Unit Circle Lesson Plan 4j442l

The Unit Circle and Its Values Kaitlin Carr Grade 10-12/ Mathematics

Common Core Standards: Extend the domain of trigonometric functions using the unit circle HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. HSF-TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. HSF-TF.A.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π– x, π+x, and 2π–x in of their values for x, where x is any real number.

Lesson Summary: In this lesson, students will be learning the radian values on the unit circle. Students will also be learning the values for the major radian measures of the unit circle. They will understand how to calculate the values using methods previously learned. This lesson is the second part in the introduction to Trigonometry. It is important that students understand these values since more lessons will be based upon them. I will show them how radian measures are calculated and how they correspond to degrees of angles. They will be given a handout of the unit circle and be asked to fill out the common degrees and corresponding radian measures. Students will engage in a review game to help them the radian measures of the unit circle. They will then be divided into groups and given a worksheet that contains the unit circle. They will be asked to calculate certain parts of a triangle, outside of the unit circle. They will then scan a QR code and a video will appear that will explain the values of the triangle they have just found and how they apply to the unit circle. This will allow them to get an understanding of the unit circle values as it is an integral part of trigonometry. Estimated Duration: This lesson will be divided into two 50 minute periods. The first will discuss radians and the most common on the unit circle. The second will discuss the values attached to the radian measures. Commentary: I believe the hardest part of this lesson will be getting the students to apply what they

have already learned. Once they see how the Geometry they have learned before applies to this lesson, I believe that they will understand the values even more so. I think the students will become excited when they see the pattern of values involved with the values. Each quadrant contains the same values, but with different signs (positive and negative). While the thought of ing the entire unit circle is daunting, once they realize that they only need to one quadrant, I believe this will allow them to be more open to the new concepts to come.

Instructional Procedures Day 1: The first ten minutes will be an overview of the lesson from the day before. We will go over sine, cosine, and tangent again. The next twenty five minutes will be the lecture of radian measures. I will begin by discussing degrees, which the students have studied before. I will then show them the equation for finding the circumference of a circle and show them how it can be used to find the measures of angles. I will identify the most common angles of the unit circle and emphasize the need to learn these angles. I will hand out blank unit circles and for the next fifteen minutes, I will have the students fill in the common angles. They will need to record both the measures of degrees and radians. The last five minutes will allow for any questions to be answered. Day 2: For the first ten minutes, we will review the radian measure of the unit circle. Students will then be divided into groups and given handouts of two basic triangles. They will need to use any previous knowledge to figure out the sides of the triangles. For each triangle, there will be a QR code. This will contain a tutorial video. It will show how the triangles relate to the unit circle, as well as go over the ways to solve the sides of the triangles. This should take about thirty minutes. The last ten minutes, we will discuss what was learned from the videos and any questions will be answered. The students will be provided with a QR code leading them to a review game. This game will help the students review radian and degree measures.

Pre-Assessment: Before I begin my lecture on radian measure, I will ask the class to if they the equation for finding the circumference of a circle. I will ask what it is and have them say it out loud. If there is more silence or wrong answers are given, I will write the equation on the board and do a quick example of finding the circumference.

Scoring Guidelines: I will use my judgment as to whether they need a circumference problem worked for them. If the class answers the question confidently, then I will move along. However, as stated before, if answers seem sporadic, then I will review the equation quickly, before proceeding to the lesson. Post-Assessment: The assessment will be an exam. It will cover the radian measures, degree measures, and the values related to the angles. Scoring Guidelines: The Post-Assessment exam will be graded by scoring each part of the unit circle given and then translated into a percentage. Each part of the unit circle will be a point. There will be a total of 64 points available.

Differentiated Instructional In the activity, the groups will be divided so that there are three to four individuals. This will allow the students to help one another when working on the worksheet. Students who understand the concept will be able to aid any students who do not grasp it. Also, the tutorials should help any students who are still struggling. They have the worksheet to take home and the QR code will allow them the ability to access the tutorials outside of the classroom, as well. If there are students still struggling, I plan on touring the room while they are working on the problems. For any students who grasp the concept quickly, I will instruct them to help explain the reasoning behind the work. Peer tutoring will allow more students to receive help in a timely manner. It will, also challenge them to take their work and explain it, which will give them a stronger understanding and intuition of the concepts.

Extension https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circledefinition-of-trig-functions-1 This site contains videos on the unit circle. It has introductions and examples explaining the values. It, also, has ‘practice’ problems to allow additional time working with the values. This would be a great site for any students still struggling with the concept to visit.

Homework Options and Home Connections The students will be given a QR code that leads them to a review game. This will be the homework. It will help prepare them for the exam on the values. They will be able to practice as long as it takes in order for them to become comfortable with radians. They will, also, receive a worksheet where they will be given angle measures in degrees and they will need to convert them to radians.

Interdisciplinary Connections While reviewing sine, cosine, and tangent in the beginning of the first day, I will briefly discuss a few applications of this lesson and lessons to come. I will show that the sine wave appears in science often. For example, it appears as radio waves. This will show the students why they are learning it. I will also discuss the mathematician that first developed radians (relating it to history).

Materials and Resources:

For teachers

iPad, dry erase markers and board (for lecture)

For students

iPad or iPhone, pencils, worksheets

Key Vocabulary Radians, Sine, Cosine, Tangent Additional Notes Since this lesson is very important in the understanding of many concepts to come, the emphasis will

be familiarizing the students with all of the values.