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Trigonometric Identities Presentation
Jettie Dush
Liberty University Online
Trigonometric Identities Presentation
|Grade Level: High School Algebra 2 /Trigonometry |
|Topic: Trigonometric Identities |
|Standards: |
|CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. |
|CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. |
|CCSS.MATH.PRACTICE.MP4 Model with mathematics. |
|CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. |
|CCSS.MATH.CONTENT.HSF.TF.C.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), |
|or tan(θ) and the quadrant of the angle. |
|CCSS.MATH.CONTENT.HSF.TF.C.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. |
|Objectives: Students will work collaboratively to create a PowerPoint, Prezi, Keynote, or video presentation on a trigonometric identity of their |
|choice. The presentation should include an introduction to the identity, an explanation of how and why the identity works, a sample problem |
|illustrating the identity, and a real-world application in which the identity may be used. Students will then present their identity to the class in|
|a 5-7 minute window. |
| |
|Students will be able to: |
|Present and explain the trigonometric identity tasked to their group. |
|Use the identity to simplify trigonometric expressions. |
|Apply the identity to a real-world scenario. |
|Create a presentation to share with classmates. |
|Explain the identity and its applications to classmates. |
|Answer questions posed by classmates during or at the conclusion of their presentation. |
|Materials: |
|Internet access |
|Access to PowerPoint, Prezi, Keynote, or other presentation platform |
|Projector or Smart Board for presentation |
|Scoring Rubric |
|Procedures: Approximately two weeks before beginning the trig identities unit, the teacher will assign the following task to students in order to |
|provide ample time to prepare and refine their presentations for their classmates. |
|Students will form groups of four and be allowed to choose a trig identity. Groups may not share identities. If needed, groups can be made larger |
|in order to avoid such an overlap. |
|Students will be instructed to use Internet resources and/or print resources to investigate their identity. They may wish to view instructional |
|videos to develop a foundation of understanding from which to build from. |
|Students will be encouraged to use a technology platform that allows them to collaborate outside of class without having to meet in person, such as |
|Hangouts, Skype, Moodle, etc. Students will create the presentation outside of class time, but will be expected to submit the project in intervals in|
|order to assure quality and accuracy before the concluding presentation. |
|Interval 1: Students must submit 1-2 slides or a 1-2 minute video clip presenting an introduction the their identity. |
|Interval 2: Students must submit 1-2 slides or a 1-2 minute video clip presenting an explanation of how and why their identity works. |
|Interval 3: Students must submit 1-2 slides or a 1-2 minute video clip presenting a sample problem illustrating the identity. |
|Interval 4: Students must submit 1-2 slides or a 1-2 minute video clip presenting a real-world application in which the identity may be used. |
|Students will then present their project to their peers and answer any questions they may have. |
|Students will be allowed to anonymously rate one another based on the amount each member contributed. |
| |
|QAIT Model |
|Quality: Evidence of the quality of the learning activity is present in that the lesson has built in multiple “check-points” in order to allow the |
|teacher to monitor progress and check for accuracy / understanding as students prepare a polished product. |
|Appropriateness: This lesson will be appropriate for students in Algebra 2 / Trigonometry as they will have already received instruction on the basic|
|trigonometry functions and how each behaves independently. Students have the ability to determine a pace appropriate for themselves, as the research|
|potion of the activity is the “learning” piece and may be completed at a pace they are comfortable with. |
|Incentive: Students will be actively engaged by means of a collaborative component of the project and intrinsically motivated to create a quality |
|presentation to share with peers. |
|Time: Students will be given two weeks to complete the project before presenting to their peers in class. Students will be required to submit their |
|work in intervals to help ensure that they are indeed presenting quality information to their peers and also to assist in promoting responsible time |
|management plan for students. |
|Diversity / Differentiation for Exceptionalities: |
|Learning Styles: Students with multiple intelligences can learn from this project. Verbal-linguistic learners will benefit from listening to |
|instructional videos as well as writing the information used in the presentation. Mathematical-logical learners will learn from the problem-solving |
|portion of the project and theorizing why/how the identity works. Visual-spatial learners will benefit from watching instructional videos as well as|
|making / viewing the presentations. Bodily-kinesthetic learners will also benefit from creating the presentations, and also actually presenting the |
|project. Interpersonal learners will benefit from the collaborative work. |
|Gifted: These students may elect to view one or two instructional videos and spend more time on investigating and understanding the real-world |
|applications of their trigonometric identity. |
|LEP: Students with limited English proficiency may receive additional clarification from the teacher and explanation of English words as needed. |
|They may also choose to work with students who are fluent in both English and their native language if possible. LEP students will be expected to |
|contribute to the in-class presentation portion. |
|LD, ED, ADD: Students with IEP and 504 Plan accommodations will receive prescribed accommodations. These students will also receive additional |
