L4+O'Halloran,Erin+Marissa


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


 * Teacher’s Name:** Ms. Erin O'Halloran **Lesson:** 4
 * Grade Level:** 10 **Topic:** Special Triangles and Their Properties

__**Objectives**__

 * Student will understand that** problems could be solved using geometric properties.
 * Student will know** isosceles triangles, scalene triangles, equilateral triangles, 45-45-90 triangles, 30-60-90 triangles, acute triangles, obtuse triangles.
 * Student will be able to** describe the functions of right angles in everyday life.

__**Maine Learning Results Alignment**__
//Maine Learning Results: Mathematics- C. Geometry// //Geometric Figures// //Grades 9 - Diploma// //Students justify statements about polygons and solve problems//


 * Rationale:** By being able to identify special triangles, students will be able to use properties of the triangles in order to solve problems.

__**Assessment**__
The teacher will pre-assess students on their knowledge on special triangles to see if any of the students know (or can guess) what isosceles triangles, scalene triangles, equilateral triangles, 45-45-90 triangles, 30-60-90 triangles, acute triangles, obtuse triangles are. During the lesson, the teacher will have students complete a worksheet/graphic organizer, Cluster/Word Web 3.
 * Formative (Assessment for Learning)**

After learning about special triangles, students will make a Comic Life file describing the relations of angles and sides to the triangles described in class. Students will need to create characters and a situation involving certain angles and congruent sides. Pictures and a setting should be determined. Students can use images from online or use Paint or any other drawing tool. At least three special triangles should be mentioned along with the properties of the triangles. There is no page minimum or maximum; students don't need to print the comic, but it will be posted to the class wiki. The grade will be determined out of 100 points. This assignment is worth 10% of the student's final grade. The assignment will be graded with a rubric.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology:** Students will use Comic Life to create a comic book along using the graphics included in the software. Pictures in the comic book can be created by hand and scanned, from the internet (as long as properly sited), or created using Paint, Photoshop, or some other type of drawing program.


 * Physics:** In physics, it is very important to identify special triangles, especially 30-60-90 triangles and 45-45-90 triangles. This makes solving certain problems easier than using Pythagorean Theorem.

__Groupings__
Students will be put into Team Pair Solo and be split up into groups of even numbers, if possible. Once in their groups, students will be given a series of problems about special triangles and their properties. Together, the group of students will do the first problem. Once they all agree on the answer, students will split into pairs and do the second problem, and finally, students will be able to do the third problem on their own. This will repeat as many times as needed until all the students understand the concept of special triangles.

__**Differentiated Instruction**__

 * Strategies:**
 * Linguistic**: Have students create a story board for their Comic Life. They would need to include what the characters are saying, what is happening in the slide, and which of the special triangles they are using. The story board would be to help the students who want to make sure that they have all the requirements needed for the final product.
 * Intrapersonal**: This project is intrapersonal because each of the students will be making their own comic book. There will be plenty of class time where they will be able to work on their final product in class. They can choose to work on it alone or talk to one of their classmates, but students are to create a project with their own ideas.
 * Interpersonal**: Students are allowed to talk to their classmates about the project; they can help each other with ideas. There will be plenty of class time where they will be able to work on their final product in class. They can choose to work on it alone or talk to one of their classmates, but students are to create a project with their own ideas.
 * Musical**: Students can add music to their comic book. They would have to add the music file separately on the class wiki because music cannot be added to the Comic Life file; however, the idea would definitely be creative.
 * Spatial**: Students can draw the pictures of triangles/the characters themselves. They can scan them onto the computer and upload them into the Comic Life file. Drawing the shapes themselves would help a spatial intelligent student to remember the concepts of the special triangles.
 * Logic**: Students can use the properties of the special triangles to solve problems in the comic book. Rather than just identifying the properties, students can assign numbers as the lengths of the sides of triangles and solve problems using the idea of the properties of special triangles. They can use the concept of isosceles triangles having equal legs by assigning numbers to the legs and then proving that they are equal.

