Planning Guide
Creating Learner-Focused
Schools
* Madison-Oneida BOCES- This document may not be reproduced in any form without the expressed written consent of the District Superintendent or his designee.
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LU Title: Pi Plate Trig |
Author(s): Donna Briedis |
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Grade Level: 11 |
School Address: Heuvelton Central School |
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Subject Area: Course III Mathematics |
School Phone/Fax: 315-344-2414 |
CONTENT KNOWLEDGE
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Declarative |
Procedural |
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ESSENTIAL QUESTIONS
INITIATING ACTIVITY
Know, Want to know, Learned
Do KWL for special triangles (30-60-90)(45-45-90) and compare sides to larger similar triangles.
Connection to State Learning Standards
Content Area: Mathematics
Level: Course III
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Benchmarks: Writing |
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Benchmarks: Use trig functions to model real world relationships. |
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Standard: Demonstrate how to perform an intricate task such as how to find areas of the room using polar coordinates. |
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Standard:Modeling/Multiple Representation |
Unit Theme:
PI PLATE TRIGONOMETRY
This unit has been developed to make learning trig.functions fun and easy. Students will love all of the activities and the simple mnenomic methods for memorization of common Trig. Functions.
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Standard: Patterns/Functions |
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Standard: Measurement |
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Benchmarks: Develop methods to solve trig equations and verify trig functions. |
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Benchmarks:Relate trig relationships to the area of a triangle and to the general solutions to triangles. Define trig functions in terms of a unit circle. Derive and apply formulas relation angle measure and arc degree measure in a circle. |
Learning Experiences
Declarative Knowledge
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What declarative knowledge should e in the process of acquiring & integrating? As a result of the unit, the student will know or understand… |
What experiences or activities will be used to help students acquire & integrate this knowledge? |
What strategies will be used to help students construct meaning, organize and/or store the knowledge? |
Describe what will be done. |
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Basic trig function.
The difference between radians and degrees.
How to display trig graphs on the TI-82 graphing calculator. |
Teacher will demonstrate the basic trig functions by using special triangles, modeling pi plate design, using flash cards, mini quizzes and jeopardy games.
Teacher will demonstrate the special triangles, modeling pi plate design, using flash cards, mini quizzes and jeopardy games.
Teacher will teach polar coordinates on the TI-82 graphing calculator to help students find coordinates of various points. |
Designing a pi plate. Flashcards.
Flash quizzes
TI Calculator Instruction |
(see learning experience "Pi Plate Trigonometry") Students will create flashcards for the common trig functions and common radian measures and play flash card games. (sin 30=?radians=?degrees Cos45=?radians=?degrees SinÀ/6=?radians=?degrees) Students will have quick knowledge checks where the students can use their pi plates, then quick quizzes where if they do not use their pi plates they will receive extra credit. Students will use the TI-82 Calculator in Polar mode (r=1) Trace around the circle and compare x and y values to cos and sin values. |
Learning Experiences
Procedural Knowledge
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What procedural knowledge will students be in the process of acquiring & integrating? As a result of this unit, students will be able to: |
What will be done to help students construct models, shape & internalize the knowledge? |
Describe what will be done. |
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Use a paper plate to demonstrate the primary trig functions.
Display trig functions in multiple representations. Represent polar coordinates on a TI-82 graphing calculator. Find polar coordinates of various angles on the TI-82 graphing calculator.
Describe by using polar coordinates where particular objects are in the room. How to solve trig equations
Apply formulas relating angle measure with length of arc. |
Teacher will direct students in creating a pi plate and the opportunity to practice recreating the pi plate. Teacher will us the pi plate as a graphic organizer, one in which the students help to design, thus giving them ownership of the model The teacher will use the pi plate, TI-82 calculator and the rectangular coordinate system to display trig functions in multiple representations
Teacher will help students focus on critical steps and difficult aspects of the process.
Teacher will help students turn the classroom into a polar coordinate graph with the center of the room as the origin. Teacher will lead students in discussion on how to solve a variety of trig equations both linear and quadratic. Assignments in the book will be given. Pi plates may be used in checking solutions. Also TI-82 graphing calculators may be used in checking solutions.
Teacher will help students memorize trig functions by using mnemonics. |
See Learning Experience Pi Plate Trigonometry
Assignments will be given to promote use of the TI-82 calculator in order to answer specific questions. Demonstrations of polar graphing will be done on the TI-82 graphing calculator overhead projector projected onto a dry erase board. This dry erase board provides a medium that both teacher and student can utilize in order to draw specified angles and point. Students will describe locations of objects, such as the pencil sharpener, door into the room, book shelf…by polar coordinates. Students will participate in the carousel brainstorming problems that will challenge groups.
