L5+McKeown,+Sarah

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


 * Teacher’s Name:** **Ms. Sarah C. McKeown Date of Lesson:** Lesson #5: Application
 * Grade Level:** 10th or 11th grade **Topic:** Right Triangles

__**Objectives**__

 * Student will understand that** the unique properties of right triangles can be used to solve other geometric problems.
 * Student will know** the properties of right triangles learned in previous lessons.
 * Student will be able to a**pply prior knowledge of triangles to new shapes.

__**Maine Learning Results Alignment**__
Mathematics - C. Geometry Geometric Figures Grades 9 - Diploma 1. a. Students can use the properties of triangles to prove theorems about figures and relationships among figures.

This lesson will involve students adding line segments to polygons to create right triangles within the polygon. Students will then use their knowledge of right triangles to solve for the angles and/or sides of the polygon. This is a direct application of this standard.
 * Rationale:**

__**Assessment**__
As a pre-assessment, I plan on performing another "five finger poll". At the beginning of class, I will ask students how they feel about triangles. Through a show of 1, 2, 3, 4, or 5 fingers (1 being poor, 5 being confident), students will indicate how they feel about their personal mastery of the content. Then I will ask how they feel about other geometric figures, such as octagons or hexagons. this will allow students to think about what they know about shapes. After the class, students will be asked the same questions and take part in the same poll. This enables students to gauge their own learning while providing me, the instructor, with information about how much they have improved over the course of the class period.
 * Formative (Assessment for Learning)**

For a summative assessment, students will be asked to create a brochure using Microsoft to advertise the "appeals" (properties) of right triangles with the target audience being another shape. This project will synthesize all students have learned about right triangles throughout the unit and also demonstrate their understanding of how those properties relate to other shapes. Students should be sure to appeal to at least two other shapes that the triangle can be applied to. Students will be graded on the accuracy of their representation of the relationships (in other words, something they should NOT do is tell me how a triangle can help solve the surface area of an ink blotch). Students should focus on the shapes discussed in class.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology:** This lesson employs technology through the use of Microsoft to create the Right Triangle brochure.


 * English**: This lesson will require students to employ their persuasive writing skills to make a brochure that effectively appeals to their targent audience.


 * Industrial Arts or "Shop Class"**: This lesson appeals to the Industrial Arts because we will be examining different situations in which triangles are present within buildings to make them stronger structures.

__Groupings__
As students enter the room, the instructor will hand out index cards to each student. On each card is a picture of a shape that will be discussed in class. Students will be asked to find other students with the same shape as them and be seated at a desk cluster with their group (in all, there will be four different shapes: An isosceles triangle, a square, a hexagon and a parallelogram). Within these groups, students will decide which shape they would like to become an "expert" on. Students will remain in these groups for the duration of the lesson.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal Linguistic**: As always, class will be presented in a verbal and written presentation.
 * Mathematical Logical**: For my logical thinking students, I will provide a logical analysis as to why we find triangle within shapes.
 * Visual Spacial**: This will be a very rich lesson for my visual spacial students because the entire lesson relies on interpretation of pictures.
 * Bodily Kinesthetic**: For the bodily students, the opening activity should meet their kinesthetic needs and enable them to interact with the material in a manner appropriate to them.
 * Musical Rhythmic**: For my musical students, I will provide an example that they may relate to: When you're improvising, and someone tells you what key the rest of the ensemble is in, you need to know what notes are //in// that key to help you play. You need to know that the first, third and fifth notes of C minor are C, E flat and G in order to make what you're playing fit in. It's all about recognizing the components (or chords) that scales are made up of.... like triangles within squares!
 * Interpersonal**: This lesson will be packed with group activities (or at least, more so than past lessons) that include, the initial group work and almost the entire class time is spent doing triangle evaluation in groups.
 * Naturalistic**: To relate to my naturalistic students, I will compare the shapes within shapes to the rings within the trunk of a tree.


 * Modifications/Accommodations**

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

If student knows that he or she will be absent, they are required to follow the school's planned absence policy and retrieve all work (this includes the lecture notes) from me prior to the absence. Any student encountering an unexpected absence must see me as soon as possible (preferably prior to the next class with me) to get the missed work. Students in both situations will have the opportunity and are highly encouraged to talk with me during my office hours if they have any questions although it is not mandatory.