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


 * Absent:** If students are absent, then they will need to get the notes listing the special triangles and their properties from another student in the class. Should the absent student have a question, they can email the teacher and set up an appointment. If student is absent when the project is assigned, he/she would need to contact the teacher and they will receive the assignment. Because the comic will not be presented in class, an extension could be made pending the reason for the student's absence.


 * Extensions:** Students will use Comic Life to create a comic book along using the graphics included in the software. Pictures in the comic book can be created by hand and scanned, from the internet (as long as properly sited), or created using Paint, Photoshop, or some other type of drawing program. The teacher would challenge students by having them apply their intelligence to create situations based on how they learn: linguistic, logical, spatial, kinesthetic, musical, interpersonal, intrapersonal, or naturalist. Finding examples of special triangles both in the real world and in a specific intelligence would help students connect to the material.

__**Materials, Resources and Technology**__

 * LCD Projector
 * Computer to show software and slides
 * Text book
 * Hand outs
 * Graphic organizer
 * Web that lists the polygons and students have to list the properties of that polygon
 * Rubric
 * Story board template
 * Comic Life tutorial

__Source for Lesson Plan and Research__
Graphic Organizer: [|Word/Cluster Web 3] where students will classify the properties of certain special triangles. Cooperative Learning: [|Team Pair Solo]

[|Isosceles triangles] and some [|examples] [|Equilateral triangles] and some [|examples] [|45-45-90 triangles & 30-60-90 triangles] [|isosceles, acute, obtuse, scalene, equilateral triangles]

__**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:**
 * Beach Ball:** Because there are many different intelligences, students can relate the idea of the properties of triangles to many different real world applications. This is a very open-ended project where students get to pick which triangles they want to represent and which direction they want to go. How they create the Comic Life file is up to the students; they can use pictures from online, draw the pictures, create pictures on the computer using Paint, Photoshop, etc.
 * Clipboard:** Students have the option of making a story board before creating their final product. This way, students who need to have the procedure in front of them can easily create the Comic Life file by following their directions. It is clear that students need to include three special triangles and their properties in the story.
 * Microscope:** Students will be able to discuss their ideas in class and they can talk with other students during this time. Even though the ideas might be collaborative, students need to create separate Comic Life files using their own ideas. Students can discover how they want to represent the special triangles by using an intelligence that they feel comfortable with.
 * Puppy** Again, students will be able to talk amongst their classmates about ideas they had about this project. They have the liberty to talk to friends, other classmates, and/or the teacher. With everybody working on the project at once, students will feel comfortable doing the assignment in class as long as they stay focused.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:** Refer to content notes. //Student will be able to describe the functions of right angles in everyday life.// Identifying special triangles in events, actions, and ideas can help a student explain the concept of those triangles. By being able to notice where certain triangles are in the everyday world, students can relate the topic to themselves and the material would become more personal. It is clear that when the material becomes more personal, the students remember the material better and actually learn from the process. When a student can teach the material to someone else who has never seen this before, then that student has mastered the material using explanation.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * Rationale:**
 * Linguistic**: Have students create a story board for their Comic Life. They would need to include what the characters are saying, what is happening in the slide, and which of the special triangles they are using. The story board would be to help the students who want to make sure that they have all the requirements needed for the final product.
 * Intrapersonal**: This project is intrapersonal because each of the students will be making their own comic book. There will be plenty of class time where they will be able to work on their final product in class. They can choose to work on it alone or talk to one of their classmates, but students are to create a project with their own ideas.
 * Interpersonal**: Students are allowed to talk to their classmates about the project; they can help each other with ideas. There will be plenty of class time where they will be able to work on their final product in class. They can choose to work on it alone or talk to one of their classmates, but students are to create a project with their own ideas.
 * Musical**: Students can add music to their comic book. They would have to add the music file separately on the class wiki because music cannot be added to the Comic Life file; however, the idea would definitely be creative.
 * Spatial**: Students can draw the pictures of triangles/the characters themselves. They can scan them onto the computer and upload them into the Comic Life file. Drawing the shapes themselves would help a spatial intelligent student to remember the concepts of the special triangles.
 * Logic**: Students can use the properties of the special triangles to solve problems in the comic book. Rather than just identifying the properties, students can assign numbers as the lengths of the sides of triangles and solve problems using the idea of the properties of special triangles. They can use the concept of isosceles triangles having equal legs by assigning numbers to the legs and then proving that they are equal.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * Rationale:**Using both the formative and summative assessments assigned for this lesson, the teacher can determine if the students fully understand the different polygons and their properties. Because the formative and summative assessments are using two different sides of the brain, students with different learning styles will be able to learn the way they want to.

