L6+Mitchell,+Jesse


 * LESSON PLAN FORMAT

Teacher’s Name: Jesse L Mitchell Date of Lesson: Lesson 6 Grade Level: 9-12 Topic: Trigonometry

Objectives Student will understand that the six trigonometric functions are essential in solving for unknowns. Student will know all knowledge learned in previous lessons. Student will be to compare different approaches to solving problems.

Maine Learning Results Alignment

Maine Learning Results: Mathematics- C. Geometry Geometric Figures Grades 9-Diploma 3. Students understand and use basic ideas of trigonometry. b. Use trigonometry to solve for missing lengths in right triangles.

Rationale: It is important for students to be able to see different approaches to solving the same problem. Some ways work better for, and more sense to some students more than others. It is important that students realize that many situations have more than one approach. During this lesson, students will compare several approached to solving problems, discovering which approaches better speak to their needs as an individual.

Assessment

Formative (Assessment for Learning) The class will begin by viewing the video New Math. This will start a discussion of how there are many approaches to the same problem. Students were introduced to problem solving approached earlier in the unit, and this lesson will build on that, going more in depth than the previous lesson. Students will first brainstorm individually different ways to approach the same trigonometric problems. While students are working, I will float around the room, giving each student individual feedback. Once students have completed the worksheet, they will get into groups of 2-3, that they choose, in order to compare worksheets and to receive feedback on their approaches to solving the problem. There is a sample worksheet attached. Once students have been given feedback, then will have time to revise the worksheet based on this feedback. The worksheet must be turned in by the end of class. After a small period to reflect on the worksheet, I will move to part two of the day’s assignment, filling out a Venn diagram. Summative (Assessment of Learning) After the worksheets are completed, there will be a short class discussion of the many ways approaches that can be used to solve the same problem. Once students have shared any view points that they wish to talk about, and all questions have been answered, Venn diagrams will be handed out. Students will be give time in class to begin this assignment. Each student will receive a problem that utilizes trigonometry. Then, they must compare two different ways to solve the problem using their Venn diagram. By allowing students to begin their Venn diagrams in class, they will be able to ask any questions they might encounter while beginning the comparison. This assignment is due at the start of the next class period, as well as entry in their blog describing the day’s events. After posting to the blog, students will receive feedback from their peers via comments on each others' blog entries. After receiving feedback, students will have the opportunity to make changes to their entry due the following class. If the choose to make any changes to their blog, they may gain some additional points to their final grade. There is a sample Venn diagram, as well as a sample blog entry attached. *Note: at the end of the class period, I will be introducing the performance task, which students will work on during the next class period, and is due the class after that.

Integration Reading Comprehension- Students will be using Venn diagrams to compare approaches to problem solving.

Technology- Students will start the period by viewing the video New Math.

Groupings Once students have completed their worksheets, they will be given the opportunity to get into groups of 2-3 to give feedback on their ideas. Students will choose their partner or partners. Each student will then take turns describing one way to solve the problem, while their partner(s) give feedback on the approach. As students are working, I will be circulating around the room to ensure that each student is contributing to the group. After each student has been given feedback on their ideas, they will be given time to make any revisions they would like, based in this feedback, before handing in the worksheet at the end of class. Students will return to working individually to begin their Venn diagrams.

Differentiated Instruction

Strategies Verbal- Class discussion. Logical- Brainstorming ways to problem solve. Interpersonal- Share brainstorming with a partner. Intrapersonal- Do initial brainstorming individually. Spatial- Filling out chart of pros and cons, as well as Venn diagram. Musical- Class began with song about different approaches to problem solving. . Modifications/Accommodations

I will review student's IEP, 504, or ELLIDEP and make appropriate modifications and accommodations. Absent students are responsible for coming to see me during the next day that they are in class in order to receive any make-up work. Upon meeting with me I will decide, based upon any activities they missed, whether or not they must stay and make up time after school, or if an alternate assignment would be just as sufficient. Absent students have 3 days upon returning to school in order to make up missed work, or, under extenuating circumstances, to make arrangements with me as to when this work will be due. Absent students will lose points for classroom participation, but will be given the option of doing an alternate assignment of my choice in order to make up the lost points.

