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					              Critical Assignment 1 - Designing A Technology-Rich Lesson
Teacher: Mr. Nixon                                Subject: Trigonometry  Grade Level: 10th – 11th
Lesson Topic: Trigonometric Functions             Time Required: 4 weeks
Sunshine State Standards:
  Low Cognitive Complexity

MA.912.T.1.3: State and use exact values of trigonometric functions for special angles: multiples of

and (degree and radian measures).
MA.912.T.1.4: Find approximate values of trigonometric and inverse trigonometric functions using
appropriate technology.

  Moderate Cognitive Complexity
MA.912.T.1.1 Convert between degree and radian measures.

MA.912.T.1.2 Define and determine sine and cosine using the unit circle.

MA.912.T.1.5 Make connections between right triangle ratios, trigonometric functions, and circular
functions.

MA.912.T.1.7 Define and graph inverse trigonometric relations and functions.

MA.912.T.2.1 Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant,
cosecant) in terms of angles of right triangles.

MA.912.T.2.4 Use the area of triangles given two sides and an angle or three sides to solve real-world
problems.

MA.912.T.3.4 Solve trigonometric equations and real-world problems involving applications of
trigonometric equations using technology when appropriate.

  High Cognitive Complexity
MA.912.T.1.6 Define and graph trigonometric functions using domain, range, intercepts, period,
amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology.

MA.912.T.1.8 Solve real-world problems involving applications of trigonometric functions using graphing
technology when appropriate.

MA.912.T.2.2 Solve real-world problems involving right triangles using technology when appropriate.

MA.912.T.3.4 Solve trigonometric equations and real-world problems involving applications of
trigonometric equations using technology when appropriate.




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Access Points:

MA.912.T.2.In.a Compare the length of the straight sides in a right triangle with the length of the side
opposite the right angle (hypotenuse) by measuring the sides.

MA.912.T.2.In.b Identify and construct right triangles to solve real-world problems.

MA.912.T.2.Pa.a Recognize a right triangle in objects, pictures, or signs in real-world situations.

MA.912.T.2.Su.a Measure the sides of a right triangle to determine which side is the longest.

MA.912.T.2.Su.b Use right triangles to solve real-world problems.


Instructional Analysis - Prior Knowledge

Declarative Knowledge - Students should already know that…
1. Functions are setup with an independent variable x and a depend variable y; and should always be
setup in the form y=x or x=y
2. The horizontal axis of a graph is the independent variable x of a function and domain of the graph
3. The vertical axis of a graph is the dependent variable y and the range of the graph.
4. A right triangle has at least one angle equal to 90 degrees and the sum of the other two angle equal
90 degrees.

Students should already know how to…
1. Use a calculator to do basic arithmetic
2. Setup function properly to be entered and graphed in a graphing calculator.
3. Maneuver through websites and programs; and log into websites to access homework and blogs.


Prior Knowledge Assessment Plan
 As students enter the classroom, they will be handed a piece of paper with 10 problems that
they will need to start as soon as they are seated. The problems will vary according to the
knowledge needed to start this lesson. After the class has started, 6 students at a time will put
answers on the board. In a class of 30 and 6 students per a problem, each student writes up at
least 2 answers. This will allow me to access the student’s prior knowledge; as well as, the
student’s confidence level in their abilities. The problems will be worked out on a separate
sheet of paper and handed in after any necessary review of prior knowledge.




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Instructional Analysis – Declarative Knowledge

In this lesson, students will learn that….

    1. Radian is a measurement of an arc length
    2. The evaluation of trigonometric functions through a measurement of degrees or radians is a
       ration of the sides of a right triangle created by that measurement of degrees or radians.
    3. A unit circle is a circle with a radius of one and an arc length of 2π.
    4. Relationship between the Pythagorean Theorem, unit circle, and trigonometric functions.

Instructional Analysis – Procedural Knowledge

In this lesson, students will learn how to….

    1. Enter trigonometric functions into a graphing calculator
    2. Setup the graphing calculator to view period length of the function.
    3. Translate trigonometric functions along the x and y axis, increase or decrease the frequency,
       and increase or decrease the amplitude.
    4. Evaluate without a calculator all six trigonometric functions of given angles in increments of
       n(π/2), n(π/3), n(π/4), and n(π/6) from 0 to 2π.

