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RICTEACHER Kevin Simpson DATE February 12, 2009
CLASS/GRADE LEVEL Algebra 2 (CP) LESSON TITLE: Unit Circle
RIBTS: 2.3 Select instructional materials and resources based on their comprehensiveness, accuracy, and usefulness for representing particular ideas and concepts.
5.1 Design lessons that extend beyond factual recall and challenge students to develop higher level cognitive skills.
NCTM STANDARD(S): Use trigonometric relationships to determine lengths and angles.
Use visualization, spatial reasoning, and geometric modeling to solve problems
GLEs/GSEs: M(G&M)–12–5 Applies the concepts of similarity of right triangles with the trigonometric functions defined as ratios of sides of triangles, and uses the ratios of the sides of special right triangles (30 0 -60 0 -90 0 and
45 0 -45 0 -90 0 ) to determine the sine, cosine and tangent ( 30 0 ,45 0 , 60 0 ) and solve related problems.
OBJECTIVES
INSTRUCTIONAL MATERIALS
AND RESOURCES
INSTRUCTIONAL ACTIVITIES
AND TASKS
KEY Qs: ↓
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Where would the terminal side for a 45º angle be?
How might we find the exact coordinates of the intersection point in our x-y plane?
How could we apply what we know about a 45-45-90 triangle to find the exact coordinates of this point?
How might we apply the information we have found for Quadrant I to find the values in the other 3 quadrants?
What is the student to know and be able to do as a result of this lesson?
 Students will create the unit circle.
 Students will be able to apply the properties of the special right triangles to completing the unit circle.
What instructional materials will you need for this lesson?
 Handout to remind students of the special right triangle (45-45-90, 30-60-
90).
 Worksheet with incomplete unit circle.
 Chalkboard and chalk
What technological resources (if any) will you need for this lesson?
 Calculator (if needed), ELMO and projector.
What instructional activities and tasks will you use to accomplish your objectives?
A. LAUNCH: (10-15% of lesson) 10 minutes
 We will review the previous night’s homework, which involved converting between radians and degrees, identifying and drawing angles based on degree and radian measure.
 Today we are going to learn about the unit circle. The unit circle is one of the most useful tools in trigonometry. It is a circle with a radius of one unit placed on an x-y plane. Just like we talked about earlier this week, we measure the angles starting from the positive x-axis counterclockwise.
The x-axis corresponds to the cosine function and the y-axis corresponds to the sine function.
B. EXPLORE: (60-70% of lesson) 45 minutes
 Draw the unit circle on the board. Based on what we have talked about this week, where would the terminal side for a 45º angle be? How might we find the exact coordinates of this point in our x-y plane?
 Draw the 45-45-90 triangle inside the unit circle on the board. What is the length of the hypotenuse of this triangle? How do we find the length of the other two sides of this triangle? Draw the same triangle outside the unit circle to refresh the memories of the students if needed.
 Ask the students, based on this triangle, what is the cos and sin of the angle that has been made with the x-axis. Show them how these values give us the x and y coordinates of the intersection point on the unit circle.
 Repeat this same procedure with the 30-60-90 triangle with 30 as the

2 central angle.
 Break the class into 6 groups of 4 and 2 groups of 3. Give them the creating the unit circle handout to help guide them. They will now work in groups to complete the unit circle quiz worksheet.
 The worksheet requires them to give the degree measure, radian measure and ordered pair for each of the given points on the unit circle.
C. SHARE & SUMMARIZE; CLOSURE: (20-25% of lesson) 15 minutes
 Each group will be asked to give their answers for two of the 16 points that are on the graph. We will be using the ELMO and projector to show the graph on the board so that all the students can share the findings of the other groups.
 Watch for student misunderstanding of how to represent the ordered pair.
Also make sure that radicals are in simplified form.
 Students may also need to be guided when converting degrees to radians.
 Once each group has had a chance to share their answers, I will recap what we have developed. What patterns do you see when looking at the coordinates of each of the points on the unit circle? Without using a calculator, who can tell me what the cos(60) is?
APPLICATION OR
EXTENSION
 The homework for today’s class will be for the students to complete another version of the unit circle. This worksheet is similar to the one we worked on today, but shows the triangles within the circle. This homework should help reinforce what we have worked on during class.
ASSESSMENT ACTIVITIES How will you determine what the students know and are able to do during and/or at the end of the lesson (in addition to embedded assessment)?
 The assessment for this lesson will be based on questions asked while helping the groups complete the task. Also, by the answers given when the groups present their findings to the class.
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REFLECTION I feel this lesson went well for the most part. I didn’t get to complete my entire lesson plan, but there was definitely some learning going on within the small groups. This lesson tied together quite a few of the concepts that we have been talking about over the past couple of weeks; trigonometry, special right triangles, converting radians to degrees and simplifying radicals. These are some very big ideas to work with, but I think overall the students are handling it well. I had them continue to work on completing the unit circle for homework and will spend a good part of the next class continuing the lesson. I still need to work on my use of the board space. Sometimes I feel like I’m all over the place. For the continuation of this lesson, I’ll try to guide the students by showing one of the special right triangles in all 4 quadrants and how the values for each of these triangles related.