Sean's+Trig+Lesson


 * Link to Sean's Main Page **
 * Lesson On Sine/Cosine waves **
 * Author: Nathan Pike and Sean Murphy **


 * Based on lesson by: **

2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content. 4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.
 * Date created: 10/16/2012 3:39 PM EST ; Date modified: 12/12/2012 9:05 AM EST **
 * ** GENERAL INFORMATION ** ||
 * ** Subject(s) ** || Mathematics ||
 * ** Course Name ** || Algebra2/Trig ||
 * ** Grade/Level ** || Grade 11 ||
 * ** Unit Name ** || Trig Functions ||
 * ** Number of Students ** || 21 ||
 * ** Summary ** || The students will be exploring the effects of changing variables in trigonometric functions through the use of multiple means of writing. ||
 * ** Lesson Goal(s) ** || Students generate their own knowledge by exploring the sine function and how it can be altered. ||
 * ** LESSON IMPLEMENTATION AND NY STATE STANDARDS ** ||
 * ** Objective(s) ** || By completing the worksheet, using multiple forms of writing, the students will understand what A,B,C, and D stand for in the equation y=Asin(B(x-C))+D through inductive inquiry. ||
 * ** NY Math Learning Standards ** || ** Display: **
 * NY- New York State Common Core Standards (2011) **
 * Subject: ** English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects
 * Grade Range for ELA CCR Anchor Standard: ** 6–12
 * Strand: ** Writing
 * Area: ** Text Types and Purposes
 * CCR Anchor Standard: **
 * Area: ** Production and Distribution of Writing
 * CCR Anchor Standard: **
 * CCR Anchor Standard: **

5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
 * Subject: ** Mathematics
 * Grade: ** High School
 * Content Area: ** Functions
 * Domain: ** Trigonometric Functions F-TF
 * Area: ** Model periodic phenomena with trigonometric functions
 * Standard: **

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions. Predict the next triangular number by examining the pattern 1, 3, 6, 10, X. Use inductive reasoning to construct, evaluate, and validate conjectures and arguments, recognizing that patterns and relationships can assist in explaining and extending mathematical phenomena. || > Worksheet, calculators. > http://www.youtube.com/watch?v=lTdq5P-kp4o > This video would be used after the lesson to aide with homework problems. > > http://illuminations.nctm.org/ActivityDetail.aspx?ID=174 > This site provides an interactive sine curve for students to explore. > > http://www.mathwarehouse.com/trigonometry/graphing-sine-function/how-to-graph-sine-from-unit-circle.php > This site would allow students to make the connection between sine waves and the unit circle.
 * NY- New York State Standards **
 * Subject: ** Mathematics, Science, and Technology (1996, 2005 Math update)
 * Learning Standard 1 : ** Analysis, Inquiry, and Design
 * Level: ** Intermediate
 * Key Idea: ** Mathematical Analysis 2: Deductive and inductive reasoning are used to reach mathematical conclusions.
 * Performance Indicator: **
 * ** Learning Context ** || Before this lesson we talked about the graphing of the basic sine and cosine functions. We also previously talked about the definitions of amplitude, frequency, and period. After this lesson we will be going into the unit circle and how it relates to the sine/cosine curve. ||
 * ** Detailed Procedure ** || After the bell rings and the students get situated have a student draw the graph of the sine function on the board; sin(x)=y. Another student will draw cos(x)=y on either the same or a different graph. From here as a class we will review the basic properties of these functions, that being amplitude, period, and frequency. We will use the overhead to set equal parameters for evey student's calculators. A worksheet will be given to the students for them to complete in groups. This worksheet will focus on two main writing strategies to enhance literacy. The students will use drawing and illustrating to construct a visual representation of manipulated sine curves. Secondly, the students will use a written conversation method to answer the worksheet questions in their own words. While the students are completing the hand out I will be walking around the room clearing up any questions that the students have. Once the students have completed the worksheet we will regroup and discuss the worksheet. Students will share their discoveries with the rest of the class. Any further questions will be answered after reviewing the worksheet. ||
 * ** Closure ** || We will review the worksheet and answer any questions that are presented. Class will end with a thought provoking question (possibly tangent waves). ||
 * ** Extension ** || What about tangent waves? ||
 * ** Differentiated Instruction ** || The groups will be coordinated to fit the nees of each student in the class. As I am walking around during the group explorations, this will allow me to aide students in any questions/problems they may pose. ||
 * ** Collaboration ** || Students will work collaboratively. Students will work in groups of 3. ||
 * ** Time Allotment ** || 1 class periods. 40 Mins. per class. ||
 * ** Post-Implementation Reflections ** ||  ||
 * ** MATERIALS AND RESOURCES ** ||
 * ** Instructional Materials (handouts, etc.) ** || Worksheets, overhead, graphing calculators, graph paper, chalk board, document cam. ||
 * ** Resources ** || * Materials and resources:
 * Technology resources:
 * The number of computers required is 1. ||
 * ** ASSESSMENT ** ||
 * ** Assessment/Rubrics ** || The worksheet will be used to create homework questions such as "Graph the following trig equation..." We can also collect this worksheet to gage each students level of understanding. Formative assessment will be conducted by us walking around during group exploration. ||