brandonbower.weebly.com€¦ · web view8.g.6 – explain a proof of the pythagorean theorem and...

Brandon BowerCI 4490 Dr. Heath12/10/12

Instructional Design Project – Field Experience

Unit Topic: Pythagorean Theorem with Real World Applications

Learning Goals and Objectives:

Essential Questions:

What is the Pythagorean Theorem and when does it apply? What is the relationship among the lengths of the sides of a right triangle? How do I know that I have a convincing argument to prove the Pythagorean Theorem? How can I use the Pythagorean Theorem to find the distance between two points? How does the Pythagorean Theorem relate to the distance between two points on the

coordinate system? How can I use the Pythagorean Theorem to find the length of the hypotenuse and/or the

legs of a right triangle on a coordinate plane? How can the Pythagorean Theorem be used to solve problems?

Learning Goals:

I will use inverse properties to simplify, solve and evaluate algebraic expressions and equations involving integer exponents and square roots.

I will be able to prove the Pythagorean Theorem and its converse. I will be able to find the distance between two points on a coordinate plane. I will be able to apply the Pythagorean Theorem to determine unknown side lengths in

right triangles in real-world and mathematical problems in two and three dimensions.

Common Core State Standards:

8.G.6 – Explain a proof of the Pythagorean Theorem and its converse 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right

triangles in real-world and mathematical problem in two and three dimensions. 8.G.8 – Apply the Pythagorean Theorem to find the distance between two points in a

coordinate system. 8.EE. 2 – Process - Use square root and cube root symbols to represent solutions to

equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

21 st Century Skills

Effective Communication


Collaboration Critical thinking and Problem Solving Creativity and Innovation Flexibility and Adaptability Initiative and Leadership Productivity and Accountability Curiosity and Healthy Skepticism

Horizontal AlignmentMathematics Language Arts Social Studies Science

8.G.6 - ContentExplain a proof of the Pythagorean Theorem and its converse.

R.IT 8.9 – PWhat: two or more texts

8.RH.9What: Analyze the relationship between a primary and Secondary source on the same topic.

8.P.1.3What: Compare chemical and physical changes

8.G.7 - ProcessApply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

R.RL 8.9 – PWhat: analyze modern work of fiction

8.G.8 – ProcessApply the Pythagorean Theorem to find the distance between two points in a coordinate system.

8.RH.3What: Identify key steps in a text’s description.

8.EE. 2 – ProcessUse square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube

L.5.2a. Use punctuation to separate items in a series.

8.RH.4What: Determine the meaning of symbols, key terms, and other domain-specific words and phrases.


roots of small perfect cubes. Know that √2 is irrational.

Vertical AlignmentCompetency Goal

Understand the Pythagorean Theorem

Standard Verb BloomsTaxonom

y

What About

8.G.6Content

Explain 2 A proof of the Pythagorean theorem and its converse

Pythagorean Theorem

8.G.7Process

Apply 3 The Pythagorean Theorem

Determine 4 Unknown side lengths Right Triangles8.G.8Process

Apply 3 The Pythagorean Theorem

Find 3 Distance between points Coordinate systems

Competency Goal

Work with radicals and integer exponents

8.EE.2Process

Use 3 Square root and cube root symbols

Represent 2 Solutions to equations x2 = p and x3 = pEvaluate 3 Square roots of small

perfect squares and cube roots of small perfect cubes

Square roots and cube roots


Student Background, Knowledge, and Experience

Before beginning a unit on Pythagorean Theorem with students they should be able to effectively identify and solve equations using exponents. First students should have successfully solved equations with exponents such as x2 + 224 = 500 to understand how the Pythagorean Theorem formula, a2 + b2 = c2, works. Lesson Plan 1 will encompass these instructional activities to get students prepared for understanding and using the Pythagorean Theorem. The pre-assessment I gave them was an oral assessment asking them who knew what the Pythagorean Theorem was and only two of my students knew what it was.

During my internship I have had four different blocks of students including first, second, third and fifth period. My first period students would be considered above average students because they understand the material when being taught. My second period students would be classified as average or slightly below average because you have to give them more instructional time, methods, and examples of work. Third period students are my academically gifted students who excel at all the tasks they complete which in turn they need more and higher level learning activities. Fifth period is my inclusion class which would be the lowest class I have therefore the need more time to work on class work and they need more examples to understand the material given to them.