The teacher will pre-assess students on their knowledge on special triangles to see if any of the students know (or can guess) what isosceles triangles, scalene triangles, equilateral triangles, 45-45-90 triangles, 30-60-90 triangles, acute triangles, obtuse triangles are. During the lesson, the teacher will have students complete a worksheet/graphic organizer, Cluster/Word Web 3.
 * Formative (Assessment for Learning)**

After learning about special triangles, students will make a Comic Life file describing the relations of angles and sides to the triangles described in class. Students will need to create characters and a situation involving certain angles and congruent sides. Pictures and a setting should be determined. Students can use images from online or use Paint or any other drawing tool. At least three special triangles should be mentioned along with the properties of the triangles. There is no page minimum or maximum; students don't need to print the comic, but it will be posted to the class wiki. The grade will be determined out of 100 points. This assignment is worth 10% of the student's final grade. The assignment will be graded with a rubric.
 * Summative (Assessment of Learning)**

__Teaching and Learning Sequence__
For classroom arrangement, I will have students sit in a perimeter so they everyone can see the screen without other peoples' heads in the way. It is vital to see which polygon is being discussed during the lecture to minimize confusion. During the Team Pair Solo exercise, the desks will be arranged in groups depending on how many are in the group. The notes for my class will be displayed from a computer using an LCD projector.

Day 1 Introduce hook, or fractal activity (20 minutes) Introduce acute triangles (5 minutes) Introduce obtuse triangles (5 minutes) Introduce isosceles triangles (5 minutes) Introduce equilateral triangles (5 minutes) Introduce scalene triangles (5 minutes) Break (5 minutes) Team Pair Solo activity where students will do problems presented in class and then create graphic organizer (30 minutes)

Day 2: Introduce 45-45-90 triangles (10 minutes) Introduce 30-60-90 triangles (10 minutes) Team Pair Solo activity where students will do problems presented in class and then complete graphic organizer (15 minutes) Introduce Comic Life project: show tutorial, explain concept, answer questions (45 minutes)

Day 3: Have students work in class on their projects. (80 minutes)

Student will understand that problems could be solved using geometric properties **//Students justify statements about polygons and solve problems//.** It is the students' job to discover where special triangles are used in real-life. Any type of triangle covered in this lesson can be related to art or tiles. If students are interested further in the idea of triangles in tiles, they can research tessellations and find many examples of any type of polygon. The importance of angles is greatly appreciated in the world of physics and using 45-45-90 or 30-60-90 triangles' properties can help solve many physics related problems. To get students interested in the topic, the teacher will introduce the idea of fractals, especially Koch snowflake. Students will use this [|program]to make their own snowflake or fractal that uses triangles. That way, students will realize that this lesson's concept is the foundation for something interesting. **Where, Why, What, Hook, Tailors: Visual, Interpersonal, Interpersonal, Logical**

Students will know isosceles triangles, scalene triangles, equilateral triangles, 45-45-90 triangles, 30-60-90 triangles, acute triangles, obtuse triangles. By creating the graphic organizers together after the lecture, students will be know what to put on the organizer and where. They can use the Word/Cluster Web to easily list the special triangles covered in class and therefore would know which ones to include in the file Comic Life product. The teacher would check for understanding by going through the exercised with the students while in the Team Pair Solo groups. Each team would be doing the same problem so the teacher can easily identify who got the correct answer. They would show evidence of learning by helping each other during the Team Pair Solo exercise. If one student does not understand the concept, the team or pair's job is to help that student. **Equip, Explore, Rethink, Revise,** **Tailor: Interpersonal, Intrapersonal, Visual, Logical, Kinesthetic**

