L3+Mitchell,+Jesse

=**UMF LESSON PLAN FORMAT**=

**Grade Level: 9-Diploma Topic: Trigonometry**

 * =**Objectives**:= ||
 * Student will understand that the six trigonometric functions are essential in solving for unknowns within a right triangle. ||
 * Student will know terminology: reciprocal, opposite, adjacent, unit circle, and relationships: between trigonometric functions, and between the different parts of a triangle. ||
 * Student will be able to use trigonometry to solve for missing lengths in right triangles. ||

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.
 * =**Maine Learning Results Alignment**= ||
 * //Maine Learning Results:// Mathematics- C. Geometry

Rationale: Students have already studied the basics of trigonometry, and so this lesson builds upon that by applying these basic to real world applications. This lesson shows that trigonometry has many uses, and leads up to lesson 5, in which students must research a profession that utilizes trigonometry daily. By introducing the applications of trigonometry, students are able to strengthen their knowledge of the basics, as well as continue to expand their knowledge of the subject to other applications. ||

Students will start the lesson by learning how to solve problems using trigonometry. They already know the relationships between the trigonometric functions themselves, and will know review the relationships between the different parts of a triangle. During the lesson, they will be given plenty of scrap paper to take notes on problem solving, then they will be asked to do a few problems at their seats. If students show a strong understanding of the material, then I will move in to today’s activity (finding the missing length of a tree in the schoolyard). If they seem to be struggling, I will do a few more problems on the board, step by step, and allow the students more time to work on sample problems and ask individual questions. Once they are ready for to move on, I will introduce their partners and the class activity of the day. || For a final product, students will be computing the height of a tree in the schoolyard using information from today’s lesson. After the formative assessment, I will put the students into pairs and introduce the activity of the day. Each pair will brainstorm a game plan for solving for the height of the tree. After that, the class will come back together to ask any questions they might have about solving problems using trigonometry. Once all student questions are answered, we will go outside to complete the activity. I will have come outside in advance to pick trees to use, and to complete the activity myself beforehand. Each student must turn in a copy of their work by the next class, as well as be ready to discuss the activity at the start of the next class period. Before the period is over, the class will return to the classroom. Each pair will then be given an opportunity to rehearse what they will say about the activity during the next class’s opener. Each student will also have to create an entry in their blog, outlining the day’s activity. The blog entry is also due by the start of next class. 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 they choose to make any changes to their blog, they may gain some additional points to their final grade. ||
 * =Assessment= ||
 * **Formative** (Assessment for Learning)
 * **Summative** (Assessment of Learning)

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 * =**Integration**= ||
 * Reading/Comprehension- Students will have to brainstorm ways to find the height of a tree based on the day's lesson.

Art- Students will have to turn in a diagram of the tree, showing the triangle they used to find the height of the tree. Also, students will have to go out and take measurements themselves, before they can begin their homework and calculate the height. ||


 * =**Groupings**= ||
 * Students will be placed into pairs for their group activity, that I will decide ahead of time. I will put each student into pairs based on my own observations of the classroom. In previous activities they have worked with multiple partners, and based in which students work well together, I will put them in to pairs for this activity. Each student will take equal responsibility for completing the assignment and finding the height of tree. To monitor group work, I will float around while students are working to ensure that each student is contributing to the activity. Each student will have turn in their own sheet of how the problem was solved, as well as write an entry in their blog. At the end of the period, student will also be given the opportunity to fill out a questionnaire about their group work, which will help provide me with feedback for the next time I put students into groups. The questionnaire is attached. ||