Extensions

Students will begin the class with a discussion about how there are many different ways to approach the same problem. Students were introduced to this idea in an earlier lesson, and this lesson will continue off of that, and go much more in-depth. Once students have brainstormed ideas individually, they will chose a partner or partners of their choice to compare techniques with. Based in this feedback, students will refine their worksheets before handing them in at the end of class. Next, students will be given Venn diagrams to fill out. Each student will get a problem using trigonometry, and they must compare two different approaches to solving the problem using the Venn diagram. While students are working, I will be floating around the room, monitoring student work, and giving feedback when necessary. The Venn diagrams will be due at the start of the next class period.

Materials, Resources and Technology Scratch Paper and Pencils Laptops with an Internet Connection

Source for Lesson Plan and Research Blogger.com- Students will post the day's events on their blogs.

New Math Video- This is a video hook that will begin a discussion on different approaches to problem solving.

Maine Standards for Initial Teacher Certification and Rationale

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: This lesson addresses the Maine Standards for Initial Teacher Certification by providing students with various flexible learning opportunities. This is a great lesson for students who are microscopes. Microscopes will enjoy analyzing and compare the two approaches to solving their problem using the Venn diagram. For my students who are clipboards, I always provide a list of the day’s agenda on the board, as well as make sure that when I am floating that they are staying on task by giving added instructions as needed. Clipboards thrive best with structure, so allowing them to have a list of events helps to ensure that they are staying in track. Beach balls enjoy brainstorming, so allowing students to brainstorm their own approaches to problem solving speaks to the strengths of a student who is a beach ball. Group work is essential to a puppy’s strength. A student who is a puppy gains the most from peer-to-peer tutoring, as well as participating groups, making the formative assessment a great part of the lesson for them. By speaking to all types of learning styles, all students are able to show their strengths and stay involved, creating a much more engaging classroom atmosphere.

• Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by creating an environment where students must use higher level thinking. Students will have to explain their viewpoints to one another in order to receive peer feedback on their worksheets. Each student will need to interpret the trigonometry problem presented to them in multiple ways in order to partake in the formative assessment, as well as to complete the summative assessment. In order to discover an appropriate way to solve each of the trigonometric problems given to them, each student will have to apply all of their previous knowledge of trigonometry to the task at hand. During the feedback session, each student will consider another student’s perspective on how to approach the problem, as well as show empathy for the approach in order to truly understand their viewpoint. Finally students will be able to show self-knowledge as they reflect upon each idea, considering their knowledge, and what they need in order to understand the assignment. When students partake in all stages of higher level thinking, they are able to gain so much more from a lesson; higher level thinking creates a much richer atmosphere for everyone.

• Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. Rationale: students’ needs. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by incorporating a variety of methods designed to speak to multiple intelligences in the classroom. Providing an opportunity for several intelligences in a classroom environment ensures that more students will be given a chance to show their strength and provide a better learning environment overall.

Verbal- Class discussion. Logical- Brainstorming ways to problem solve. Interpersonal- Share brainstorming with a partner. Intrapersonal- Do initial brainstorming individually. Spatial- Filling out chart of pros and cons, as well as Venn diagram. Musical- Class began with song about different approaches to problem solving.

For each class period, students will post blog entry reflecting that days assignment. Peers will then be able to go onto the class blog to provide peer feedback to the student. If the student so chooses, they will be able to update the assignment before the next class period based in the peer feedback they received. The blog will include a post for each lesson, as well as their final assessment. Additional blogs maybe assigned at my discretion.

• Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing each student with several opportunities for feedback throughout the lesson. The lesson will begin by viewing the video New Math. This will start a class discussion about various ways to approach the same problem. I will discuss several problems that require trigonometry, as well as several ways to approach each one (see teacher notes). After a short lecture, I will give students a worksheet to fill out on similar material. Students will complete the worksheet individually while I float around the room, answering student questions and ensuring that all students have the tools necessary to complete the assignment. Once students have completed the worksheet, they will choose a partner to compare answers, as well as to give and receive feedback with. As students are working together, I will continue circulating around the room, giving additional feedback and making sure that each student is contributing to the feedback process. Next students will return to working individually in order to refine their worksheets before handing them in. After all the worksheets have been handed in, I will introduce the homework assignment. Students will each get a Venn Diagram to fill out comparing different ways to approach the same trigonometric problem. I will give students different problems to look at (see teacher notes). Students will begin working on this assignment in class so I can address any problems the students might have as they start the assignment. The Venn diagram is due next class, along with a blog entry that describes the day’s events. The blog entry should be posted by the start of the next class period (see attached sample blog). After posting to the blog, students will receive feedback from their peers via comments on each others' blog entries. After receiving feedback, students will have the opportunity to make changes to their entry due the following class. If the choose to make any changes to their blog, they may gain some additional points to their final grade.

Teaching and Learning Sequence:

The classroom will be set-up in a traditional classroom format, facing the board. The class will start with a group discussion about the video New Math (hook). After the discussion, students will work individually on a worksheet about comparing approaches to problem solving. Once each student has completed the worksheet, they will get into pairs to compare answers and give each other feedback. Students will then return to working individually to begin their homework assignment, a Venn Diagram comparing different approaches a trigonometry problem that I will assign (see attached teacher notes). This classroom set-up allows students to easily go from working individually, to getting in pairs, then moving back to their seats to begin their homework.


 * Students watch New Math (5 minutes)
 * Discussion and lecture about different approaches to problem solving (10 minutes)
 * Students complete worksheet individually (10 minutes)
 * Peer feedback session (10 minutes)
 * Students refine and hand in worksheets (5 minutes)
 * Venn Diagram introduced (5 minutes)
 * Students begin Venn Diagram in class (10 minutes)
 * Performance task introduced (15 minutes)
 * Students may choose between working on Venn Diagram and starting work on Performance task.
 * Students will be given a 5 minute warning to pick up before the end of class, 10 minutes for any student who may have a laptop out (for work on performance task)

Throughout this lesson students will build upon the idea that the six trigonometric functions are essential in solving for unknowns within a right triangle. Students will begin with a video called New Math that introduces a new way to add numbers. This will begin a discussion about how there are many ways to approach the same problem. After a short lecture, students will complete worksheets individually that cover the material in the lesson (see attached). Students will then get into pairs of their choice to engage in peer-to-peer feedback. Once students have had a chance to refine their worksheets and hand them in, I will introduce the homework assignment, which they will begin in class. Students will each be given a problem that requires trigonometry to solve. Then will then fill out their Venn diagrams by comparing two different ways to solve the problem. As students are working, I will continue to circulate around the room, answering questions and giving student feedback as necessary to ensure that each student understands the key concepts behind the assignment. This lesson builds upon the ideas introduced in lesson 4. Each problem has many ways to solve, each way may be easier or harder for any particular student. It is important for students to understand that there is many ways to go about the same situation, so it is okay to explore ideas when trying to solve a problem that they are having trouble with. This lesson also speaks to a variety of student intelligences as I have mentioned earlier in the lesson plan [See rationale statement for standard 5]. Providing an opportunity for students to express their strengths throughout the their multiple intelligences allows for a greater learning experiences for all students. What, Where, Why, Hook, Tailor: Verbal, Logical, Interpersonal, Intrapersonal, Spatial, Musical

Students will know all knowledge learned in previous lessons, as well as a stronger understanding of the idea that there are many different approaches to the same problem. The lesson will begin by having students view the video New Math. This will start a discussion on how they are different approaches to the same problem, some better then others given a particular situation. There will then be a short lecture where I go other several different problems, and multiple ways to approach them, and the pros and cons of using each method in each situation. I will stress that each method works best in any given situation, but most can be applied to any situation (see teacher notes). Students will then fill out a worksheet (see attached) that details the same idea. They will be given a trigonometric problem, and several ways to solve, and must justify the ‘better’ approach. After students have filled out their worksheets, they will choose a partner to engage in peer-to-peer feedback with. As students work individually on the worksheets, I will be answering students’ questions at their seats. I will also be circulating to observe student work, giving suggestions when necessary to ensure student understanding. Next students will be given an opportunity to refine their worksheets based on the peer feedback before handing in a final copy. Next I will introduce the homework assignment. Students will each be given a problem that requires trigonometry to solve. Then will then fill out their Venn diagrams by comparing two different ways to solve the problem. As students are working, I will continue to circulate around the room, answering questions and giving student feedback as necessary to ensure that each student understands the key concepts behind the assignment. Students will begin the assignment in class, and it is due at the start of next class. Equip, Tailor: Verbal, Logical, Interpersonal, Intrapersonal, Spatial, Musical

