Mathematics Patterns Relations and Functions Advanced Algebra

Advanced Algebra In the Area of: Patterns, Relations, & Functions
1	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Explain the historical foundations of mathematics.	Show how math work focused on the problem of the times.	View video, Music of the Spheres on history of math.			Video: Music of the Spheres.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
2	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop, use matrices operations to solve linear equations.	Instruct in capabilities of graphing calculator in matrix options (including use of inverse, determinant).	Do systems of equations activity using graphing calculator.			Use graphing calculator to solve matrices allows presentation of more realistic problems.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
3	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Represent real situations using linear and nonlinear functions, matrices.	Introduce idea of "step" functions (postage, parking garage, movie prices, etc.)	-Experiment with various relationships to see what kinds of fens occur (e.g. height vs. arm span, circumference of head vs. arm length, etc.). Collect data and chart. -Many of previously named.			Sketching Graphs worksheet.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
4	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop real world situations with a variety of functions.	-Emphasize use of graphing or scientific calculator because most real world problems are "not neat and tidy." -Sketch and interpret graphs arising from situation, presented verbally and pictorially.	-Cooperative group work on creating graphs from various scenarios. -Many of the previously named activities, esp. exponential functions.	-Be able to find domain range values when given definition of fen. -Solve set of problems by identifying and sketching functional relation.	Create, "scenario," given a graph.	-Analysis Level Z. -Language of Functions by Shell Centre of Math Education.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
5	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Analyze functions using graphing calculator and computer.	Use graphs to determine visually idea of domain and range.	Many of the previously named experiments and worksheets.	Give function to input in calculator; ID domain, range, kind of function.	Write domain and range from rule only.
Advanced Algebra 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
	Develop geometric and arithmetic sequences and series through real world situations.	Use money/savings situations that apply to students.	Apply geometric and arithmetic sequences and series to money/saving situations.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
7	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Analyze circular functions to model real world functions.	Use idea of Ferris wheel to model circular function.	Battleship Game in polar coordinates or complex coordinates helps learn notation.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
8	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Use real world situations to explain sine and cosine functions.	- Use high tide/low tide. Temperature charts/month. - Real world applications of sine and cosine function.	-Use graphs to create sine/cosine equations. -Radio wave functions look like sine/cosine. -Pattern of eye motion during sleep=sine.	Interpret data from charts to create graph or vice versa.	Geometry project DGT, p. 219. - Biorhythm charts. - AM/FM charts (formulas for graphs more difficult due to decimals). - Identify real world examples of sine and cosine functions.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
9	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Verify trigonometric identities & equations both graphically and analytically.	Instruct in use of graphing calculator to show that both sides of triangle identify graph to same curve.	Prove identities algebraically and verify result graphically.
Advanced Algebra 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
	Use connections between trigonometric functions and: polar coordinates, exponential functions, logarithmic functions, complex numbers.
Advanced Algebra In the Area of: Patterns, Relations, & Functions
11	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Represent problems using difference equations.
Advanced Algebra 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
	Define limit by examining infinite sequences, series, and areas under curves.	Teach idea of limits - algebraically (rule) graphically (heading toward same value?) test series of numbers -Investigate limits.	Sierpinski and triangle exercise.	Sierpinski Carpet.	Research life and work of Waclaw Sierpinski.	Advanced Algebra Through Data Exploration, pp. 86-88.