Mathematics Patterns Relations and Functions Analysis

Analysis In the Area of: Patterns, Relations, & Functions
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	Apply logarithms	Compare Interest, Radioactive decay; initial discussion followed by student projects.	- Coordinate various interest rates and half-lives to random amounts. - This will generate needed data for students to compile and compare.	Compile class charts reflecting differences in interest and decay.	Class divided into two groups-group I researches interest rates, group 2 researches radioactive half-lives.	Pre-calculus,International Fair, p. 30-31.
Analysis In the Area of: Patterns, Relations, & Functions
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	Model real world phenomena with a variety of functions.	- Discuss applications of functions in real world, assign the story project. - Give outline of all families of functions. Go over transformations and how they affect a, "parent graph," - Sketch & interpret graphs arising from situations presented verbally and pictorially.	- Link the concept of function with its role in everyday life - In assigned groups each group presents to class a 'family" of functions. - Sketch and identify functions representing real situations.	-Solve set of problems by identifying and sketching functional relations.	- Create an illustrated story based on one or more function relations. - Do an experiment, record data, and determine which kind of function best models the data. - Create original situations which they can sketch and model.	- Activity book. - Language of Functions & Graphs, Shell Centre of Math Education.
Analysis In the Area of: Patterns, Relations, & Functions
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	Graph function, patterns, & relations using polar coordinates.	- Explain use of polar graph paper. - Explain graphing calculator capabilities for polar graphing. - Combine concepts of polar coordinates and the graphing calculator.	Trace polar coordinates and graph polar equations.			Graphing calculator.
Analysis In the Area of: Patterns, Relations, & Functions
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	Develop 3-D graphs.	- Explain,"Transformations," and how values affect graphs.	Work a set of problems in groups with open ended questions that allow students to judge effects based on reasoning, justification and communication skills.	Students correct problem sets based on the overall skills used in determining the solutions.		Progressive Pre-calculus Problems.
Analysis In the Area of: Patterns, Relations, & Functions
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	Analyze the effects of parameter changes on graphs of functions.	- Help students see relationships between functions and their graphs.		Present a graph. Have students, "play around," with parameter values until they get a good rule which creates the graph.	- Create an original problem for others to solve.
Analysis In the Area of: Patterns, Relations, & Functions
6	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Extend recursive functions using computers in real world situations.
Analysis In the Area of: Patterns, Relations, & Functions
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	Demonstrate an understanding of the connection between trigonometric and circular functions.	Unit circle mini project- Assign unit circle sheet to students individually.	Recognize the patterns found in circular functions. Be able to use unit circle as reference.	Completed models can be used by students in several future quizzes and assessments.	In graphs, complete from the given, several unit circle models. Difficulty increases with each.	Algebra II Activities, Instructional Fair, pp. 76-81.
Analysis In the Area of: Patterns, Relations, & Functions
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	Apply general graphing techniques to trigonometric functions.	- Issue caution on use of razor and demonstrate one example of razor cut on candles. - Connect transformational graphing to trigonometric function.	- Recognize period and amplitude based on curve changes with different information by performing the candle/ paper cutting. - Do CBL Experiments to fit curves to data. - Tic Toc with pendulum.Stay Tuned with tuning fork.	- Create a table summarizing differences of different width candles and slants. - Student work.	- Cut a length of paper and wrap around a candle. Using a razor and cut candle. Unwrap paper to produce additional trig functions. - Practice such transformations.	- Functions, Statistics, Trigonometry - Scott Foresman, p. 388. - Real World CBL Experiments.
Analysis In the Area of: Patterns, Relations, & Functions
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	Solve, use, apply trigonometric equations and verify trigonometric identities.	Track field trip- take students to track. Explain staggered end points and then run some sample races.	Collect data on the track measurements and other factors in order to design a track with specific instructions.	Diagrams of tracks will be presented and displayed.	Further illustrate other connections between trigonometry and sports.	Functions, Statistics, Trigonometry - Scott Foresman, p. 329.
Analysis In the Area of: Patterns, Relations, & Functions
10	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Describe, analyze the connections between trigonometric functions and polar coordinates, complex numbers, and series.
Analysis In the Area of: Patterns, Relations, & Functions
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	Develop, demonstrate the complex number system and its operation.	- Enter the Lottery- Briefly explain how lotteries are run a probability. - Use basic fractals to visually illustrate the complex number system.	- Expand knowledge of probability and complex numbers. Connect lottery advertising to actual probabilities. - Use their graphing calculator and explore various points on a given function to understand complex numbers (i.e. the mandelbrot or logistic).	- Compile a chart of lottery games and their probabilities. - Group work submitted.	- Gather rules and information concerning a lottery game and compute probabilities for first prize and other special prizes. - Explore other fractals and how they are related to complex numbers.	Functions, Statistics, Trigonometry - Scott Foresman,p. 515.
Analysis In the Area of: Patterns, Relations, & Functions
12	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Solve problems using difference equations.