L2+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** #2: Explain
 * Grade Level**: 10th or 11th grade **Topic**: Right Triangles

Student will understand that the Pythagorean Theorem can only be used under certain conditions and will be able to recognize when it is appropriate to use. Student will know the anatomy of right triangles (terms such as hypotenuse, leg, right angle, and the Pythagorean Theorem). Student will be able to do problems using the Pythagorean Theorem.
 * Objectives**


 * Maine Learning Results Alignment**

Maine Learning Results: Mathematics - C. Geometry Geometric Figures Grades 9 - Diploma 3. Students understand and use basic ideas of trigonometry.

Rationale: This lesson will equip students with the information necessary to compute trigonometric relations in the future.

The formative assessment for this lesson will be very informal and provide students the chance to reflect on their own comprehension with minimal teacher intervention.We will pose the question "why is the Pythagorean Theorem useful?" and "what if this leg was different?" to take a different approach on the material. If students' answers seem vague and unsure or if they seem confident and bored, I will either seek an easier method of explanation of the concept or present more challenging examples for the students, respectively. To self-assess, students will answer problems individually then partner with someone who computed a different answer and compare results. Students must ask "what was different about my method in comparison to my partner's approach?" to gain more perspective on the concept. I will then review the proper method (even if the entire class got all of the practice problems correct) to solidify the concept. For a summative assessment, students will be asked to demonstrate their understanding of the Theorem by using Comic Life to create a short epic story that applies the Pythagorean Theorem to real life. This project will demonstrate students' initial understanding of the Pythagorean Theorem in a way that allows them to utilize the media. Students must include at least two ways in which Pythagorean Man (or whatever they choose to name their character) can use the Pythagorean Theorem to "save the day". This assignment will be graded using a check list that checks the level of comprehension of the Theorem and the validity of the examples.
 * Assessment**


 * Integration**


 * Technology**: Technology is integrated into this lesson through computer interaction while introducing students to the program comic life.


 * English**: The summative assessment also integrates writing because creating an epic is method through which students can interact with their fiction writing skills.


 * Art**: The use of comic life will push the students to create some kind of media to accompany their story.

For the activity, we will arrange in randomly assigned groups. In a hat there will be four different categories of numbers (positive odds, positive evens, negative odds and negative evens) and upon drawing one of these numbers, students will fall into one of the four subcategories. Students will then group with others who had the same type of number and sit in desk clusters angled towards the front of the room.
 * Groupings**

Strategies:**
 * Differentiated Instruction


 * Verbal Linguistic**: the majority of my lesson will be presented in a traditional lecture format which relies heavily on verbal communication.
 * Logical Mathematical**: in all lessons, I will do a step by step break down of how the concept works, This will allow mathematical students to see the very logical process through which it functions.
 * Visual Spacial**: for my visual learners, I will draw diagrams relevant to the content (in this case, many triangles).
 * Musical Rhythmic**: to help my musical students connect with the content, I have created a song to the tune of "Yankee Doodle" to remember the Pythagorean Theorem (Re-mem-ber the Pythag-orean Theo-rem, a squared plus b squared, adds up to e-equal the hypotenuse that is c squared).
 * Interpersonal**: during the lesson, I have allow for students to spend time developing the concept with partners. This will help my interpersonal students explore the Pythagorean Theorem in a manner which is beneficial to them.
 * Naturalistic**: in order to engage the Naturalistic students in my classroom, I will come to class equipped with examples of right triangles that occur naturally as a means to personalize the lesson and give it meaning for these learners.


 * Modifications/Accommodations**

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

If a student misses this class, I will make my personal notes, triangle anatomy diagram and the graphic organizer available to him or her and I will also set up a time for him or her to meet with me during office hours to do the triangle building exercise.

For this lesson, students will need to use comic life. For many students, this will be their first encounter with the program, thus the experience will be somewhat Type II for them. The synthesizing of artwork, a written story and new technology will create a multi-faceted experience for most students.
 * Extensions**

Students will need a laptop/desktop computer to access comic life. Pencils Paper Whiteboard and markers Calculators Printed copies of the graphic organizer Supplies to build triangles (pipe cleaners, popsicle sticks, duct tape, paper clips, just odds and ends really)
 * Materials, Resources and Technology**

An interactive breakdown of the Pythagorean Theorem and the history behind it. Graphic Organizer to be used in class. Comic Life software download site, and how to use it in the classroom. Anatomy of a triangle.
 * Source for Lesson Plan and Research**


 * 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:** Students will be given the opportunity to make their own choices when partaking in the experience part of this lesson (the building a triangle). Given the array of materials, students will select what objects they believe will be the most beneficial in creating their triangle and are given the freedom of deciding how they will make the structure (beach ball). To give a sense of direction to the class, students will be provided with a class agenda at the beginning of the lesson (to be written on the board prior to class). For the activity, to avoid fully range of freedom, students will have to comply with the requirements of the project (it must have three sides and three angles ONLY) which will enact guidelines that many students find useful (clipboard). This exercise in general, will be very analytical and will allow students to discover for themselves as they create a shape that the entire unit will focus on (microscope). I will make myself easily accessible during this time and will frequent each group as they progress through the activity to encourage students (puppy).