Interdisciplinary connections:
   Students will be able to relate trigonometric concepts to applications in physics, such as, lunar and
solar trajectories, ocean tidal shifts, alternating current wave propagation, and applied forces to planes
in the form of right triangles.


Common Misunderstandings or Misconceptions:

   1. Inputting trigonometric functions into the calculator with the wrong angle of measurement to
      that of which the calculator is set for. Example is degrees when the calculator is set for radians.
   2. Order of operations of trigonometric functions.



Plan to address these:
   1. To alleviate entering wrong angle of measurements into the calculator, during the lesson of
       conversion between degrees and radians explain that the calculator will give trigonometric
       responses based on the mode in which it is set for. Also during examples, remind the students to
       determine what mode the calculator is set in.
   2. After the lesson on the description of each trigonometric function is established, a short review
       of functions within functions. Explaining that trigonometric functions are functions, such as, f(x)
       and should be treated as such. If there is an equation within the trigonometric function, then it
       needs to be solved first to establish the angle of the function. The same as, f o g(x); f(x) needs to
       be solved before g(x) can be solved.


Learning Objectives:

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Knowledge –
   1. Students will know how to convert degrees to radians and radians to degrees.
   2. Students will be able to define all six trigonometric functions
   3. Students will know the relation all six trigonometric functions have to the unit circle and right
      triangle

Comprehension –
   1. Students will be able to show the values for all six trigonometric functions that correspond to
      increment values along the unit circle of n (π/2), n (π/3), n (π/4), and n (π/6) from 0 to 2π.
   2. Students will be able to fully describe the unit circle and label all the important radian measures
      along the unit circle

Application -
   1. Students will be able to demonstrate the use of trigonometric functions to find the postion of
        objects that travel on circular arcs or distance between two points on a circle 80% of the time
   2. Students will be able to demonstrate the use of trigonometric functions to find the height of an
        object given their distance and angle of attack at least 80% of the time
   3. Students will be able to demonstrate the use of a right triangle to find the distance between two
        objects by using right triangles at least 80% of the time.

Analysis –
   1. Students will be able to identify a right triangle
   2. Students will be able to distinguish the hypotenuse from the other legs of a triangle and how all
        three legs are associated to all six trigonometric functions
   3. Will be able to distinguish sinusoidal graphs from co-sinusoidal graphs
   4. Students will be able to identify the parts of a trigonometric function of the constanstce a,b,c,
        and d; a*f(bx+c)+d.

Synthesis -
    1. Student will be able to compose a function based a given graph of a standard trigonometric
       function af(bx+c)+d
    2. Students will be able to formulate the necessary information to evaluate the distance between
       two points.

Evaluation -
    1. Students will be able to assess heights of objects using right triangles
    2. Students will be able to choose correct formulas that relate to situational conditions.



Learner Analysis:
    1. Age Range & Gender – Girls and boys ranging from 15-18 years of age
    2. Race – White, Hispanic, and African American
    3. Socio-economic background – Middle class to upper class
    4. Learning Style Preferences – Visual, auditory, and kinesthetic
    5. Disabilities & Exceptionalities – ESE students will be allotted all their extra provision that are
       outlined according to their IEP.

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    6. Motivation – All students will be allowed to retake any test, but may have accompanying
       knowledge of current material and past material. Before they are allowed to retake the test they
       must show all homework that has been assigned and problems in the blog. The better grade will
       replace the test. Because future material builds on previous material, this will serve as an
       incentive to go back over previous material.
    7. Cognitive Skills (concrete, abstract, etc.) – The student will need to rely on their concrete
       knowledge and back ground of geometry and algebra to understand how to derive the abstract
       concepts of trigonometric functions and evaluate the functions at various intervals along the
       unit circle. The units cognitive skills will range from low to high, but will predominantly be in the
       moderate to high level of cognitive skill.


Assessment Plan

Formative:

    1. Students will be given a “Bell Ringer” at the beginning of class to find out how much they have
       retained from previous lessons.
    2. Homework will be reviewed and students will write and answer problems on the board.
    3. The students’ blogs will be reviewed to make sure that they are keeping up with the work and
       performing up to standards of the class.


Summative:

    1. Students will be given a unit test that will cover all the material presented in class and in the
       blog. The unit test will evaluate that students knowledge and understand of the material and
       ability to apply it to real world problems
    2. All real world situational problems that were in the blog will be pulled together and submitted
       as a quiz grade.
    3. The Web Quest project will show that the student can analyze and evaluate a real world
       problem given the knowledge base of the current material and will create a final project to be
       submitted as a test grade.