This lesson integrates technology through the use of Microsoft to create the Right Triangle brochure. This allows students to gather information digitally and explore software that will continue to be of use to them throughout their lives. This will also allow them to synthesize all the exploration they have done online through blogs and the discussion on the wikispace in a format that enables easy sharing and opportunity for timely feedback from the instructor.
 * Extensions**

__**Materials, Resources and Technology**__
White board, markers. Examples of polygons in real life (either pictures or real manipulatives) Four sets of two mirrors. Students will need computer access to create their brochure and refer back to their previous blogs and the class wikispace.

__Source for Lesson Plan and Research__
What students have already learned about the Pythagorean Theorem. What students have already learned about special right triangles. What students have already learned about trigonometric functions.

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** In this lesson, students will have flexibility in this lesson through their choice of what shape they will become masters of (beachball). To give direction to the classroom atmosphere, I will outline the day's agenda at the beginning of class (clipboard). During the activity, I will provide an ongoing list of things students should be noticing as they progress through the lesson (clipboard). Students will be given time to reflect upon their findings from the lesson and will be encouraged to think about why shapes can be found within other shapes and to think about just how helpful that is in real life (microscope). Students are highly encouraged to share their analysis with the class. To create a safe environment, I will make sure to float amongst the class and make myself available in close proximity to the students while they work. This will enable me to have one on one contact with students if they find themselves struggling. This in turn will establish an encouraging atmosphere to the work they are doing (puppy).
 * //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:** In this lesson, students will synthesize all they have learned about right triangles to apply them to new shapes. Because this lesson involves a cummulative view of the content, students will be pushed to reach a new level of comprehension and begin to piece together how all the previous lessons tie into eachother. Ultimately, this lesson will lead to students mastering the content, meeting the standard and completeing the end of the unit project.
 * //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 Linguistic**: As always, class will be presented in a verbal and written presentation.
 * Mathematical Logical**: For my logical thinking students, I will provide a logical analysis as to why we find triangle within shapes.
 * Visual Spacial**: This will be a very rich lesson for my visual spacial students because the entire lesson relies on interpretation of pictures.
 * Bodily Kinesthetic**: For the bodily students, the opening activity should meet their kinesthetic needs and enable them to interact with the material in a manner appropriate to them.
 * Musical Rhythmic**: For my musical students, I will provide an example that they may relate to: When you're improvising, and someone tells you what key the rest of the ensemble is in, you need to know what notes are //in// that key to help you play. You need to know that the first, third and fifth notes of C minor are C, E flat and G in order to make what you're playing fit in. It's all about recognizing the components (or chords) that scales are made up of.... like triangles within squares!
 * Interpersonal**: This lesson will be packed with group activities (or at least, more so than past lessons) that include, the initial group work and almost the entire class time is spent doing triangle evaluation in groups.
 * Naturalistic**: To relate to my naturalistic students, I will compare the shapes within shapes to the rings within the trunk of a tree.

This lesson integrates technology through the use of Microsoft to create the Right Triangle brochure. This allows students to gather information digitally and explore software that will continue to be of use to them throughout their lives. This will also allow them to synthesize all the exploration they have done online through blogs and the discussion on the wikispace in a format that enables easy sharing and opportunity for timely feedback from the instructor.
 * Extensions:**

Rationale:** As a pre-assessment, I plan on performing another "five finger poll". At the beginning of class, I will ask students how they feel about triangles. Through a show of 1, 2, 3, 4, or 5 fingers (1 being poor, 5 being confident), students will indicate how they feel about their personal mastery of the content. Then I will ask how they feel about other geometric figures, such as octagons or hexagons. this will allow students to think about what they know about shapes. After the class, students will be asked the same questions and take part in the same poll. This enables students to gague their own learning while providing me, the instructor, with information about how much they have improved over the course of the class period. For a summative assessment, students will be asked to create a brochure using Microsoft to advertise the "appeals" (properties) of right triangles with the target audience being another shape. This project will synthesize all students have learned about right triangles throughout the unit and also demonstrate their understanding of how those properties relate to other shapes. Students should be sure to appeal to at least two other shapes that the triangle can be applied to. Students will be graded on the accuracy of their representation of the relationships (in other words, something they should NOT do is tell me how a triangle can help solve the surface area of an ink blotch). Students should focus on the shapes discussed in class.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

__Teaching and Learning Sequence__
Come into class and seat within groups - 3 minutes Mirror "Hook" - 3 minutes Formative assessment - 1 minute Review all previous graphic organizers - 7 minutes Assign areas of expertise - 2 minutes Handout necessary materials to respective teams - 2 minutes Students work in groups on their handouts - 20 minutes Regroup and have students present their shape - 20 minutes Do examples of each - 15 minutes Second Five Finger Poll - 1 minute Begin homework - 6 minutes