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. || Each student will be put into pairs in order to brainstorm activities. Their partners will be chosen ahead of time, based on personal observations in past classroom settings of who works well together. Each pair will be given plenty of time to brainstorm and ask questions before beginning the activity. During the activity, I will be floating around to ensure that all students are contributing equally to solving the problem, and that all students are working together well. If some students are having disputes, or not participating, I will make appropriate accommodations, possibly changing partners if I have to. At the end of the period, students will again be given an opportunity to reflect upon their work and ask questions about the assignment. They must be well prepared next class in order to talk about the activity, as well as hand in a sheet detailing how they solved for the missing height. They also must post an entry to their blog detailing the day’s events. By having students fill out a group work questionnaire, I will receive appropriate feedback on which students work well together, and will be able to make appropriate accommodations for the next classroom activity. ||
 * =Differentiated Instruction= ||
 * **Strategies**
 * Logical**- Solving for missing lengths in a right triangle.
 * Interpersonal**- Working in groups of 2-3.
 * Verbal**-Discuss/Sketch problem solving ideas in class.
 * Spatial**- Go outside to visualize the trees in context.
 * Naturalist**- Spend part of the class period outside, solving for missing heights of trees.
 * Bodily-Kinesthetic**- Students are up and moving around most of the class period. ||
 * **Modifications/Accommodations**
 * **Extensions**

Scrap Paper Graph Paper Pencils Meter Sticks ||
 * =Materials, Resources and Technology= ||
 * Class Outside- Dress Appropriately


 * =Source for Lesson Plan and Research= ||
 * [|Measuring Tall Objects Using Trigonometry]- this link provides an overview of how to find the height of a person using trigonometry.

[|Blogger.com]- students will post day's events on class blog. ||


 * =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. Students will be working in pairs in order solve for the missing height of the tree. Before they are allowed to go outside, however, they will be meeting with their partner inside to brainstorm a game plan for solving the problem. As students are brainstorming, I will be moving around the room, observing student work and giving feedback when appropriate. Once outside, they will put their plans into action to find the height of the tree using trigonometry. Again, as they work, I will be circulating about them to ensure that all students are contributing to their group, and that each group is moving in the right direction. This activity speak to many learning styles by listing the day’s events on the board, allowing students to work in pairs and give each other feedback, as well as by giving them time to brainstorm before they begin the activity. Each learning style is represented, so that all students with strengths in a particular area will benefit from this activity. ||
 * __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 each have to explain their ideas for completing the class activity to one another, showing that they understand the day’s lesson of solving problems of the same nature. Students will then critique each others ideas, until they agree upon a plan to solve for the height of the tree. In order to solve the problem, students will need to apply their knowledge of trigonometry to the new situation. All of the trigonometry that they have learned in the past will be useful as they go about finding values, as well as doing calculations. Each student will have their own perspective on the class activity, which will be reflected in the blog entry that they will be assigned for homework. They must write a short paragraph about the day’s events, due at the start of next class. Students will also have to show empathy as they consider their partner’s different ideas for completing the class activity. At the end of the activity, students will be given a questionnaire to assess their group work. The questionnaire will not be graded, it is for informational purposes only. This will allow students time to reflect upon the activity. This lesson allows students to partake in all stages of higher learning, creating a much richer learning environment for everyone. ||
 * __Standard 5__ - Understands and uses a variety of instructional strategies and appropriate technology to meet 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.

Logical- Solving for missing lengths in a right triangle. Interpersonal- Working in pairs. Verbal-Discuss/Sketch problem solving ideas in class. Spatial- Go outside to visualize the trees in context. Naturalist- Spend part of the class period outside, solving for missing heights of trees. Bodily-Kinesthetic- Students are up and moving around most of the class period.

