VIEWS: 123 PAGES: 12 POSTED ON: 1/23/2010
Berrien County ISD Collaborative Curriculum Advanced Algebra – Algebra Overview Big Ideas: Skill Mastery: Topics Click on a bullet below to link to the curriculum details for that topic. ALG 1.1 Problem Solving with Circular Functions ALG 1.2 Sequences and series ALG 1.3 Analyzing graphs ALG 1.4 Making Predictions ALG 1.5 Normal Distribution ALG 1.7 Circular Functions ALG 1.10 Solve Problems using a variety of techniques ALG 1.11 Coordinate plane representations of real and complex numbers. ALG 1.12 Set relationships ALG 1.13 Determine the properties of a number system or operation Advanced Algebra Algebra DRAFT for field review 5/2005 Page 1 Berrien County ISD Collaborative Curriculum Strand: Algebra Topic: ALG 1.1 Problem solving with circular functions MCF Benchmarks Related: MI I HS.2.6 Increase their use of functions and mathematical models to solve problems in context. Michigan GLCEs Addressed: PS Vocabulary/Symbolic Representation Sine Cosine Tangent Amplitude Period Phase Shif Knowledge and Skills 1. Solve Trigonometric equations for desired information Prior Knowledge Developed: Graphing of trig functions Prior Knowledge Secured: Context The vertical motion of a water particle on a 10 in. wave occurs every 4 sec. Write an equation that models the height of the water particle as it moves from crest to crest. Resources Algebra 2, McDougal Littell Instructional Strategies Given information about wave motion, determine a graph of the situation. Given information about the swing of a pendulum, determine the associated graph as well as its amplitude and period Graph standard forms of trigonometric equations (i.e. y=a sin bx, y=a cos bx, etc) Identify amplitude and period of each trigonometric equation. Show the characteristics of graphing a tangent function. Demonstrate how to draw. Using a graphing calculator, demonstrate the graphing of each function. Assessment Advanced Algebra Algebra DRAFT for field review 5/2005 Page 2 Berrien County ISD Collaborative Curriculum Strand: Strands, patterns, relationships, and functions. Topic: ALG 1.2 Sequences and series MCF Benchmarks Related: MI I HS.1.1 Analyze and generalize mathematical patterns including sequences, series, and recursive patterns. MI I HS 1.4 Explore patterns (graphic, numeric, etc.) characteristic of families of functions; explore structural patterns within systems of objects, operations or relations. Michigan GLCEs Addressed: PA Vocabulary/Symbolic Representation Sequence Series Recursive Explicit an d r Arithmetic mean Geometric mean Limit Knowledge and Skills 1. Find the nth term of a sequence 2. Find the first term of a sequence 3. Find the sum of a finite series 4. Find the sum of certain infinite series Prior Knowledge Developed: Prior Knowledge Secured: Context Fibonacci sequences are often found in nature. Looking at flowers, determine which term of a Fibonacci sequence is illustrated. Resources Advanced Algebra Algebra DRAFT for field review 5/2005 Page 3 Berrien County ISD Collaborative Curriculum Strand: Patterns, Relationships, and Functions Topic: ALG 1.3 Analyzing graphs MCF Benchmarks Related: MI I HS.1.2 Analyze, interpret and translate among representations of patterns including tables, charts, graphs, matrices and vectors. MI I HS.2.2 Develop a mathematical concept of function and recognize that functions display characteristic patterns of change (e.g., linear, quadratic, exponential. Michigan GLCEs Addressed: PA Vocabulary/Symbolic Representation Quadratic Linear Absolute Value Cubic Root Reciprocal Knowledge and Skills 1. 