L3+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 #3: Reflect
 * Grade Level:** 10th or 11th grade **Topic:** Right Triangles

__**Objectives**__

 * Student will understand that** there exist useful relationship between angles and sides of right triangles.
 * Student will know** Students will know the 30/60/90 and 45/45/90 triangles as well as the definitions of "complementary" and "supplementary".
 * Student will be able to** reflect on the relationship between sides and angles

__**Maine Learning Results Alignment**__
Maine Learning Results: Mathematics - C. Geometry Geometric Figures Grades 9 - Diploma 3. a) Identify and find the values of trigonometric ratios for angles in right triangles

This lesson will introduce students to the idea of a relationship between sides and angles which will help them understand trigonometric functions in the following lessons.
 * Rationale:**

__**Assessment**__
For this lesson's formative assessment, a short quiz covering the material of the day will be presented. This will give the teacher a concrete idea of how the students are comprehending the material (quiz will include questions about the 45/45/90 and 30/60/90 triangles and a few examples where they must figure out the lengths of either both sides or a side and the hypotenuse).
 * Formative (Assessment for Learning)**

Students will take the quiz at "@http://www.funtrivia.com/playquiz/quiz14712910d9bc0.html". They will record their results and write the correct responses for the questions they answered incorrectly. Students are to list three things they could do to change their score if they were to take it again. This quiz supplies questions about right triangles and their properties, and taking it will enable the students to gauge their own personal comprehension. Either on paper or on your blog (the blog would be preferred), students are to post their findings and personal suggestions. This assignment will not be graded critically, it is an "all or nothing" assignment.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology**: Once again, technology is integrated in this class through use of online journaling. Students will be required to present their results from the online quiz about right triangles and reflect upon their score in a blog.


 * Art**: By examining tesselations at the beginning of class, students will be introduced to the works of M. C. Escher.


 * English**: Students will need to employ their effective writing skills to write a blog about their online quiz.

__Groupings__
For this lesson, students will be working in pairs. As they walk into the classroom, the teacher will hand a card bearing a right triangle to each student. Each right triangle has measurements for both of the legs. In order for students to determine who they are partnered with, they must compute the length of the hypotenuse and find the other individual in the classroom whose hypotenuse has the same measure. In their pairs, students will be asked to sit at a desk tangent to that of their partner.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal Linguistic**: for the verbal students, as always, I will present my lesson using a collection of written and oral verbs and nouns that accurately describe the process and relationship.
 * Mathematical Logical**: for the mathematical students, I will provide the formula through which one can deduce the side lengths for both the 45/45/90 and 30/60/90 triangles.
 * Visual Spacial**: for the visual students, as always in a geometry class, I will include visual representations and labels of the triangles discussed and incorporate those drawings into my explanation.
 * Bodily Kinesthetic**: for the physical students, I have designed the class activity to be one that directly manipulates the relationship between angles and sides which will aid these students in first-hand comprehension.
 * Musical Rhythmic**: for the musical students I will include an example that directly relates to music. Generally, when the dynamics of a piece increase, an ensemble has a tenancy to increase the tempo as well. Similarly, when playing legato, an ensemble tends to slow down the tempo. These are relationships that just happen naturally (even if they usually produce undesired effects) similar to how a side will increase directly with the increase of the angle opposite to it.
 * Intrapersonal**: students will be given approximately two minutes prior to the test to reflect upon the day's lesson and ask questions before the quiz at the end of class (closed note). This will give the intrapersonal students time to consider what they have learned.
 * Naturalistic**: for the naturalistic students, I will also include an example that directly relates to their area of expertise. As animals grow, their skills and abilities refine directly with their age. For example, when a lion cub is born, it does not yet see, let alone can it hunt. As it grows larger, it's abilities increase... very similar to the relationship between an angle and it's opposite side.


 * 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 and the Cluster/Word Web graphic organizer) 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 and to do the pencil exercise, although neither will be mandatory.
 * Extensions**

__**Materials, Resources and Technology**__
Pencils Yarn/String Laptops for the blog entries (to be completed outside of class time). Printed copies of the graphic organizer.

__Source for Lesson Plan and Research__
Everything anyone could want to know about special right triangles. Interactive website that can be used to demonstrate the same concept as illustrated in the pencil activity. The website to post student blogs to.