Students will be able to compare different approaches to solving problems. Students will begin the lesson with a video (see hook) that will start a discussion about the pros and cons of different approaches to problem solving. After a short lecture, students will explore this concept by individually filling out a worksheet about similar material. While students are completing the worksheet, I will be floating around, answering individual questions. This gives students a chance to rethink their worksheets. After worksheets are completed, each student will choose a partner to engage in peer-to-peer feedback with. By receiving peer feedback, students are able to revise any of their answers based in this feedback. As students are working in pairs, I will continue to float around to ensure that each student is contributing to the feedback process. Next students will be given the opportunity to individually refine their worksheets before handing them in. Once all the worksheets have been completed, I will introduce the homework. Students will have to fill out a Venn Diagram comparing two different approaches to solving the same trigonometric problem, which I will give to them. They will begin the diagrams in class so that I can answer any questions that they might have as they start the assignment as I continue to float around the classroom to observe student work. The Venn Diagrams are due at the start of next class. I will facilitate the learning process by having student engage in all six stages of higher level thinking. Students will have to explain their viewpoints to one another in order to receive peer feedback on their worksheets. Each student will need to interpret the trigonometry problem presented to them in multiple ways in order to partake in the formative assessment, as well as to complete the summative assessment. In order to discover an appropriate way to solve each of the trigonometric problems given to them, each student will have to apply all of their previous knowledge of trigonometry to the task at hand. During the feedback session, each student will consider another student’s perspective on how to approach the problem, as well as show empathy for the approach in order to truly understand their viewpoint. Finally students will be able to show self-knowledge as they reflect upon each idea, considering their knowledge, and what they need in order to understand the assignment. When students partake in all stages of higher level thinking, they are able to gain so much more from a lesson; higher level thinking creates a much richer atmosphere for everyone. Explore, Experience, Rethink, Revise, Rehearse, Refine, Tailor: Verbal, Logical, Interpersonal, Intrapersonal, Spatial, Musical

Students will be giving plenty of opportunities for self-assessment, as well as feedback. The lesson will begin by viewing the video New Math. This will start a class discussion about various ways to approach the same problem. I will discuss several problems that require trigonometry, as well as several ways to approach each one (see teacher notes). After a short lecture, I will give students a worksheet to fill out on similar material. Students will complete the worksheet individually while I float around the room, answering student questions and ensuring that all students have the tools necessary to complete the assignment. Once students have completed the worksheet, they will choose a partner to compare answers, as well as to give and receive feedback with. As students are working together, I will continue circulating around the room, giving additional feedback and making sure that each student is contributing to the feedback process. Next students will return to working individually in order to refine their worksheets before handing them in. After all the worksheets have been handed in, I will introduce the homework assignment. Students will each get a Venn Diagram to fill out comparing different ways to approach the same trigonometric problem. I will give students different problems to look at (see teacher notes). Students will begin working on this assignment in class so I can address any problems the students might have as they start the assignment. The Venn diagram is due next class, along with a blog entry that describes the day’s events. The blog entry should be posted by the start of the next class period (see attached sample blog). After posting to the blog, students will receive feedback from their peers via comments on each others' blog entries. After receiving feedback, students will have the opportunity to make changes to their entry due the following class. If the choose to make any changes to their blog, they may gain some additional points to their final grade. This assignment has a strong real world connection (see teacher and learning sequence paragraph one), which connects strongly to the performance task (see webquest). Throughout the performance task students will combine all the material learned throughout all six lessons. Evaluate, Refine, Tailor: Logical, Verbal, Spatial, Interpersonal, Intrapersonal, Naturalistic, Bodily-Kinesthetic, Musical**

= =