Instructional Strategies:

How will you introduce the lesson?

The introduction of the unit will be presented in a power point. The power point will give a true relation
between what the student is learning and how they will use it every day.

How will you teach concepts during the lesson?

 New material will begin with a 15-20 minutes lecture that will present the new concept and a few
examples. Then 15-20 minutes will be used for the students to present random problems in the book on
the board and present them to the class. The following day, class will start with a bell ringer; and a
review of the material that was presented the day before, and go over the home work the night before.

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The rest of the class time will be used for collaborative team work on the current blog questions; which
will be 6 real life questions composed from the current and previous material.

How will you conclude the lesson?

The lesson will be concluded with a web quest that will be a culmination of the real life blog questions.
The details of the web quest will be introduced two weeks before the web quest is to be started.




Classroom & Technology Management Strategies:
While students are using the blog within the classroom, the teacher will roam among the computer
stations to provide help, keep students on task, and make sure the work is being completed in the time
allotted.



Learning Activities:

During the introduction of the lesson, students will:
     Students will listen and ask question during the power point presentation
     The power point presentation is to facilitate an overall understanding what the lesson is about
     The student will gain a purpose of what the lesson is for, and future uses and what

During the lesson, students will (Mention Web Quest):
        First day of new material
     Have a 15-20 minute lecture that will present new concepts and include examples on the use of
        the new material.
     Spend 15-20 minutes working problems on the board and presenting their answers to the class.
        Second day of new material
     The class will begin with a bell ringer and 10 minutes review the homework assigned the night
        before.
     The rest of class the students will divide into groups of 4 members that will not change during
        this lesson and will work on the collaborative class blog site.
     The blog will have questions relative to the current lesson and will have an overall encompassing
        facilitation toward the web quest that will be do at the end of the lesson.
     As groups complete the blog assignments they will use the website to navigate to web quest and
        continue review or completing necessary work for the web quest.

At the conclusion of the lesson, students will:
     Understand the basic principles of trigonometric functions
     How trigonometric functions relate to right triangles
     Combine all blog questions into a portfolio and turn in for a quiz grade
     Complete the web quest in which the students will use current knowledge to analyze and apply
        to real life situations and create a solution.

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Materials & Resources: (List everything you will need)

Supplies:
    Outline of the lesson
    Dry erase markers
    Computers
    Graphing calculator

Technology tools (Software and hardware):
    Teacher created website that will direct students to the power point, blog, and web quest
    Blog site to post helpful information for other groups to access
   

URL’s you will use:
    (Will be determined as the blog and web quest are created)


Self-Evaluation:

Teacher NETS addressed:
I plan on meeting NETS by teaching the appropriate use of technology and integrating it into the lesson
in meaningful ways. I will model appropriate technology use throughout all the lessons. The lessons
allow for students to incorporate digital resources in creative ways, allowing for student growth in both
mathematics and technology. Using the blog and webquest as assessment tools, I am able to expose the
students to non-standard ways of expressing mastery of a concept. I plan to provide this lesson to
others who are teaching this subject area so that they may share this learning experience with their
students or use the lesson as a springboard for developing their own unique lesson.

Student NETS addressed:
Throughout the course of this lesson, all of the NETS for students will be addressed. The students will be
actively using technology, participating in a digital community, conducting research, collaborating, and
problem solving. By the end of the lesson, students will not only be proficient in trigonometric functions,
but also in the many forms of technology integrated into this lesson.


Lesson Strengths:
The lesson draws its strength from it being student driven with a small amount of time used for teacher
provided lecture and examples. This will allow students to gain confidence in understanding and
applying the material to the homework problems. The student driven process will help foster or
continue the student’s active learning experience by allowing them to seek the answers to the blog
questions and web quest.

Lesson Weaknesses:
 Because the lesson is student driven, then the momentum of the lesson is primarily depicted by the
students. This can cause the learning time to slow or even stale cause the instructional time to increase.



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Possible Solutions or Action Plan for Improvement:
If the teacher is not use to positively motivating students, then I would recommend a work shop that
teaches how to change body language and syntax to help create a positively motivating atmosphere.
Also, it is important to keep on top of student’s questions as they arise. If a student is waiting for a
question to be answered, then chances are the student is not moving along with the lesson and will also
cause the momentum to stale.




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posted:12/5/2011
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