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** In this lesson, students will have a lot of flexibility in determining how they approach the activity (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 a 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 this specific relationship exists between the sides and angles of triangles (microscope). Students are highly encouraged to share their analysis with the class.
 * //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 be able to reflect upon the intricate relationship between angles and sides of right triangle to make educated predictions about the behavior of other triangles and even other shapes. Students will look at information given to them and be able to incorporate their knowledge of this relationship to solve problems based on their understanding of the behavior of sides and angles.
 * //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**: for the verbal students, as always, I will present my lesson using a collection of written and oral verbs and nouns that accurately describe the process and relationship.
 * Mathematical Logical**: for the mathematical students, I will provide the formula through which one can deduce the side lengths for both the 45/45/90 and 30/60/90 triangles.
 * Visual Spacial**: for the visual students, as always in a geometry class, I will include visual representations and labels of the triangles discussed and incorporate those drawings into my explanation.
 * Bodily Kinesthetic**: for the physical students, I have designed the class activity to be one that directly manipulates the relationship between angles and sides which will aid these students in first-hand comprehension.
 * Musical Rhythmic**: for the musical students I will include an example that directly relates to music. Generally, when the dynamics of a piece increase, an ensemble has a tenancy to increase the tempo as well. Similarly, when playing legato, an ensemble tends to slow down the tempo. These are relationships that just happen naturally (even if they usually produce undesired effects) similar to how a side will increase directly with the increase of the angle opposite to it.
 * Intrapersonal**: students will be given approximately two minutes prior to the test to reflect upon the day's lesson and ask questions before the quiz at the end of class (closed note). This will give the intrapersonal students time to consider what they have learned.
 * Naturalistic**: for the naturalistic students, I will also include an example that directly relates to their area of expertise. As animals grow, their skills and abilities refine directly with their age. For example, when a lion cub is born, it does not yet see, let alone can it hunt. As it grows larger, it's abilities increase... very similar to the relationship between an angle and it's opposite side.


 * Technology**: Once again, technology is integrated in this class through use of online journaling. Students will be required to present their results from the online quiz about right triangles and reflect upon their score in a blog.

Rationale:** For this lesson's formative assessment, a short quiz covering the material of the day will be presented. This will give the teacher a concrete idea of how the students are comprehending the material (quiz will include questions about the 45/45/90 and 30/60/90 triangles and a few examples where they must figure out the lengths of either both sides or a side and the hypotenuse). For the lesson's summative assessment, students will take the quiz at "@http://www.funtrivia.com/playquiz/quiz14712910d9bc0.html". They will record their results and write the correct responses for the questions they answered incorrectly. Students are to list three things they could do to change their score if they were to take it again. This quiz supplies questions about right triangles and their properties, and taking it will enable the students to gauge their own personal comprehension. Either on paper or on your blog (the blog would be preferred), students are to post their findings and personal suggestions. This assignment will not be graded critically, it is an "all or nothing" assignment.
 * //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__
Break into groups - 8 minutes Introduction/Hook - 9 minutes Pencil activity - 4 minutes Lecture - 25 minutes Quiz - 15 minutes Correct quiz - 10 minutes Introduce/Start homework - 9 minutes.

For this lesson, the desks will be arranged similar to how they were during the previous class, in rows but grouped in twos. After this lesson, students will be able to reflect on the relationship between sides and angles. This lesson will strengthen the life-long skill of making connections by developing students' ability to recognize subtle patters within a subject and will enable them to meet the MRL standard Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma, 3. a) Identify and find the values of trigonometric ratios for angles in right triangles. Students will be asked to look at tessellations and, as a class, recognizing the relationship between the shapes and images. This will give a precursor to the lesson and introduce them to the idea of hidden relationships. We will then apply this idea of "hidden relationships" to dating and hypothesize the rate of change within the chocolate/movies ratio (to clarify, we will discuss how when Jimmy puts in a lot of energy and buys Sally chocolate, Sally will go to the movies with Jimmy more often. This same idea will directly relate to what the lesson covers with side/angle ratios) . **Where, Why, Hook, Interpersonal, Visual, Logical, Verbal.**

