked to write a Blog about the different representations and comment on student's comments about their Blog entry.

Music: During the hook, I ask students to think about other classes they are currently taking in high school and to relate the four representations to those classes. I give the students some examples, such as chorus or any other type of music class to relate the represenations to the musical chords.

__Groupings__
When students are doing the Numbered Heads Together 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 the class into groups of four, as evenly as possible using small slips of paper with each representation written on it. Along with each representation, there will be a number on each slip of paper, 1 through 4, corresponding with each represenation. There are four representations, symbols which is numbered 1, tables which is numbered 2, graphs which is numbered 3, and verbal rules which is numbered 4, to consider. Each group will have one of each representation in the group. Before class begins, the teacher will have put an even amount of each representation of the amount of students are in the class. Each person, as they walk into class, will recieve a slip of paper. Students will divide themselves into groups making sure there is one representation for each group. If this is done properly, there should be several groups of four people, each group with each representation. Within the groups each member has a number and as a group the team must answer questions. The questions the groups will be asked to answer are, What formulas should you know in order to graph an equation? When is it easier to use verbal rules to explain specific examples? Is it possible to estimate information from a graph or table in order to make an equation? If yes, then how? How can you represent an equation in a table? Why is it good to use different representations of the same data? Where would you use the different representations in real life? Students will be asked to answer all questions during share time in the group. The Spider Map will have students think about each representation and how another class used that representation to explain some type of data. The students will have a chance to incorporate any information recorded from the [|Spider Map Graphic Organizer]. When the teacher says a number of a student then that numbered person from each group gives the answer that they discussed in their group. Once everyone has shared their answers we will discuss it as a class.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal:** We will open with a group discussion.
 * Visual:** Students will use a Spider Map to brainstorm ideas.
 * Musical:** Students will have a chance to incorporate music and how it relates to the four represenations during the hook.
 * Logical:** Students had to think about the different representations of Algebra and how they are used in other courses.
 * Kinesthetic:** Students will need to get into groups during the Numbered Heads Together activity.
 * Intrapersonal:** Students are working alone when they write in their journal.
 * Interpersonal:** During the Numbered Heads Together activity 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 to write a Blog that shows example of each type of representation. The students will post the blog for his or her peers to comment on. Do they understand the graphic you posted? In the blog entry explain the process that created the image and discuss which representation is better to use in what kind of situation. You should have a situation for each representation. All students will comment at least once about the blog and the student who posted the blog will make one comment back to his or her peers.
 * Extensions**

English: During the Formative Assessment, students are asked to write a journal entry before and after the lesson about the different representations. Writing these journal entries will show what the students already know about the different representations and what they have learned after the lesson. During the Summative Assessment, students are asked to write a Blog about the different representations and comment on student's comments about their Blog entry.

Music: During the hook, I ask students to think about other classes they are currently taking in high school and to relate the four representations to those classes. I give the students some examples, such as chorus or any other type of music class to relate the represenations to the musical chords.

__Materials, Resources and Technology__
Student laptops Internet Teacher computer Blank lined paper Checklist Journals [|Spider Map Graphic Organizer] [|Numbered Heads Together activity] [|Blogger] Small slips of paper
 * Materials:**

[|Spider Map Graphic Organizer] [|Numbered Heads Together activity]
 * Resources:**

Laptops (Student's and Teacher's) [|Blogger]
 * Technology:**

__Source for Lesson Plan and Research__
Numbered Heads Together activity: [] This site shows how to use the Numbered Heads Together activity. Spider Map Graphic Organizer: [] This site gives the PDF file for usage. Blogger: [] This site is where students will have an account in order to post a blog.

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** Students will be asked to consider the task of judging which representation of a symbol, table, graph, or verbal rule to use throughout this lesson on polynomials. To address the "beach ball learner", students will be introduced to the concept of polynomials through brainstorming ideas, peer discussion, and lecture and group discussion. Students will be provided with lectures, notes, peer perspectives, online resources, textbook, and feedback in order to absorb all information. This lesson asks students to use new activities to process their thinking when it comes to judging 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 Blogs will provide the students with a verbal 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 judge 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 some questions about the representations and where to find them in other areas of study. 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 judge which representation of a symbol, table, graph, or 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 writing a Blog entry. This is a personal representation of their knowledge of judging which representation of a symbol, table, graph, or verbal rules are being used. They will have to interpret 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:** We will open with a group discussion.
 * Visual:** Students will use a Spider Map to brainstorm ideas.
 * Musical:** Students will have a chance to incorporate music and how it relates to the four represenations during the hook.
 * Logical:** Students had to think about the different representations of Algebra and how they are used in other courses.
 * Kinesthetic:** Students will need to get into groups during the Numbered Heads Together activity.
 * Intrapersonal:** Students are working alone when they write in their journal.
 * Interpersonal:** During the Numbered Heads Together activity the students are asked to work in groups.

