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Advanced Algebra – Algebra

VIEWS: 123 PAGES: 12

									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


								
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