Rationale:** This lesson is an explain because it introduces students to a new idea and supplies them with the necessary tools to describe (or explain) the concept in their own words based on the lesson. This will be a very basic class with a microscopic view of the Pythagorean Theorem. Information acquired during it will present itself in a "regurgitation" style when students are asked to tell what they learned (more or less a form of recitation).
 * 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:** the majority of my lesson will be presented in a traditional lecture format which relies heavily on verbal communication.
 * Logical Mathematical**: in all lessons, I will do a step by step break down of how the concept works, This will allow mathematical students to see the very logical process through which it functions.
 * Visual Spacial**: for my visual learners, I will draw diagrams relevant to the content (in this case, many triangles).
 * Musical Rhythmic**: to help my musical students connect with the content, I have created a song to the tune of "Yankee Doodle" to remember the Pythagorean Theorem (Re-mem-ber the Pythag-orean Theo-rem, a squared plus b squared, adds up to e-equal the hypotenuse that is c squared).
 * Interpersonal**: during the lesson, I have allow for students to spend time developing the concept with partners. This will help my interpersonal students explore the Pythagorean Theorem in a manner which is beneficial to them.
 * Naturalistic**: in order to engage the Naturalistic students in my classroom, I will come to class equipped with examples of right triangles that occur naturally as a means to personalize the lesson and give it meaning for these learners.

For this lesson, students will need to use comic life. For many students, this will be their first encounter with the program, thus the experience will be somewhat Type II for them. The synthesizing of artwork, a written story and new technology will create a multi-faceted experience for most students.
 * Extensions**

Rationale:** The formative assessment for this lesson will be very informal and provide students the chance to reflect on their own comprehension with minimal teacher intervention.We will pose the question "why is the Pythagorean Theorem useful?" and "what if this leg was different?" to take a different approach on the material. If students' answers seem vague and unsure or if they seem confident and bored, I will either seek an easier method of explanation of the concept or present more challenging examples for the students, respectively. To self-assess, students will answer problems individually then partner with someone who computed a different answer and compare results. Students must ask "what was different about my method in comparison to my partner's approach?" to gain more perspective on the concept. I will then review the proper method (even if the entire class got all of the practice problems correct) to solidify the concept. For a summative assessment, students will be asked to demonstrate their understanding of the Theorem by using Comic Life to create a short epic story that applies the Pythagorean Theorem to real life. This project will demonstrate students' initial understanding of the Pythagorean Theorem in a way that allows them to utilize the media. Be sure to include at least two ways in which Pythagorean Man (or whatever you choose to name your character) can use the Pythagorean Theorem to save the day! You will be graded using a check list that comprises of your comprehension of the Theorem and the validity of your examples.
 * 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**

(Prep time- - arrange the room to accent triangles - 10 minutes) Discuss examples of triangles in the room - 2 Break into groups - 3 minutes Build triangles - 10 minutes Presentation and examples - 15 minutes Measure the made triangle and solve for the hypotenuse - 5 minutes Graphic Organizer - 3 minutes Synthesize G.O. List - 5 minutes Examples - 5 minutes Partner and compare answers - 7 minutes Discussion - 5 minutes Comic Life Tutorial - remaining time (approximately 20 minutes)

To really draw the class's attention to triangles, the desks will be arranged in the center of the room in a triangular shape. First, as a class, we will take note of the numerous triangles that appear in the room and discuss their importance. For this lesson, the class will be arranged with desks in set of two due to the heavy partner usage. Desks will be in four groupsall will be facing the whiteboard (or the front of the room). I am going to open up the class by asking the students if they have every done anything that seemed to be the right thing to do at the time, but later discovered that it was, in fact, a very bad idea (today's lesson will ensure that students __never__ make this mistake with the Pythagorean Theorem!). Students will be encouraged to talk with their partner and have the option of contributing to the entire class. **Where, Why, What, Hook, Visual, Interpersonal**

The Pythagorean Theorem says that the measure of one leg, squared, when added to the measure of the other leg, also squared, equates to the measure of the hypotenuse squared. To check for learning, I plan on frequently asking individuals to define these parts and/or solve problems for either the measure of a leg or the hypotenuse using the Pythagorean Theorem (eventually, each student will answer at least two questions). **Equip, Rethink, Revise, Refine, Logical, Visual, Verbal, Interpersonal**