By using the Word/Cluster Web organizer, students are able to organize their thoughts and will be able to identify the different triangles by their properties. Once the organizers are finished in class, students will be split into Team Pair Share groups so that they can have a chance to teach students who might not understand the material right away. Each team would be doing the same problem so the teacher can easily identify who got the correct answer. They would show evidence of learning by helping each other during the Team Pair Solo exercise. If one student does not understand the concept, the team or pair's job is to help that student. This is how the teacher would assess the evidence of learning. If some students are still not understanding the material after it was explained to them by their fellow classmates, those students will need extra help and can schedule time with the teacher. Once students have a better idea of the topic, they can start creating the Comic Life product. By using the time in class, students can revise their ideas and include more detail by using ideas from other students. **Explore, Experience, Revise, Refine, Tailors:** **Interpersonal, Intrapersonal**, **Logical, Lingustic**

At the end of the project, students will be able to assess themselves on the entire lesson. Did they understand the concept right away or did you need help from your classmates? Were you the one in the group who was explaining it to the rest of the group? They will also be able to reflect on the Comic Life product. Students will be able to answer questions on the validity of the project and the process they used. After the assignments are handed in, students will receive their grades 2-3 days later from when they are posted on the class wiki. The idea of special triangles ties into the concept of Pythagorean's Theorem and transformations which are the next lessons. **Evaluate, Tailors:** **Interpersonal****, Linguistic, Visual**


 * Content Notes**

Types of Triangles by Length
In an **equilateral triangle,** all three sides are the same length. An equilateral triangle is always equiangular //(see below)//.
 * [[image:http://www.factmonster.com/images/equilateral.gif width="140" height="122"]] ||

In an **isosceles triangle,** two sides are the same length. An isosceles triangle may be right, obtuse, or acute //(see below)//.
 * [[image:http://www.factmonster.com/images/isoceles.gif width="62" height="120"]] ||

In a **scalene triangle,** none of the sides are the same length. A scalene triangle may be right, obtuse, or acute //(see below)//.
 * [[image:http://www.factmonster.com/images/scalene.gif width="140" height="49"]] ||

Types of Triangle by Angle
In an **equiangular triangle,** all the angles are equal—each one measures 60 degrees. An equiangular triangle is a kind of acute triangle, and is always equilateral.
 * [[image:http://www.factmonster.com/images/equilateral.gif width="140" height="122"]] ||

In a **right triangle,** one of the angles is a right angle—an angle of 90 degrees. A right triangle may be isosceles or scalene.
 * [[image:http://www.factmonster.com/images/rightangle.gif width="110" height="110"]] ||

In an **obtuse triangle,** one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene.
 * [[image:http://www.factmonster.com/images/obtuse.gif width="140" height="90"]] ||

In an **acute triangle,** all angles are less than right angles—each one is less than 90 degrees. An acute triangle may be equilateral, isosceles, or scalene.
 * [[image:http://www.factmonster.com/images/acute.gif width="75" height="120"]] ||

The 45-45-90 Triangle

Listed below are the values shown in the diagram as well as another common set of values for this triangle. Be sure to notice that the two legs have the same length, so, the leg length is listed only once.
 * **Hypotenuse**
 * Length** || **Leg**
 * Length** ||
 * 1 || 0.7071 ||
 * 1.4142 || 1 ||

The 30-60-90 Triangle


 * **Hypotenuse**
 * Length** || **Leg Length**
 * Opposite 30 Deg** || **Leg Length**
 * Opposite 60 Deg** ||
 * 1 || 0.5000 || 0.8660 ||
 * 2 || 1 || 1.7320 ||
 * 1.1547 || 0.5773 || 1 ||


 * Handouts**
 * Graphic organizer
 * Web that lists the polygons and students have to list the properties of that polygon
 * Rubric
 * Story board template
 * Comic Life tutorial