To understand more about how these classes are different you have to understand the demographics of the school in and of itself. There is a lot of diversity in West Wilkes Middle School however, it is not the type of diversity one immediately thinks about which is by race or ethnicity. This middle school is diverse mainly because of the vast amount of students who come from different socioeconomic background. The population of students is primarily Caucasian but the socioeconomic status varies from very high to very low. For the most part that is how each block of students differs in my classroom because third period is primarily students who come from families that have a high income rate at home. First and second block could be thought to be in the middle because as you observe the students you generally can tell that those students come from middle class families. Then fifth block by looking at what they wear, how they talk, and meeting some of their parents one can tell that they come from families that have a low socioeconomic status.

The best way I was able to identify where the students were coming from was after school when I attended parent night where the parents would come and talk to each teacher about how their child was doing. Out of all my periods my third block, which is my academically gifted students, had the most parents to show up and only two parents from my fifth block appeared that night. I asked myself well why that was the cause and I came up with after meeting all of the parents was because the parents with a high income care about how their students are doing in school because they take education very seriously. That is not to say that parents who


have low incomes do not care about their students success at school but there was a tremendous difference in the parent attendance between my third and fifth block. This is a very beneficial way to understand, get to know your students, and individualize each one of their needs.

Most of what I learned about working with and attending to my students needs was working with my cooperating teacher Katrina Hurley. After having enough time to observe and get to know the students for the first week on my own we sat down during planning to talk about the students. Most of what we talked about was the inclusion class and how to deliver the instruction to them in the best way possible. She would ask me questions about what I noticed with each of the classes and we would go over the best possible way to handle situations with certain students and in other areas in the classroom. The discussion followed implementing taking more time with fifth block so they could understand the material better and showing them the steps to take each time to succeed with getting the problem right. What I learned was that fifth block if the instruction is delivered orally rather than visually they will not retain and understand the information.

Reflection:

Knowing students background is essential to becoming a better teacher because it allows the teacher to understand what a student is going through. For instance if a student recently had a death in the family you are not going to expect them to have the homework the next day in class with all of the answers correct. Understanding your students and where they come from creates a bond between you and the student where you can understand what students are dealing with outside of school. Understanding their background also lets teacher adjust their instruction to fit the needs of each student and what is going to benefit your students the most.


Plan for assessment and Evaluation of Student Learning

Objectives Pre-Assessment

Formative Assessment

Summative Assessment

21st Century Skills

I will use inverse properties to simplify, solve and evaluate algebraic expressions and equations involving integer exponents and square roots.

-What do you know about the Pythagorean Theorem?

-Graphic Organizer

Geometry Project -Effective Communication

-Collaboration

-Critical thinking and Problem Solving

-Creativity and Innovation

-Flexibility and Adaptability

-Initiative and Leadership

-Productivity and Accountability

-Curiosity and Healthy Skepticism

I will be able to prove the Pythagorean Theorem and its converse.


-Flamingo Run(red) -Flamingo Run(blue)

-Graphic Organizer

-Applying the Pythagorean Theorem on the Coordinate Plane

-Picturing Pythagoras graphic novel

Geometry Project

I will be able to find the distance between two points on a coordinate plane.


-Graphic Organizer

-Applying the Pythagorean Theorem on the Coordinate Plane

Geometry Project

I will be able -What do you -Graphic Geometry Project


to apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

know about the Pythagorean Theorem?

Organizer

-Picturing Pythagoras graphic novel

21st Century Skills addressed in each category:


-Effective Communication


-Initiative and Leadership

-Flexibility and Adaptability


-Collaboration

-Effective Communication



-Creativity and Innovation



Essential Content Knowledge (Teacher candidate’s knowledge)

Common Core Standards Addressed:

8.G.6 – Explain a proof of the Pythagorean Theorem and its converse 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right

triangles in real-world and mathematical problem in two and three dimensions. 8.G.8 – Apply the Pythagorean Theorem to find the distance between two points in a

coordinate system. 8.EE. 2 – Process - Use square root and cube root symbols to represent solutions to

equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The content a teacher would need to know to teach this lesson involves solving equations with exponents, the Pythagorean formula, and how to find the distance on a coordinate plane using the Pythagorean Theorem. This mathematical concept is very simple for a math instructor but they also need to know how to present this information to the students in a way that they can understand and comprehend the material. First the teacher must allow their student ample time to discover how to solve equations to be able to use the Pythagorean Theorem. Once they have had enough practice with solving equations the students can then practice with using the Pythagorean formula, a2 + b2 = c2. If students were gave this formula without having enough practice with solving equations students would not be able to use this formula because it require student to know how to solve for a variable.