2. Given a graph, analyze which family of functions it belongs to. Sketch a graph by knowing the family it belongs to. Prior Knowledge Developed: Prior Knowledge Secured: Graphing functions Context Given a scatterplot for a particular situation, find the curve of best fit for the plot. Resources Advanced Algebra Algebra DRAFT for field review 5/2005 Page 4 Berrien County ISD Collaborative Curriculum Strand: Patterns, Relationships, and Functions Topic: ALG 1.3 Analyzing graphs MCF Benchmarks Related: MI I HS.1.2 Analyze, interpret and translate among representations of patterns including tables, charts, graphs, matrices and vectors. MI I HS.2.2 Develop a mathematical concept of function and recognize that functions display characteristic patterns of change (e.g., linear, quadratic, exponential. Michigan GLCEs Addressed: PA Vocabulary/Symbolic Representation Quadratic Linear Absolute Value Cubic Root Reciprocal Knowledge and Skills 1. 2. Given a graph, analyze which family of functions it belongs to. Sketch a graph by knowing the family it belongs to. Prior Knowledge Developed: Prior Knowledge Secured: Graphing functions Context Given a scatterplot for a particular situation, find the curve of best fit for the plot. Resources Advanced Algebra Algebra DRAFT for field review 5/2005 Page 5 Berrien County ISD Collaborative Curriculum Strand: Patterns, Relationships, and Functions Topic: ALG 1.4 Making Predictions MCF Benchmarks Related: MI I HS 1.5 Use patterns and reasoning to solve problems and explore new content. MI I HS 1.3 Study and employ mathematical models of patterns to make inferences, predictions and decisions. MI III HS 1.1Collect and explore data through observation, measurement, surveys, sampling techniques and simulations. Michigan GLCEs Addressed: PA Vocabulary/Symbolic Representation Line of best fit Trend Scatter plot Knowledge and Skills 1. Produce a scatterplot from data that is given or collected, determine the line of best fit, and make predictions based upon the outcome. Prior Knowledge Developed: Determine the line of best fit Prior Knowledge Secured: Make a scatterplot Context Based upon current statistics, make a prediction about the future Resources Advanced Algebra Algebra DRAFT for field review 5/2005 Page 6 Berrien County ISD Collaborative Curriculum Strand: Patterns, Relationships, and functions Topic: ALG 1.5 Normal Distribution MCF Benchmarks Related: MI I HS.2.1 Develop a mathematical concept of function and recognize that functions display characteristic patterns of change (e.g., linear, quadratic exponential.) MI III HS.2.2 Describe the shape of a data distribution and determine measures of central tendency, variability and correlation. Michigan GLCEs Addressed: RE Vocabulary/Symbolic Representation Normal distribution Mean Median Mode Variation Trend Standard Deviation Distribution Knowledge and Skills 1. 2. For a set of data, determine mean, median, mode, and standard deviation. Determine if data conforms to a normal distribution. Prior Knowledge Developed: Prior Knowledge Secured: Construct a graph Context Given a set of test grades, determine how many students should get A’s, B’s, C’s, D’s, and F’s, based upon a normal distribution. Resources Advanced Algebra Algebra DRAFT for field review 5/2005 Page 7 Berrien County ISD Collaborative Curriculum Strand: Algebra Topic: ALG 1.7 Circular functions MCF Benchmarks Related: MI I HS.2.5 Use concepts of position, direction and orientation to describe the physical world and to solve problems. Michigan GLCEs Addressed: PA, UN Vocabulary/Symbolic Representation Radian Degree Sine Cosine Tangent Cosecant Secant Cotangent Arc Length Amplitude Period Phase Shift Knowledge and Skills 1.Graph any of the circular functions 2.Given f(x)=ACos(Bx+C)+D, determine how the constants A, B, C, and D affect the graph. Prior Knowledge Developed: Graphs of Trig. Functions Prior Knowledge Secured: Graphs of functions Context Given the graphs of yellow, red, and blue light waves, determine their equations. Resources Advanced Algebra Algebra DRAFT for field review 5/2005 Page 8 Berrien County ISD Collaborative Curriculum Strand: Algebra Topic: ALG 1.10 Solve problems using a variety of techniques. MCF Benchmarks Related: MI V HS 1.2 Compute with real numbers, complex numbers, algebraic expressions, matrices and vectors