|coaching from the teacher as needed and, if necessary, may receive a modified rubric. |
|Multicultural Connections: Students may explore how their identity can be used in the real-world and expand their search to incorporate cultures |
|different from their own. |
|Evaluation: |
|A. The teacher will complete the front of the rubric based on presentation. |
|B. Students will anonymously complete the back of the rubric and assess one another based on the collaborative efforts during the completion of the |
|project. |
|Risk Analysis |
|A. The biggest risk in completing this project is the out-of-class nature if which it has been structured. Because students are completing the |
|activity outside of class, the teacher must be adamant about the intermediate submissions of the project and provide timely feedback in order to |
|allow students adequate time to make the necessary adjustments. |
|B. Another risk student absenteeism during the day of their group’s presentation. A possible solution to this is to allow absent students the |
|option of presenting to the teacher and a handful of their peers (for which the student is responsible for securing) during after school hours. |
|C. The final risk in this learning activity is a lack of participation by group members. The category for student assessment on the rubric should |
|help to deter this situation. |
Sample Rubric: Trigonometric Identities Presentation Student Name: _______________________
|CATEGORY |4 |3 |2 |1 |
|Product: |All content throughout the |Most of the content is |The content is generally |Content is typically |
|Content - Accuracy |presentation is accurate. |accurate but there is one |accurate, but one piece of |confusing or contains more |
| |There are no factual errors. |piece of information that |information is clearly flawed|than one factual error. |
| | |might be inaccurate. |or inaccurate. | |
|Product: |Information is organized in a |Most information is organized |Some information is logically|There is no clear plan for |
|Sequencing of Information |clear, logical way. It is easy|in a clear, logical way. One |sequenced. An occasional card|the organization of |
| |to anticipate the type of |card or item of information |or item of information seems |information. |
| |material that might be on the |seems out of place. |out of place. | |
| |next card. | | | |
|Product: |All intervals of the |Three intervals of the |Two intervals of the |One or no intervals of the |
|Interval Submission |presentation were submitted on|presentation were submitted on|presentation were submitted |presentation were submitted |
| |time. |time. |on time. |on time. |
|Presentation: |Student is completely prepared|Student seems pretty prepared |The student is somewhat |Student does not seem at all |
|Preparedness |and has obviously rehearsed. |but might have needed a couple|prepared, but it is clear |prepared to present. |
| | |more rehearsals. |that rehearsal was lacking. | |
|Presentation: |Presentation is 5-7 minutes |Presentation is 4 minutes |Presentation is 3 minutes |Presentation is less than 3 |
|Time-Limit |long. |long. |long. |minutes OR more than 7 |
| | | | |minutes. |
|Presentation: |Listens intently. Does not |Listens intently but has one |Sometimes does not appear to |Sometimes does not appear to |
|Listens to Other Presentations |make distracting noises or |distracting noise or movement.|be listening but is not |be listening and has |
| |movements. | |distracting. |distracting noises or |
| | | | |movements. |
|CATEGORY |4 |3 |2 |1 |
|1. Student Evaluations: |Almost always listens to, |Usually listens to, shares |Often listens to, shares |Rarely listens to, shares |
|Collaboration with Peers |shares with, and supports the |with, and supports the efforts|with, and supports the |with, and supports the |
| |efforts of others in the |of others in the group. Does |efforts of others in the |efforts of others in the |
| |group. Tries to keep people |not cause \"waves\" in the |group but sometimes is not a |group. Often is not a good |
| |working well together. |group. |good team member. |team member. |
|2. Student Evaluations: |Almost always listens to, |Usually listens to, shares |Often listens to, shares |Rarely listens to, shares |
|Collaboration with Peers |shares with, and supports the |with, and supports the efforts|with, and supports the |with, and supports the |
| |efforts of others in the |of others in the group. Does |efforts of others in the |efforts of others in the |
| |group. Tries to keep people |not cause \"waves\" in the |group but sometimes is not a |group. Often is not a good |
| |working well together. |group. |good team member. |team member. |
|3. Student Evaluations: |Almost always listens to, |Usually listens to, shares |Often listens to, shares |Rarely listens to, shares |
|Collaboration with Peers |shares with, and supports the |with, and supports the efforts|with, and supports the |with, and supports the |
| |efforts of others in the |of others in the group. Does |efforts of others in the |efforts of others in the |
| |group. Tries to keep people |not cause \"waves\" in the |group but sometimes is not a |group. Often is not a good |
| |working well together. |group. |good team member. |team member. |
|4. Student Evaluations: |Almost always listens to, |Usually listens to, shares |Often listens to, shares |Rarely listens to, shares |
|Collaboration with Peers |shares with, and supports the |with, and supports the efforts|with, and supports the |with, and supports the |
| |efforts of others in the |of others in the group. Does |efforts of others in the |efforts of others in the |
| |group. Tries to keep people |not cause \"waves\" in the |group but sometimes is not a |group. Often is not a good |
| |working well together. |group. |good team member. |team member. |
References
Common Core State Standards Initiative. (2014). Mathematics Standards. Retrieved January 20, 2015,
from
Slavin, R. E. (2012). Educational psychology: Theory and practice. (10th ed.) New York, NY: Pearson.
Thorsen, C. (2009). TechTactics: Technology for Teachers (3 ed.). Boston: Pearson.
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