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 before handing a final copy. Students will begin the lesson by having a group discussion based on around leading questions such as "Can any of you name a profession that utilizes trigonometry?", "How can you use trigonometry in your daily life? In nature?" The lesson of the day will consist of learning how to see trigonometry to solve problems. Throughout the lesson, I will give students sample problems to work on. While students are working, I will be circulating around the room, answering individual questions as well as giving feedback on student work. After the lesson, I will give a couple more sample problems to do. If all students have mastered this concept then I will move on to the class activity. If many students are still struggling, I will continue to cover the material. For the class activity, students will be put into assigned pairs to brainstorm ways to apply their knowledge of trigonometry to finding the missing height of a tree in the schoolyard. Allowing students to work with a partner before going outside to complete the activity, gives them the opportunity to revise and refine their ideas using peer feedback and discussion before putting them into action. Once each pair has created a plan based in the day’s lesson, we will go outside as a class to complete the assignment. Throughout this time, I will be floating around from pair to pair to ensure that each student is contributing to the assignment, and to make sure that each pair is moving on the right direction. I will give feedback as necessary to ensure that each student has a strong understanding of the key concepts needed to complete the class activity. Before the end of the period, students will return inside to complete a questionnaire about the day’s activity. They will be asked to reflect upon working in groups vs. working alone, etc. The questionnaire is attached. The questionnaire will not be graded, and is for informational purposes only. The class activity must be completed by the start of next class, and students should have gotten all the information necessary to complete their calculations during the class period. Each student will also have to fill out a blog entry describing the day’s events, which also must be posted by the start of next class. 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 they 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 arranged in a traditional classroom setting, facing the board. The lesson will begin the a group discussion, and then students will be doing individual work at their seats. This setting allows me to easily circulate throughout the room to monitor student work. This setup allows also students to easily put desks to together to brainstorm ideas for the completing the class activity. Students will then go outside to complete the activity, but will return to the classroom 20 minutes before the end of the period in order to close the lesson and fill out questionnaires. At the end of class, the desks will be but back so that students can complete their questionnaires individually.


 * Hook students with leading questions (5 minutes)
 * Have short class discussion (5 minutes)
 * Begin lesson about problem solving (10 minutes)
 * Students complete problems individually (10 minutes)
 * Class activity introduced (5 minutes)
 * Students put into pairs to brainstorm ideas (10 minutes)
 * Students go outside to complete activity (20 minutes)
 * Students return inside to ask any final questions (5 minutes)
 * Questionnaire is filled out (5 minutes)
 * Students given 5 minute warning before end of class to pack up, and are reminded to write blog entry describing day's events.

Throughout this lesson, students will learn how to solve for unknowns using trigonometry. At key points during the lesson, students will be required to work individually as I float around the room to ensure that each student is mastering the concepts used throughout the lesson. As needed, I will provide feedback and answer questions in order help students to gain a strong understanding of the material. Next students will partake in a class activity that helps to show that trigonometry has many real-life connections (which students also talked about during the hook). Students will be put into pairs in order to solve for the height of a tree in the schoolyard. As a summative assessment, students will have to turn in, next class, a sheet detailing their thinking process when brainstorming ways to complete the class activity, as well as all the steps involved in actually solving the problem. Students will receive prompt feedback on this assignment, as it is essential an essential part to trigonometry, and will be able to revise the assignment again in order to gain back any points that they lost when the assignment was graded. In order to hook the students into the class period, I will start a discussion using leading questions such as "Can any of you name a profession that utilizes trigonometry?", "How can you use trigonometry in your daily life? In nature?" Students will begin to make real world connections through trigonometry throughout this lesson. 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: Logical, Verbal, Interpersonal, Naturalist, Bodily-kinesthetic, and Spatial ||
 * Students will know terminology: reciprocal, opposite, adjacent, unit circle; and relationships: between trigonometric functions, and between the different parts of a triangle. Students will begin the class period will a short class discussion (see hook), and then the lesson of the day. Today’s lesson will teach students how to solve for unknowns in a triangle. Throughout the lesson, I will be circulating around the room as students do sample problems at their seats. I will check each students work to ensure that they are on the right track, as well as provide feedback and answer student questions as necessary. Once the students have shown a mastery of the concepts required to solve for missing lengths, I will introduce the class activity. Students will be put into partners in order brainstorm ideas before going outside to complete the activity. While students are brainstorming, as well as working on solving for the missing height, I will be continuously circulating and monitoring student work. I will make sure that all students are contributing to their group, and that all groups are headed in the right direction. Feedback and suggestions will be given as necessary to ensure that all students understand the key concepts behind the class activity. For detailed description of the lesson, as well as the class activity, see the attached teacher notes.