From this lesson, students understand that Pythagorean Theorem is very conditional and will be able to evaluate the proper situation in which to use it which will help them meet the standard Maine Learning Results: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma, 1. Students justify statements about polygons and solve problems, c. Use the Pythagorean Theorem in situations where right triangles are created by adding segments to figures. Students will explore this material by making their own triangles within their groups. After building triangles, I will present the Pythagorean Theorem. Then students will be asked to apply the theorem by taking measurements of their own triangles and solving for the hypotenuse. After doing numerous examples as a class, students will be asked to fill in the "ladder" graphic organizer with information they would need to understand the Pythagorean Theorem (for example, students may write "definition of hypotenuse" or "how to square a number"). As a class, we will then synthesize all of the responses into one collective list. Using that list, we will solve more triangles with the Pythagorean Theorem while identifying each quintessential aspect as depicted by student responses, then try a few individually. By taking a class poll, I will collect their answers ("Let's go around the room. [insert name here], what answer did you get for an answer?"). Students will then be asked to pair with someone who computed an answer different from their own. In pairs, students will reflect on the different approach the other took to analyze the best method to use. Following that, I will then pose such thought-provoking questions as "why is this useful?" and "what if this leg was different?", allowing students to answer them. At the end of this lesson, students will know the Pythagorean Theorem and how to apply it to given information in order to meet the MLR Mathematics- C. Geometry Geometric Figures Grades 9 - Diploma, 3. Students understand and use basic ideas of trigonometry. This is important to learn because this Theorem is used very heavily in construction of many buildings we enter everyday (triangles are actually the most sturdy structure). In order to illustrate the abundance of right triangles, the room will be arranged in a manner that accents the triangles contained within preexisting structures. **Where, Why, What, Equip, Explore, Experience, Rethink, Revise, Evaluate, Verbal, Logical, Visual, Interpersonal.**

Students will explore the material by creating their own triangles! Before students sit down, they will be asked to do the grouping activity (which consists of silently arranging themselves by birth date). Students will then sit at a desk pair with their partner. Without providing students with any contextual information (for that might create a bias), the groups will be asked to get up and select objects from the provided materials to create their triangle. The only direction or hint that they will receive as to what we are doing is "Just make a triangle". After creating their triangles in pairs, students will set their model aside while I introduce the lecture; Can the Pythagorean Theorem be used? After introducing the content, students will be asked to refer back to their models and evaluate if they could use the Pythagorean Theorem on their own triangle to find the length of a side. Each group will then share why their triangle can or cannot be compatible with the Pythagorean Theorem. This is a direct application of the goal for the day (Students will be able to evaluate the proper situation in which to use the Pythagorean Theorem). If students deemed their triangle incompatible with the Theorem, they will be asked to discuss with their partner or reflect by themselves what would need to change on their triangle to make it compatible. To check for learning, I plan on frequently asking individuals to solve the problem on the board (engaging each student in turn). Students will be grouped bases on a random assignment (positive even, positive odd, negative even and negative odd numbers drawn from a hat) and both students will be encouraged to share the "triangle engineering" role. After learning the formula for the Pythagorean Theorem, students will be asked to look at the triangle they have built and will be encouraged to use the measurements of the legs to solve for the hypotenuse. At the end of the lesson, students will be able to create a short story using Comic Life that depicts three practical applications of the Pythagorean Theorem. Experience, Evaluate, Rethink.

To self-assess, students will answer problems individually then partner with someone who computed a different answer and compare results. Students must ask "what was different about my method in comparison to my partner's approach?" to gain more perspective on the concept. I will then review the proper method (even if the entire class got all of the practice problems correct) to solidify the concept. Students will receive immediate feedback based on their answer. "Great job getting the right answer! For those of you who didn't, I'm sure you'll get it next time! Just keep practicing". This lesson is the gateway into all following lessons in this unit. By knowing the Pythagorean Theorem, students will be able to begin to comprehend the relationship between angles and sides, which is more or less the heart of this lesson.

Content Notes


 * The Pythagorean Theorem is a2 + b2 = c2. This uses the length of two legs of the triangles, squared, and added to equal the length of the hypotenuse squared.
 * A "leg" is the side of the triangle that is NOT the hypotenuse.
 * A hypotenuse is the side of the triangle that is opposite the ninety degree angle.
 * The word "supplementary" is defined as an angle (or two angles together) that create a measure of 180 degrees when added to the third angle.

Handouts -"Ladder" Graphic Organizer