Students will learn the mnemonics: So/h Ca/h To/a Another Stupid Trig Class Students will play Jeopardy with categories of Functions, Angles, Radians, Polar Coordinates |
Learning Experiences
Extending and Refining
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What knowledge will students be extending and refining? Specifically, they will be extending and refining their understanding of… |
What reasoning process will they be using? |
Describe what will be done. |
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Students will discover trig functions through special triangles.
Students will use unit circles to find the differences between radians and degrees.
Students will learn trig functions for basic angles and calculator key strokes in order to find the trip values on a polar coordinate graph.
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Deductive Reasoning
[ ]Deductive Reasoning
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Pi plates design assignment: (See learning experience "Pi Plate Trig") Through the design of the pi plate students will deduce basic trig function values as related to special triangles.
Radian measure assignment: With their pi plates and string students will deduce the differences between radians and degrees. They will have to cut string the length of one radius and then measure the distance around the circle using the radius length string.
Calculator assignment: Students will compare their pi plate to the polar coordinates on their calculator. They will record similarities and differences between the unit circle on their pi plate and the unit circle on their calculator. They will also record similarities and differences between a non unit circle on their calculators and the unit circle on their pi plate. |
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Planning Guide MUT |
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Unit: Pi plate trig |
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Step 1 |
Step 2 |
Step 3 |
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What knowledge will students be using meaningfully? Specifically, they will be demonstrating their understanding of and ability to........... |
What reasoning process will they be using? |
Describe student's products and performances and the criteria for evaluation. |
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Students will be given the opportunity to choose their meaningful use task. (Decision Making) The choices are: 1. Create a children's book tailored to the course III students that describes in a fun and easy manner what trig functions are and how they are used. (Invention, Problem Solving) 2. Create a treasure map using polar coordinates and the classroom as the treasure island. Follow MUT instructions for you write up. (Invention, Problem Solving) 3. Create a graph of the sin coordinates and the cos coordinates from your pi plate onto a cartesian coordinate system. Use spaghetti or string to make the graph tactile. Follow MUT instructions for your write up. Make sure you interpolate and extrapolate. (Teacher should model interpolating and extrapolating) (Invention, Decision Making) |
[x] Decision Making |
Products/Performances: Students will hand in finished products, free of spelling and grammatical error. Each project must be explained using the MUT outline below and scored by the MUT rubric also outlined below. Students will hand in either a story book, treasure map and report, or sin and cos curve and report. Each MUT will be evaluated according to the MUT rubric. |
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Criteria for evaluation |
Meaningful Use Task Reporting Design:
INVESTIGATION QUESTION:
What are you investigating? Be specific. Anyone reading this report should be able to understand what you are trying to accomplish.
HYPOTHESIS:
What is your guess as to how you would answer your investigation questions.
METHOD:
Detailed description of how you solved your problem.
DATA:
Organize all data into tables, graphs, charts, scatter plots, anything to help the reader understand what you did to solve the problem.
DATA ANALYSIS:
This is where you get to interpret the different pieces of information that you have. You may add any additional comparisons that you feel are important or interesting. Extrapolate in this section.
CONCLUSIONS:
Summarize your findings, state any unique observations, applications to the real world, or a general rule about the solution.
RUBRIC FOR SCORING MUT
1. The task is clearly and thoroughly explained so that a reader who has E VG G M P NC never seen this task before would fully what it is you have to do. 10 9 8 7 4 0
2. All pertinent diagrams, charts, graphs, tables, etc., are done neatly, E VG G M P NC are well labeled and are strategically placed into the report itself. Appropriate 10 9 8 7 4 0 tools such as computers and/or straightedges and compasses are used to give these parts a professional appearance.
3. All formulas used are identified and critical points E VG G M P NC labeled. 10 9 8 7 4 0
4. All significant steps in the solution are shown and explained using appropriate E VG G M P NC math language to show the student's depth of understanding of the mathematics 10 9 8 7 4 0 involved in the task.
5. The solutions for all calculations are E VG G M P NC correct. 10 9 8 7 4 0
6. The report contains a summary which reflects the significance of the E VG G M P NC findings in the project. 10 9 8 7 4 0
7. The student's work includes such things as unique observations, applications E VG G M P NC to the real world, or a general rule about the solution. 10 9 8 7 4 0
8. The work is "ready to publish" by being free of errors in English or typing, E VG G M P NC cross outs, or other flaws that give the work less than a professional appearance. 10 9 8 7 4 0
Total Score:
Have You Considered These Yet?
Learn to Learn Skills:
Assessment Modifications:
Unit Schedule/Time Plan:
Written Overview: