SUBJECT Mathematics Topic Unit circle and Trigonometry LEVEL

• SUBJECT: Mathematics • Topic: Unit circle and Trigonometry • LEVEL: Form Three

INTRODUCTION • Introduction to Trigonometry, the students will be introduced Unit Circle to define three trigonometric Functions. In fact, students were first introduced to right‐triangle trigonometry and its applications in Math 2. In this unit, students will expand their understanding of trigonometry as they are asked to use the unit circle to define the trigonometric functions.

• These situations will be provided through this Web. Quest and will guide students to gaining the knowledge they need to understand the Unit Circle completely. At the conclusion of the activities, students should be able to find values of trigonometric functions by using the unit circle.

TASKS

• Students will work in small groups (4 members in each group) to develop a student portfolio on unit circle and Trigonometry.

• You will be tasked with solving some problems related to the Unit Circle. At the end you should have a complete understanding of how to use the Unit Circle to solve trigonometric problems. •

COMPONENTS OF THE TASK: Specifically you will learn: • to use the unit circle to define the trigonometric functions • define and understand angles measured in degrees and radians • applications of the three trigonometric functions of general angles in standard position • finding values of trigonometric functions using points on the terminal sides of angles in standard position

These individual tasks contain skills and a variety of activities to provide hands on experiences with the unit circle. All concepts are initially developed using degree measurements. Radians will be introduced during the last task activity and will require you to walk through the previous concepts mastered in degree form. The final project will highligh multiple applications of the concepts in this unit through rides at a typical county fair

PROCESS Members of each group will gather information from the websites to create new ideas about unit circle and trigonometric functions

RESOURCES • Computers, • Internet supply • Class textbook

• In this lesson you will complete the following assignments: • Task #1: Getting Started with Trigonometry and the Unit Circle • Task #2: Right Triangles and Coordinates on the Unit Circle; More Relationships in the Unit Circle • Task #3: Un. Wrapping the Unit Circle - Graphs from the Unit Circle • Task #4: What is a Radian?

EVALUATION • In class, you will be given a blank unit circle, and you will have 10 minutes to fill in the blanks. • In class, you will be given a fille din unit circle and you will have 15 minutes to find all the mistakes. You must identify the mistakes, explain why you know if is a mistake, correct the mistake and explain how you know you are right. •

• You should also know how to convert degrees to radians and radians to degrees • How you will be evaluated on this task: • In class, you will be given problems that require you to convert degrees to radians or radians to degrees. • Finally, you should be able to solve trigonometric functions for values of x. • How you will be evaluated on this task: • In class, you will be given problems to solve

• Lastly you will present your lesson on the Unit Circle • How you will be evaluated on this task: • Your classmates will fill out observations on your presentation. They will evaluate you on creativity of the lesson idea and the content contained in the lesson.

WEB QUEST • Introduction http: //zunal. com/introduction. php? w=250659 • Tasks http: //zunal. com/tasks. php? w=250659 • Process http: //zunal. com/process. php? w=250659 • Evaluation http: //zunal. com/evaluation. php? w=250659

CONCLUSION The students will present their portfolios for whole class discussion. Whole class evaluation of each group’s portfolio.

CONCLUSION……. . Concluding questions will base on: - Briefly explain your modeled artifact showing how the concept of a trigonometric ratios can be demonstrated -What other information did you learn about the evaluation of trigonometric ratios using a unit circle? -What can you do to help other learners to know the evaluation trigonometric ratios using a unit circle? -What did you learn from others in your group and other groups?

EVALUATION Evaluation Organization Quality of content Quality of group presentation Exceptional 16 – 20 marks Very good 11 – 15 marks Satisfactory 6 – 10 marks Poor/ needs Total Score work 1 – 5 marks Presentation is Presentation well organized, communicates does not clearly neat and clearly topic quite clearly communicates information – topic the topic very clearly the but needs information – topic spoken but needs a lot even with information explanation of spoken explanation Answers all Answers some Answers very questions well few questions well and or none at all contains other interesting facts or conclusions Presentation Visuals and visuals and effects in the effects are very presentation effective and are effective - – are quite are not improve the and do not effective – and content – – and distract from the do not distract they are do not distract content from the distracting from the content

EVALUATION Evaluation Exceptional 16 – 20 marks Quality of group research Group can organize, analyze and synthesize information from a variety of sources Quality of group communicatio n Very good 11 – 15 marks Group can organize, analyze and with help can synthesize information from a variety of sources Group members with interact, some teacher collaborate and guidance can work effectively work together to collaborative produce an and effectively original project together to produce an original project Satisfactory 6 – 10 marks Poor/ needs work 1 – 5 marks Group can with Group has help organize difficulty to and analyze organize and information analyze from a variety of information sources even with help Group members with a lot of teacher guidance can work collaboratively and effectively together to produce an original project Total Score Group members have difficulty to work collaborate and effectively together even with teacher guidance Total score

APPENDIX – TEACHER GUIDE • Teacher resources webquests • Teacher resoruces planning

WEBQUEST LESSON RESOURCE & UNIT PLANNING Webquest Lesson Resource: In your subject groups make your teacher webquest resource: a Science, Technology, English or Mathematics Webquest Search for examples of Webquests on the internet – such as: • Examples of Science Webquests at: • http: //www. scsk 12. org/stt 2000_wq/science. html • Examples of English Webquests at: • https: //www. teachingenglish. org. uk/article/webquests • Examples of Mathematics Webquests at: • http: //www. mathgoodies. com/Webquests/ • Examples of Technology Webquests at: • http: //zunal. com/webquest. php? w=105056 (technology scavenger hunt webquest)

WEBQUEST LESSON RESOURCE & UNIT PLANNING • Webquest Unit Planning: In your subject groups develop a Unit Lesson Plan with 2 – 3 lessons to carry out your webquest with your students • Use the Unit Lesson Plan template • Use the Webquest Blank template