Using the Pythagorean Theorem as a unit to teach children is not only a lesson that students will use during their math class but it also will enable them to have the ability to use this mathematical strategy in various jobs. This unit shows students how the Pythagorean Theorem is everywhere including televisions, carpentry work and just about everywhere they go. The idea is for the students who ask where they are going to use this application, to understand that what they are learning in their math class can be used outside of school making this lesson valuable to students because it’s not merely something teachers ask them to do.

The Pythagorean Theorem unit requires students to touch on all the levels of Blooms taxonomy remembering, understanding, applying, analyzing, evaluating, and creating. Students have to remember the formula to understand how to apply it to problems to solve for the correct answer. With the geometry project students were required to analyze the data, evaluate the claims on the paper, and create from what they have been taught about the Pythagorean Theorem.


Instructional Procedures

Lesson Plan: Day 1 Square and Cube Roots

Essential Question:

How do I simplify, solve and evaluate algebraic expressions and equations involving integer exponents and square/cube roots?

Grade Level: 8

Learning Goals:

I will use the inverse properties to simplify, solve, and evaluate algebraic expressions and equations involving integer exponents and square roots.

Common Core Mathematical Standards:

8.EE. 2 – Process

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Resources/Materials:

Smart Board Lesson: Vortex Matching with Perfect Squares and Cubes Calculators Math-O Game: Equations with integer exponents, square, and cube roots. Plain notebook paper: MATH-O Ticket Out the Door: (3 problems) – small sheet of recycled paper

o x2 = 121o x3 = 89o x3 + 104 = 236

Overview:

At the beginning of class we will start out by reviewing previous material learned about perfect squares and perfect cubes. I have created a smart board vortex lesson where students will identify perfect/not perfect square and also perfect/not perfect cubes. This activity is to refresh their memory about squaring/cubing numbers and it is an introductory activity to Pythagorean Theorem. Next I will have students play the MATH-O game. They should use the plain sheet of notebook paper to create a 5 by 5 grid with MATH-O labeled across the top and a FREE space in


the middle. Students will randomly pick numbers 1-60 without repeating to place on their 5 by 5 grid. Students who win will receive candy. Before they leave class they need to complete 3 problems on the board for their “Ticket out the Door”.


M A T H O

Free Space

Lesson Plan: Day 2 Graphic Organizer


Essential Question:

Where does the Pythagorean Theorem come from? What is the Pythagorean Theorem and when does it apply What is the relationship among the lengths of the sides of a right triangle? How do I have a convincing argument to prove the Pythagorean Theorem?

Grade Level: 8

Learning Goals:



8.G.6 - Content

Explain a proof of the Pythagorean Theorem and its converse.


Green Sheet of construction paper Ruler Green, blue, and yellow crayon Graphing paper Glue sticks Calculators

Overview:

This lesson is for students to make an individual graphic organizer for students to investigate what the Pythagorean Theorem is. Students will be handed all of the materials listed above and be asked to share in groups of two. On graph paper the will be asked to make a 3 by 4 triangle and connect the edges with a ruler. Next they will be asked to make a 3 by 3 and a 4 by 4 square. They will color the 3by3 square yellow and the 4 by 4 square blue also indicating the area of the squares. Next students will have to figure out how to fit a square on the hypotenuse. Once they figure out it is a 5by5 square they need to color that square green indicating the area as well. They will glue this onto the green sheet of construction paper labeled Pythagorean Theorem – Graphic Organizer.

Lesson Plan: Day 3 Graphic Organizer


Essential Question:

Where does the Pythagorean Theorem come from? What is the Pythagorean Theorem and when does it apply What is the relationship among the lengths of the sides of a right triangle? How do I have a convincing argument to prove the Pythagorean Theorem?