For this lesson, the desks will be arranged into four clusters (broken up as evenly as the number of desks will allow) all of which will be angled so that they face the white board or the front of the room. From this lesson, students will understand that the unique properties of right triangles can be used to solve other geometric problems. This skill is useful for students in their everyday lives because it demonstrates how even the most daunting task can be broken down into simpler, easier to manage problems. This lesson will also meet the Maine Learning Result, Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma, 1. a. Students can use the properties of triangles to prove theorems about figures and relationships among figures. Students will be hooked on this lesson through the opening activity. After dividing into their groups, students will seat themselves at desk clusters, each of which will have two mirrors placed on them. The mirrors alone should peak student interest in the day's topic, however, the magic of this hook does not stop there! Students will be asked to hold the mirrors on either side of a group member's head and count how many times they can see this member reflected in either one of the mirrors (the answer is "infinitely many). We will then discuss the answers as a class. This will then tie into the lesson because there are infinitely many right triangles that can be drawn within a polygon just by adding line segments to the polygon. **Where, Why, Hook, Interpersonal, Logical, Kinesthetic, Visual, Verbal.**

For this lesson, students will not be learning any new information (except for the fact that it is "legal" to draw line segments inside another shape in order to create right triangles). They will be pulling all of their skills from prior lessons by referring to the graphic organizers they created in the past lessons. Students will explore this new concept of adding line segments while utilizing their knowledge of right triangles while working in groups as they become "experts" on solving their given shape. I will check for understanding by performing the Five Finger Poll both at the beginning and end of class where students will indicate by a show of fingers how well they feel they understand both right triangles and other polygons. By doing this poll at the beginning and the conclusion of class, students will have been able to evaluate the progress of their own learning while also providing the instructor with an accurate sample of how well the class is digesting the concept. **Equip, Explore, Logical, Visual, Verbal, Interpersonal.**

This lesson will truly test students' comprehension of the previous lessons. If they are successfully able to solve for the angles and sides of other polygons, this means they have mastered the past information and reached the higher level of thinking so that they can apply this knowledge to new problems. Students will be grouped randomly. As students enter the room, the instructor will hand out index cards to each student. On each card is a picture of a shape that will be discussed in class. Students will be asked to find other students with the same shape as them and be seated at a desk cluster with their group (in all, there will be four different shapes: An isosceles triangle, a square, a hexagon and a parallelogram). Within these groups, students will decide which shape they would like to become an "expert" on. Students will remain in these groups for the duration of the lesson. Students will demonstrate their comprehension of this lesson by creating a brochure using Microsoft to advertise the "appeals" (properties) of right triangles with the target audience being another shape. This project will synthesize all students have learned about right triangles throughout the unit and also demonstrate their understanding of how those properties relate to other shapes. Students should be sure to appeal to at least two other shapes that the triangle can be applied to. Students will be graded on the accuracy of their representation of the relationships (in other words, something they should NOT do is tell me how a triangle can help solve the surface area of an ink blotch). Students should focus on the shapes discussed in class. Students will have the ability to accept feedback on this assignment and resubmit it for a revised grade within one week of the actual due date. **Revise, Interpersonal, Logical, Visual, Verbal.**

Students will self assess by participating in a "five finger poll". At the beginning of class, I will ask students how they feel about triangles. Through a show of 1, 2, 3, 4, or 5 fingers (1 being poor, 5 being confident), students will indicate how they feel about their personal mastery of the content. Then I will ask how they feel about other geometric figures, such as octagons or hexagons. this will allow students to think about what they know about shapes. After the class, students will be asked the same questions and take part in the same poll. This enables students to gauge their own learning while providing me, the instructor, with information about how much they have improved over the course of the class period. Because students are going to be submitting their brochures to me online through e-mail (although students who do not have computer access will be able to turn in a hard copy), I will be able to review them and send feedback to the student almost immediately after reading through their material. **Kinesthetic, Logical, Intrapersonal.**

- Segments can be added to polygons to create right triangles within the shape. -- See aditional attachments --
 * Content Notes**

-- Work sheets for each individual grou to "master" their designated shape. -- Handout with pictoral examples of polygons that we will then solve.
 * Handouts**
 * Include at least three examples done out and one for them to do*