Students are going to produce a Blog at the end of this lesson. The Blog 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 judge the material. Students will use the Spider Map Graphic Organizer, and the Numbered Heads Together activity in order to create these artifacts that demonstrate their new knowledge about judging which representation of a symbol, table, graph, or verbal rule are being used. Students will be asked to write their own Blog entry of where these representations are found in the different areas of study, 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 Numbered Heads Together activity, they will have a chance to rethink the Algebraic content. For this activity students are asked to split into groups of four. The students will be able to share their ideas with the rest of the group. Within the groups each member has a number and as a group the team must answer questions. The questions the groups will be asked to answer are, What formulas should you know in order to graph an equation? When is it easier to use verbal rules to explain specific examples? Is it possible to estimate information from a graph or table in order to make an equation? If yes, then how? How can you represent an equation in a table? Why is it good to use different representations of the same data? Where would you use the different representations in real life? Students will be asked to answer all questions during share time in the group. The Spider Map will have students think about each representation and how another class used that representation to explain some type of data. The students will have a chance to incorporate any information recorded from the Spider Map Graphic Organizer. When the teacher says a number of a student then that numbered person from each group gives the answer that they discussed in their group. Once everyone has shared their answers we will discuss it as a class. Both the Spider Map Graphic Organizer and the answers to the questions will be checked over during the class discussion. Students will be asked to write a Blog involving all the information gained from the previous activities. The teacher will give constructive feedback about these activities in order to complete a well written Blog. Once the students have written a rough copy of their Blog, the teacher will conference with the student about the progress of the Blog. Students will be able to revise and refine their Blog before the teacher scores the final posted Blog entry 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 their journal entries before and after the lesson.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

Students will be asked to write a blog entry in which they create a symbol, table, or graph from a word problem or equation. The students will post the blog for his or her peers to comment on. Do they understand the graphic you posted? In the blog entry explain the process that created the image and discuss which representation is better to use in what kind of situation. You should have a situation for each representation. All students will comment at least once about the blog and the student who posted the blog will make one comment back to his or her peers. This Blog will be graded using a checklist.
 * Summative (Assessment of Learning)**

__Teaching and Learning Sequence__
Lesson three's primary focus is on judging which representation of a symbol, table, graph, or verbal rule 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 "Two's" arrangement. This arrangement is functional because students will not have to rearrange desks in order to do the Spider Map Graphic Organizer and it allows the class to have a discussion of what representations they have discovered in their other classes, 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 Numbered Heads Together 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 of four. The agenda appears as follows:

· Students will be asked to participate in a class discussion about what classes they are currently taking in school and when the representations are being utilized in these areas of study. (20 min) · Students will have a chance to write a journal entry about what they already know about the different representations we are focusing on before the rest of the lesson begins. (15 min) · Students will receive [|Spider Map Graphic Organizer]. (2 min) · Students will fill in the [|Spider Map Graphic Organizer] with the title and they will receive instuctions. (5 min) · Students will fill in their [|Spider Map Graphic Organizer] (30 min) · Students will be assigned to review their class materials from other classes to add more examples to their graphic organizers. (8 min)
 * __Day 1:__**

· Stu​dents will be handed a small slip of paper and a copy of the [|Numbered Heads Together activity] as they walk in to the classroom. (5 min) · Students will receive instruction on how to get into their groups. (5 min) · Students will receive instruction about the [|Numbered Heads Together activity] and what their roles are. (5 min) · Students will receive instruction about the questions. (5 min) · Students will share their answers to the questions in their groups and record all answers. (30 min) · Students will be assigned to add to their answers through the use of their graphic organizer. (5 min) · Students will be called on by thier number to discuss their answers as a class. During this time I will walk around the room and check every student's work. (15 min) · Students will have a chance to write a journal entry about what they learned from the previous activities about the different representations. (10 min)
 * __Day 2:__**

__**Day 3:**__ · Students will be introduced to the Blog assignment and logged in to a Blog account through []. (15 min) · Students will receive instruction for the Blog assignment. (15 min) · Students will work on their Blog entry and have a chance to ask questions before completing it for homework. (50 min)

Throughout this lesson, students will understand that Algebra is made up of symbols, tables, graphs, and verbal rules that need to be judged 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 think about each representation and how another class used that representation to explain some type of data. They will learn different areas of study uses Algebraic methods. The hook is a discussion about the student's classes they are currently taking. At this time students will incorporate any music class they maybe taking currently. This will get students thinking about how mathematics is not only one class in school but that mathematics is everyone in school.
 * Where, Why, What, Hook Tailor: Visual, Musical**

Students need to become familiar with the different representations of a symbol, table, graph, or verbal rules used in Algebra. The [|Spider Map Graphic Organizer] will be used to map out examples of the different representations from different areas of study, like their other classes the students are currently taking. Then, when students are using the [|Numbered Heads Together activity], they will have a chance to rethink the Algebraic content by answering questions that will later incorporate more examples. The teacher will divide the number of students in the class into groups of four, as evenly as possible using small slips of paper with each representation written on it. Along with each representation, there will be a number on each slip of paper, 1 through 4, corresponding with each represenation. There are four representations, symbols which is numbered 1, tables which is numbered 2, graphs which is numbered 3, and verbal rules which is numbered 4, to consider. Each group will have one of each representation in the group. Before class begins, the teacher will have put an even amount of each representation of the amount of students are in the class. Each person, as they walk into class, will recieve a slip of paper. Students will divide themselves into groups making sure there is one representation for each group. If this is done properly, there should be several groups of four people, each group with each representation. Within the groups each member has a number and as a group the team must answer questions. The questions the groups will be asked to answer are, What formulas should you know in order to graph an equation? When is it easier to use verbal rules to explain specific examples? Is it possible to estimate information from a graph or table in order to make an equation? If yes, then how? How can you represent an equation in a table? Why is it good to use different representations of the same data? Where would you use the different representations in real life? Students will be asked to answer all questions during share time in the group. The Spider Map will have students think about each representation and how another class used that representation to explain some type of data. The students will have a chance to incorporate any information recorded from the [|Spider Map Graphic Organizer]. When the teacher says a number of a student then that numbered person from each group gives the answer that they discussed in their group. Once everyone has shared their answers we will discuss it as a class.
 * Equip, Explore, Rethink, Tailors: Verbal, Logical, Kinesthetic, Intrapersonal, Interpersonal**

After the students have completed the [|Spider Map Graphic Organizer], students will use the [|Numbered Heads Together 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 the class into groups of four, as evenly as possible using small slips of paper with each representation written on it. Along with each representation, there will be a number on each slip of paper, 1 through 4, corresponding with each represenation. There are four representations, symbols which is numbered 1, tables which is numbered 2, graphs which is numbered 3, and verbal rules which is numbered 4, to consider. Each group will have one of each representation in the group. Before class begins, the teacher will have put an even amount of each representation of the amount of students are in the class. Each person, as they walk into class, will recieve a slip of paper. Students will divide themselves into groups making sure there is one representation for each group. If this is done properly, there should be several groups of four people, each group with each representation. Within the groups each member has a number and as a group the team must answer questions. The questions the groups will be asked to answer are, What formulas should you know in order to graph an equation? When is it easier to use verbal rules to explain specific examples? Is it possible to estimate information from a graph or table in order to make an equation? If yes, then how? How can you represent an equation in a table? Why is it good to use different representations of the same data? Where would you use the different representations in real life? Students will be asked to answer all questions during share time in the group. The Spider Map will have students think about each representation and how another class used that representation to explain some type of data. The students will have a chance to incorporate any information recorded from the [|Spider Map Graphic Organizer]. When the teacher says a number of a student then that numbered person from each group gives the answer that they discussed in their group. Once everyone has shared their answers we will discuss it as a class. Now that the students have been able to judge which representation of a symbol, table, graph, or use verbal rules are being used through the use of the [|Spider Map Graphic Organizer], and they have answered the question during the [|Numbered Heads Together activity], they are ready to start working on their Blog entry for the Summative Assessment. Students will be able to show and interpret the different represenations using []. I will start by introducing them to the [] and log students in to a Blog account. The teacher will give constructive feedback about these activities in order to complete a well written Blog. Once the students have written a rough copy of their Blog, the teacher will conference with the student about the progress of the Blog. Students will be able to revise and refine their Blog before the teacher scores the final posted Blog entry 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 their journal entries before and after the lesson.
 * Explore, Experience, Rethink, Rehearse, Revise, Tailors: Verbal, Visual, Logical, Kinesthetic, Intrapersonal, Interpersonal**

Students will be able to self-asses their progress through a journal entry 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 their journal entry and are working on their Blog entry assignment, 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 Blog entry assignment and with any questions that they still do not understand through the use of my office hours. I will have students upload their Blog link 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 their Blog entry. Writing the Blog and having students upload the link 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 have in their Blog entry, the more reference material they are going to have for the Performance Task. The next lesson focuses on rational exponents in polynomials and equations in order to put these equations into tables and graphs. 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 questions to the [|Numbered Heads Together activity]. · Question 1: What formulas should you know in order to graph an equation? · Question 2: When is it easier to use verbal rules to explain specific examples? · Question 3: Is it possible to estimate information from a graph or table in order to make an equation? If yes, then how? · Question 4: How can you represent an equation in a table? · Question 5: Why is it good to use different representations of the same data? · Question 6: Where would you use the different representations in real life?
 * __Day 2:__**

Blog Instructions: Students will be asked to write a blog entry in which they create a symbol, table, or graph from a word problem or equation. The students will post the blog for his or her peers to comment on. Do they understand the graphic you posted? In the blog entry explain the process that created the image and discuss which representation is better to use in what kind of situation. You should have a situation for each representation. All students will comment at least once about the blog and the student who posted the blog will make one comment back to his or her peers. This Blog will be graded using a checklist.
 * __Day 3:__**

**__Handouts__**
Checklist [|Spider Map Graphic Organizer] [|Numbered Heads Together activity] Questions Small slips of paper