Grade Level: 8

Learning Goals:



8.G.6 - Content



Green Sheet of construction paper Ruler Green, blue, and yellow crayon Graphing paper Glue sticks Calculators

Overview:

Students will continue working on the Pythagorean Theorem graphic organizer they created the day before. Some students may need to get caught up with the rest of the class that was absent the day before. Pass out materials listed above and make sure everyone is on task and caught up to continue in the same groups as the day before. Once the students have glued the triangle and squares in their proper place they will make another triangle on the sheet of graph paper that has the dimensions 6 by 8. Again they will make squares to fit each side of the triangle remembering to color the 6by6 yellow, the 8by8 blue, and 10by10 green. Once they have finished begin adding things that they have learned and examples of problems.

Lesson Plan: Day 4 Visual and Auditory


Essential Question:

What is the relationship among the lengths of the sides of a right triangle? How do I know that I have a convincing argument to prove the Pythagorean Theorem? How can I use the Pythagorean Theorem to find the distance between two points?

Grade Level: 8

Learning Goals:



8.G.6 - Content



Video Clip for Solving Legs Video Game design Graphic Novel – Picturing Pythagoras Picturing Pythagoras worksheet Pythagorean Theorem and Perimeter

Overview:

Students will begin by reading a graphic novel Picturing Pythagoras and answer questions 1-3 on the front as a class. This novel reiterates what we learned during the green graphic organizer lesson about Pythagorean Theorem. The two videos used is for the visual learners to get a chance to see how to apply the Pythagorean Theorem rather than just hearing information from the teacher. After the videos have been viewed and the graphic novel has been read the will work in groups of two completing the two worksheets: 1) Picturing Pythagoras 2) Pythagorean Theorem and Perimeter.

Lesson Plan: Day 5


Flamingo Run: Finding the Hypotenuse (Red)

Essential Question:


Grade Level: 8

Learning Goals:



8.G.6 - Content



Flamingo Run – Finding the Hypotenuse (Red) Answer Sheet/Work for Finding the Hypotenuse (Red)

Overview:

At the beginning of class it will be effective to go over examples of how to find the hypotenuse of a right triangle from the activities they were working in groups the previous day. Once the class is ready they need to make an answer sheet with one side having the work that they do for the problems and the other side being the answers so that it is simple and easy to check. They will be group into pairs starting at the beginning of the Flamingo Run. Once the solve for the first one they will find the solution to that problem on another red Flamingo Run sheet

Lesson Plan: Day 6


Flamingo Run: Finding the Leg (Blue)

Essential Question:


Grade Level: 8

Learning Goals:



8.G.6 - Content



Flamingo Run – Finding the Hypotenuse (Blue) Answer Sheet/Work for Finding the Hypotenuse (Blue)

Overview:

At the beginning of class it will be effective to go over examples of how to find the leg of a right triangle from the activities they were working in groups the previous day. Once the class is ready they need to make an answer sheet with one side having the work that they do for the problems and the other side being the answers so that it is simple and easy to check. They will be group into pairs starting at the beginning of the Flamingo Run. Once the solve for the first one they will find the solution to that problem on another blue Flamingo Run sheet.


Flamingo Run Answer SheetFinding the Hypotenuse (Red)

Finding the Leg (Blue)

50258.5136539514.415.611.711218.712.512.2

309.7413.1107.1411912.2413.215.28.9449.71.240


Lesson Plan: Day 7

Geometry Project

Essential Question:

How can I use the Pythagorean Theorem to find the distance between two points? How does the Pythagorean Theorem relate to the distance between two points on the

coordinate system? How can I use the Pythagorean Theorem to find the length of the hypotenuse and/or the

legs of a right triangle on a coordinate plane? How can the Pythagorean Theorem be used to solve problems?

Grade Level: 8

Learning Goals:

I will be able to prove the Pythagorean Theorem and its converse. I will be able to find the distance between two points on a coordinate plane. I will be able to apply the Pythagorean Theorem to determine unknown side lengths in

right triangles in real-world and mathematical problems in two and three dimensions.


8.G.7 – ProcessApply the Pythagorean Theorem to find the distance between two points in a coordinate system.

8.G.7 - ProcessApply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.