using technology and, for simple instances, with paper and pencil algorithms. MI V HS 2.3 Describe the properties of operations with numbers, algebraic expressions, vectors and matrices and make generalizations about t he properties of given mathematical systems. Michigan GLCEs Addressed: PS Vocabulary/Symbolic Representation Real numbers Complex numbers Matrix Graphing utility Elimination Substitution Augmented matrix Row-reduced echelon form Knowledge and Skills 1. Solve a system of three equations with three unknowns by elimination or substitution and using matrices. Finish by solving the system with a graphing utility Prior Knowledge Developed: Matrix arithmetic Prior Knowledge Secured: Solve equations Context Solve a system on n equations with n unknowns in a variety of ways Resources Instructional Strategies Use Cramer’s Rule to solve a system of m equations and m unknowns. Advanced Algebra Algebra DRAFT for field review 5/2005 Page 9 Berrien County ISD Collaborative Curriculum Strand: Algebra Topic: Alg 1.11 Coordinate plane representations of real and complex numbers. MCF Benchmarks Related: MI V HS 1.1 Present and explain geometric and symbolic models for operations with real and complex numbers, and algebraic expressions. Michigan GLCEs Addressed: RP Vocabulary/Symbolic Representation Real number Complex number Vector Scalar multiplication Magnitude Resultant Knowledge and Skills 1. Represent a real or complex number on the Cartesian plane. 2. Draw a vector diagram showing the sum of two vectors. 3. Show scalar multiplication of a vector in a plane. Prior Knowledge Developed: Vector space Prior Knowledge Secured: The Cartesian plane Context Given a plane flying at a certain heading with a specified wind direction, draw a vector diagram showing the plane’s ground speed and actual heading Resources Instructional Strategies Given a complex number in the form a+bi, graph it in the coordinate plane. Add a second vector to the first and demonstrate the commutative property for vector addition through use of the parallelogram law. Assessment Advanced Algebra Algebra DRAFT for field review 5/2005 Page 10 Berrien County ISD Collaborative Curriculum Strand: Algebra Topic: Alg 1.12 Set relationships MCF Benchmarks Related: MI VI HS 2.2 Use sets and set relationships to represent algebraic and geometric concepts. Michigan GLCEs Addressed:RP Vocabulary/Symbolic Representation Union Intersection Venn Diagram Universe Knowledge and Skills 1. 2. 3. Find the intersection of sets. Find the union of sets. Draw and label a Venn diagram to fit a situation. Prior Knowledge Developed: The concept of sets Prior Knowledge Secured: Integers, real numbers, etc. Context Draw the Venn diagrams showing the relationships among the various quadrilaterals. Resources Instruction Draw a Venn diagram showing the relationships among the various quadrilaterals Assessment Advanced Algebra Algebra DRAFT for field review 5/2005 Page 11 Berrien County ISD Collaborative Curriculum Strand: Algebra Topic: Alg 1.13 Determine the properties of a number system or operation. MCF Benchmarks Related: MI V HS 1.3 Describe the properties of operations with numbers, algebraic expressions, vectors and matrices and make generalizations about the properties of given mathematical systems. Michigan GLCEs Addressed:MR Vocabulary/Symbolic Representation Commutative Associative Mult. Inverse Add. Inverse Add. Identity Mult. Identity Distributive property Knowledge and Skills 1. Determine if a number set with an operation is a group. 2. Determine if a number set with a given operation is a field . Prior Knowledge Developed: Prior Knowledge Secured: Context Determine whether or not a number system under a described operation forms a group or a field Resources Instruction Given a set of numbers, finite or infinite, and one or two operations, determine if the set with operations(s) is a group or a field. Advanced Algebra Algebra DRAFT for field review 5/2005 Page 12