Equip, Tailor: Logical, Verbal, Interpersonal, Naturalist, Bodily-kinesthetic, and Spatial ||
 * Students will be able to use trigonometry to solve for missing lengths in right triangles. Throughout the lesson, students will be given plenty of scrap paper to take notes, as well as to complete the individual problems at their seats. After all students have shown mastery of the key concepts shown throughout the day’s lesson, they will be given another opportunity to explore the concepts behind solving for missing lengths using trigonometry by brainstorming with a predetermined partner. Students will be able to experience these concepts first hand throughout the class activity. They will need to apply these concepts first hand by going outside to solve for the missing height of a tree in the schoolyard. Throughout this lesson, students will also experience all stages of higher thinking. Students will each have to explain their ideas for completing the class activity to one another, showing that they understand the day’s lesson of solving problems of the same nature. Students will then critique each others ideas, until they agree upon a plan to solve for the height of the tree. In order to solve the problem, students will need to apply their knowledge of trigonometry to the new situation. All of the trigonometry that they have learned in the past will be useful as they go about finding values, as well as doing calculations. Each student will have their own perspective on the class activity, which will be reflected in the blog entry that they will be assigned for homework. They must write a short paragraph about the day’s events, due at the start of next class. Students will also have to show empathy as they consider their partner’s different ideas for completing the class activity. At the end of the activity, students will be given a questionnaire to assess their group work. The questionnaire will not be graded, it is for informational purposes only. This will allow students time to reflect upon the activity. Partaking in all stages of higher learning creates a much richer learning environment for all students. After the lesson, the class activity will be introduced. Students will have plenty of opportunity to rethink their plans before going outside to complete the activity by brainstorming with their partners. Once each pair has a game plan, the class will go outside to complete activity. I will be floating around to ensure that each group is working productively, and that each student is contributing to the assignment. They will be continually revising their opportunity while they work because they are able to experience the activity hands-on, as well as able to ask questions about the activity at any time. Before the end of period, students will be given one last opportunity to ask questions, in order to refine any information they gathered while outside that they are unsure about. As a summative assessment, students will need to hand in a detailed sheet including their brainstorming, as well as the steps they actually took to complete the activity, all mathematical steps and information gathered included. At the start of the next class period, there will be a short discussion summing up the activity, so students will also be given time to rehearse their material with their partner. The sheet is due at the start of next class, as well as an entry posted to their blog briefly describing the day’s events. There is a sample blog attached.

Explore, Experience, Rethink, Revise, Rehearse, Refine, Tailor: Logical, Verbal, Interpersonal, Naturalist, Bodily-kinesthetic, and Spatial ||
 * Their will be plenty of opportunities throughout the lesson for students to self-assess. At the end of the lesson, each student will be given time to fill out a questionnaire. The questionnaire will be for informational purposes only, and will not be graded. It will cover questions relating to how the students felt about the group, as well as the activity itself; the questionnaire is included in the teacher’s notes for reference. Each student will also have plenty of opportunity for feedback throughout the lesson. Not only will feedback be given throughout the formative assessment, as well as the activity (see above), but assignments will also be given back in a timely manner. After each assignment in handed in, students will receive the homework assignment back during the following class period, along with hand written comments. They will be given the opportunity to revise the assignment to gain back points. Their blog entries will also be commented as soon as they are posted to the blog, which I will check often to ensure that each student is getting feedback as quickly as possible. Feedback is a very important part of student learning, which is why I will strive to give students feedback as fast, and as accurately as possible. This lesson gives students a great introduction to real life uses of trigonometry, as well as the idea of problem solving. Throughout this lesson, students will gain a strong understanding of the key concepts behind using trigonometry to solve for missing lengths. The next lesson will build on this by allowing students to explore situations in which certain trigonometric functions should be used. In the next lesson, students will be able to recognize which trigonometric functions should be used in certain contexts. Both these lessons continue to lead up to the performance task at the end of the unit, which includes aspects from all six lesson in this unit (see webquest for details).

Evaluate, Refine, Tailor: Logical, Verbal, Interpersonal, Naturalist, Bodily-kinesthetic, and Spatial ||

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