Applying the Pythagorean Theorem on the Coordinate Plane - worksheet Geometry Project worksheet Calculator Ruler

Overview:

The geometry project is for students to apply what they have learned in the Pythagorean Theorem unit to an actual real world problem after they have used some self discovery completing the Applying the Pythagorean Theorem on the Coordinate Plane worksheet. Students


will work alone completing this project to access what they have retained during the lesson. At the end of this project students should be able to successfully solve problems using the Pythagorean Theorem, real world example problems, and be able to calculate tax in with their money spent.


Assessment/Evaluation

The type of data used in this unit on Pythagorean Theorem consisted of pre/post assessments including formative and summative assessment to determine the students’ level of understanding throughout this unit. The pre-assessment given was an oral assessment where the students were to talk about what they knew about the Pythagorean Theorem however, out of all the students asked two students knew what the Pythagorean Theorem was and how it works. The purpose of this was to determine what the students’ previous knowledge of this mathematical concept is.

The formative assessments consisted of giving the students four different assignments picturing Pythagoras, flamingo run red and blue, and also the coordinate graphing worksheet. These assignments were to determine students’ knowledge of mathematical tasks to complete and understand how to use the Pythagorean Theorem. One thing I did notice was how student struggled with solving the picturing Pythagoras worksheet. This was one of the first assignments I gave them on Pythagorean Theorem and it was expected that they would do extremely well on it since their previous knowledge consisted of knowing nothing about this topic. However, during the final two formative assessments students did considerably much better because they began to understand and comprehend how the Pythagorean Theorem works.

The final summative assessment given was a Geometry project where student were to take the knowledge that they have learned about the Pythagorean Theorem and apply it to this project. The project worksheet describes a real-world problem where they have to determine how much fencing they will need to place around their property and they also have to determine which company will be the best deal for installing their fence. Overall, students did very well with this assignment which gives an indicator to the teacher that this lesson was effective with students learning the material.

Reflection:

The formative and summative assessments given told me that throughout my instruction students were struggling with the first assignment however, after they began to understand how the Pythagorean Theorem works they began to understand better throughout this unit.


Adaptations/Modifications

Questions for Cooperating Teacher:

How many students have IEP’s in your classes and how is instruction differentiated to fit their needs as a student?

How do you accommodate students who have various backgrounds who come from well to do households and students who come from backgrounds that are opposite of that?

What is the best way to handle students with behavioral disorders and how do you accommodate classroom assignments for them?

Overall, what would be the best adaptation and modification that is universal for all students that seems to work for you?

Instructional Strategies to Accommodate Students needs:

Smart Board Lessonso Incorporating technology

Flamingo Runo Accommodates for students who need to get up a move around during the day

Group Worko Accommodates for students who work better in a group

Individual Worko Accommodates for students who work better alone

Videoso Incorporates visual aids for students to see the content

MATH-O Gameo Makes learning appear fun to the students so they stay interested in the material

Vortex Gameo Incorporates technology for the students to use

Matchingo Incorporates technology and the use of getting them out of their seats to learn

After sitting down with my cooperating teacher we addressed each one of these issues and many more. One of the methods we talked about that was beneficial to students was taking the students who are behind or do not understand the content and put them in a group. The other students should be working on the same assignment at their desk. The students that were put into a group will work with one another on the assignment as the teacher discusses and goes over the assignment with them. This allows all students to have a fair chance to complete the assignments on time as a class rather than letting students get behind. Each of these methods is designed to attend to each student’s individual needs.


Reflection:

After completing the Pythagorean Theorem unit I began to understand why teacher have to adapt and modify instruction for students. For example during the first couple of lesson which were self discovery for the students many of them were not understanding how to use this formula. However, after using the smart board, videos, and oral explanations of how to solve problems using this formula students began to comprehend the material better. The varying learning styles of students requires teacher to differentiate instruction for them to learn.


Classroom Management

Classroom management is one of the most essential qualities a teacher needs to have to be successful in the art of teaching. In order to have and stay on tasks a teacher must be prepared each and every day and have a back-up plan for things that may go wrong or get in the way of what they had planned to do that day. Managing a classroom can be difficult for a new teacher however it becomes easier to manage a classroom when a teacher finds what works best for them.