Students will need to know the properties of 30/60/90 triangles and 45/45/90 triangles as well as the definitions of "complementary" and "supplementary". Students will explore the idea of side/angle relationships firsthand by participating in the "pencil activity". In this exercise, three sides of a triangle are created by attaching a long piece of string to the end of a pencil and a flat surface such as the student's desk. By tilting the pencil backwards, students can see that the angle between the pencil and the desk increase as the distance between the tip of the pencil and the desk increases as well (as depicted by the string). This demonstrates the relationship between the angles and sides of a triangle. This activity will then be followed by a lecture during which I will introduce the properties of the 30/60/90 and 45/45/90 triangles. At the end of the lesson, students will be checked for comprehension through a short quiz that covers the material. This will give the teacher a concrete idea of how the students are comprehending the material (quiz will include questions about the 45/45/90 and 30/60/90 triangles and a few examples where they must figure out the lengths of either both sides or a side and the hypotenuse). Quizzes will be graded by the students in class, answers will be reviewed and students will have the opportunity to correct their work. Quizzes will be collected but only graded as 10 participation points. **Equip, Explore/Experience, Kinesthetic, Logical, Verbal, Visual, Intrapersonal.**

In this lesson, students will be able to reflect upon the intricate relationship between angles and sides of right triangle to make educated predictions about the behavior of other triangles and even other shapes. Students will look at information given to them and be able to incorporate their knowledge of this relationship to solve problems based on their understanding of the behavior of sides and angles. For this lesson, students will be working in pairs. As they walk into the classroom, each student will be handed a card bearing a right triangle. Each right triangle has measurements for both of the legs. In order for students to determine who they are partnered with, they must compute the length of the hypotenuse and find the other individual in the classroom whose hypotenuse has the same measure. In their pairs, students will be asked to sit at a desk tangent to that of their partner. Students will prove their comprehension of this topic by taking the quiz at "@http://www.funtrivia.com/playquiz/quiz14712910d9bc0.html". They will record their results and write the correct responses for the questions they answered incorrectly. Students are to list three things they could do to change their score if they were to take it again. This quiz supplies questions about right triangles and their properties, and taking it will enable the students to gauge their own personal comprehension. Either on paper or on your blog (the blog would be preferred), students are to post their findings and personal suggestions. This will show their mastery of the right triangle concepts covered thus far in the unit. Note: This assignment will not be graded critically, it is an "all or nothing" assignment. Referring back to the pencil exercise, the students will be given a chance to view the concepts through a different lens. They will be asked such questions as "what would happen to the triangle if the side depicted by the string was not allowed to increase as the pencil tipped backwards? What if all the sides of triangle were a fixed length? What if all the angles of the triangle were a fixed size?" . Next, the teacher should check for comprehension. "So what IS the relationship between angles and sides? Is there one at all?" and based on student response, teacher should either seek a different method of explanation (catered to the intelligence of learners who are having difficulty) or seek a more challenging way to express the idea (for example, giving hypothetical examples and having students make their own conclusions about the angle/side relationship). Referring to the summative assessment, students will be allowed to take the quiz again and resubmit their answers to prove their progress on the material. **Revise, Rethink, Refine, Logical, Intrapersonal.**

Students will have a chance to assess their learning when we correct the in class quiz. Their score should be an indicator as to whether or not they understand the material (a score below an 80% would indicate poor understanding and a score above an 80% would indicate a fairly good understanding). Students should use this information as an "amount of study time needed" indicator. By correcting the quiz right in class, students will be provided with feedback. They should also be told that the score less than an 80% is poor and the score more than an 80% is decent. This sets the students up for the means to gauge how well they will perform on online quiz that is to be assigned for homework. This lesson also sets the stage for the following class during which time trigonometric functions will be discussed. **Intrapersonal, Visual, Verbal.**

-- As one angle increases in measure, the side opposite to it will increase as well. -- In a 30/60/90 triangle, the measure of the sides will always be scalars of 1:2:3^1/2 (better known as the square root of three) ratio where "1" is the measure of the side between the 60º angle and the 90º angle, "2" is the length of the hypotenuse and "3^1/2" is the measure of the side between the 30º angle and the 90º angle. -- In a 45/45/90 triangle, the measure of the sides will always be scalars of a 1:1:2^1/2 (better known as the square root of two) ratio where "1" is the measure of both of the legs and 2^1/2 is the length of the hypotenuse. -- Complementary: angles whose sum is 90º are said to be "complementary". -- Supplementary: angles whose sum is 180º are said to be "supplementary".
 * Content Notes**



Cluster/Word Web graphic organizer. Formative assessment quiz
 * Handouts**