Everyday when my students would walk into the classroom I would have a list or procedures/tasks students needed to have out and ready for class to begin. Typically this would be their homework or an assignment they need to have completed for the day, calculators, rulers, readings from the front table, and reports that needed to be turned in. All of the desks were facing the front of the classroom so they could easily see the smart board and begin working on the work I had for them to begin working on. This method of having students something to work on immediately when they came into class was a very good strategy and worked very well because it eliminated the time I would have to spend telling them what they needed to have ready for the day. It kept my students accountable for what they needed to have out and it gave them time to get settled down and ready to begin the lesson for the day which ran very smoothly once they became accustomed to doing that each day.

One of the instructional activities that worked very well the students and me was the Flamingo Run activity. This activity involved two different Flamingo Runs where on one they had to find the hypotenuse and on the other they had to find the leg of a right triangle using the Pythagorean Theorem. Once the completed a problem on one Flamingo Run the answer would be found on the next problem they had to complete. The activity required students to be in pairs getting up out of their seat solving and finding answers around the room which was very beneficial because we all know how middle school students are; they cannot sit still very long. Before the activity began they were instructed to get a calculator and clipboard with their partner and begin working on the Flamingo Run they was paired with. While they were working on this assignment I would walk around the room to check answers and many of them would ask me for help on a problem and I would tell them have they checked with their partner to see if they knew the answer. Instead of answering the questions for them it allowed the students to rely, cooperate, and collaborate with their peers. The first Flamingo Run finding the hypotenuse took them the entire class period which is what I was anticipating and the Flamingo run finding the leg the following day did not take them as long because they had practice with similar problems the day before.


Reflection:

I remember my first few days of trying to use my classroom management skills and put them to the test, well they did not work so well. The students had been accustomed to responding to the actions of what my teacher had trained them with. After I started using her methods of classroom management things really started to change in how the classed seemed to flow and have structure. The management issue that I struggled with the most was how to use time effectively because there is only 70 minutes for each period which is a short amount of time when you want to get many things accomplished. I noticed that the first week I was here and I was teaching I was moving at too slow of a pace for the class to get what we needed to be accomplished for the day. However, towards the end of my internship I began to revamp my methods of teaching by using time more effectively, letting the students complete tasks around the room instead of myself, and allowing enough time for students to be ready to leave knowing what they needed to have next class period.


Results and Analysis of Student Learning


StudentPic, Pythagoras FlamingRun(red) Flaming Run (blue) Coordinate Graphing Geo. Project

1st Period 100 100 100 100 10070 100 100 100 89

100 100 100 100 100100 100 100 100 100

a 100 100 100 100100 100 100 100 100100 100 100 100 100100 100 100 100 a100 100 100 100 100100 100 100 100 100

78 100 100 0 a100 100 100 100 100100 100 100 100 100100 100 100 100 100

80 100 100 100 100100 100 100 100 100100 100 100 100 100

80 100 100 0 100100 100 100 100 100100 100 100 100 100100 100 100 100 100100 100 100 100 100100 100 100 100 100

2nd Period 100 95 40 100 7280 95 100 0 100

100 95 100 0 100100 95 100 0 100100 100 0 100 83100 100 100 100 100100 100 100 100 100100 100 100 100 100100 100 100 100 100100 100 100 100 85

a 100 100 90 98100 100 100 25 100100 100 100 100 96100 100 100 100 83100 95 100 100 85100 100 a 100 75100 95 95 100 84

85 100 100 100 100100 95 80 90 75100 95 100 100 76100 100 100 100 95100 100 100 100 95100 95 100 100 95100 100 100 75 95

3rd Period 103 100 100 100 10095 100 100 100 10098 100 100 100 100

0 100 100 100 a103 100 100 100 98103 100 100 100 100

88 100 100 100 100103 100 100 100 100

70 100 100 100 10093 100 100 100 10093 100 100 100 92

100 100 100 100 1000 100 100 100 98

103 100 100 100 10093 100 100 100 9898 100 95 100 10088 100 100 100 10083 100 100 100 9590 100 100 100 10098 100 100 100 10093 100 100 100 100

0 100 100 100 89103 100 95 100 100100 100 100 100 100103 100 100 100 100

95 100 95 90 9495 100 95 100 10095 100 100 100 a98 100 100 100 100

103 100 100 100 100

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