Advanced Algebra II

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Advanced Algebra II Planned Instruction
Title of Planned Instruction: Advanced Algebra II
Subject Area: Mathematics Grade Level: Grades 9-12
Prerequisites: Algebra I with a grade of A or B Course Description: This course builds on the concepts and skills learned in Algebra I. It provides students with daily opportunities to develop, experience, and apply more advanced algebraic concepts and skills in order to become confident problem solvers in their world. Advanced Algebra II is a more abstract and symbolic approach to the content of Algebra II and covers concepts at a faster pace. Required Time: 180 days Major Text(s) and Resources:
	Merrill Algebra 2 with Trigonometry: Applications and Connections, Copyright 1992 by Glencoe Macmillan/McGraw-Hill
Names of District Subject Area Curriculum Writing Committee:
	Sonya D. Curry - Indian Valley High School Mary O. Mulkey - Lewistown High School Allen C. Muir - Lewistown High School
Date of Board Approval: July 24, 2003

Major Topics
Linear and non-linear equations Matrices Graphing Quadratics Powers	Probability Systems Applications Conics Series, sequence
*Course Objectives and Performance Indicators*

Strand: 2.1 Standard: Numbers, Number Systems and Relationships Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.1.11A	Use operations.	Use properties of real numbers to simplify expressions. Use properties of powers to simplify powers. Find the greatest monomial factor of an algebraic expression. Multiply and divide monomials. Add, subtract, and multiply polynomials. Divide polynomials using synthetic division and long division. Factor polynomials. Find roots of equations. Multiply and divide radicals. Add, subtract, multiply, and divide radical expressions. Add, subtract, multiply, and divide complex numbers. Multiply pure imaginary numbers.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
	Use operations (continued).	Calculate determinants. Find composition of functions. Find inverses of functions. Find the sum and product of the roots of a quadratic. Simplify rational expressions and complex numbers. Add, subtract, multiply and divide rational expressions.

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Strand: 2.2 Standard: Computation and Estimation Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.2.11A	Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations.	Perform calculations that require multiple procedures and operations involving real numbers.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11B	Use estimation to solve problems for which an exact answer is not needed.	Perform multi-step estimates involving real numbers. Estimate the answer to problems that contain radicals.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11C	Construct and apply mathematical models, including lines and curves of best fit, to estimate values of related quantities.	Identify the graphical representation that best approximates a line of best fit for a given scatter-plot. Extrapolate an answer from a given scatter-plot. Interpolate an answer from a given scatter-plot. Find maximum or minimum values for a given situation using linear programming techniques.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11D	Describe and explain the amount of error that may exist in a computation using estimates.	Use a prediction equation derived from a scatter plot to predict a result and then compare it to the actual data. Use technology (graphing calculator) to find the correlation coefficient of the regression line and explain what the number means.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11E	Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measure.	Compare and contrast the solution(s) of an equation solved by graphing (hand and graphing calculator) the related function and solved using other techniques.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11F	Demonstrate skills for using scientific and graphing calculators.	Use scientific and graphing calculators to answer questions.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.3 Standard: Measurement and Estimation Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.3.11A	Select and use appropriate units to measure to the degree of accuracy required in particular situations.	Determine reasonable estimates for multi-step problems that involve conversion of units of measure.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.4 Standard: Mathematical Reasoning and Connections Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.4.11A	Use proof by contradiction to validate conjectures.	Make conjectures about graphical transformations and use a graphing calculator to validate or contradict (e.g., given parent graph f(x) = \|x\|, guess how graph would change for 3f(x), f(3x), f(x+3), and f(x)+3).	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.4.11B	Construct valid arguments from stated facts.	Derive the quadratic formula using completing the square technique.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.4.11E	Demonstrate mathematical solutions to problems.	Use algebraic techniques to solve problem situations involving formulas used in science (e.g., volume, distance), business, and other areas of student interest.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.5 Standard: Mathematical Problem Solving and Communication Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.5.11A	Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems.	Select, use, and display all of the mathematical procedures that are necessary to the solution of a problem situation and achieve the correct answer.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.5.11B	Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results.	Communicate all of the mathematical procedures, concepts, conclusions, etc. necessary to the solution of a problem situation using correct and appropriate mathematical representations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.5.11C	Present mathematical procedures clearly, systematically, succinctly and correctly.	Present all of the procedures important to the solution of a problem in ways that are understandable.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.511D	Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid.	Explain how a problem was solved and why the chosen procedures were used.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.6 Standard: Statistics and Data Analysis Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.6.11C	Determine the regression equation of best fit.	Find lines of regression on a graphing calculator or graph paper by drawing a scatter plot.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.6.11D	Make predictions using interpolation, extrapolation, regression and estimation using technology to verify them.	Estimate solutions to problem situations. Use a regression line from a scatter plot to make predictions. Given a set of data, interpolate or extrapolate a value, and use a graphing calculator to verify your prediction by finding a regression line or tracing a related function.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.6.11I	Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.	Find standard deviation for a set of data using a calculator. Solve problems involving normally distributed data.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.7 Standard: Probability and Predictions Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.7.11A	Compare odds and probability.	Compare the odds of an event and the probability of an event.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.7.11B	Apply probability and statistics to perform an experiment involving a sample and generalize its results to a given population.	Perform an experiment involving a sample and apply probability and statistics to describe and generalize the results to a given population.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.7.11C	Draw and justify a conclusion regarding the validity of a probability or statistical argument.	Determine a conclusion for a probability or statistical argument. Justify the validity of the conclusion for a probability or statistical argument.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.7.11D	Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.	Predict outcomes for given situations using theoretical probability distributions. Predict outcomes for given situations using information gathered from experimental probability distributions.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.7.11E	Solve problems involving independent simple and compound events.	Draw diagrams and charts to help find probability. Solve problems involving simple events. Solve problems involving compound events.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.8 Standard: Algebra and Functions Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.8.11A	Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.	Given a table of values, find a relationship between two variables. Represent the relationship between two variables by graphing and by equation. Find similarities and differences between families of parabolas. Find similarities and differences between conic sections.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11B	Give examples of patterns that occur in data from other disciplines.	Find examples of patterns that occur in data from science, business, or other areas.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11C	Use patterns to solve routine and non-routine problems.	Find the next number in a sequence. Find the nth term of an arithmetic sequence or a geometric sequence. Find the position of a given term in arithmetic or a geometric sequence.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11D	Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations.	Transform word expressions into algebraic expressions, equations, and inequalities. Write systems of equations and inequalities given information about a situation. Create a matrix given information about a problem, and solve using matrix techniques.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11E	Use equations to represent curves (e.g., lines, parabolas).	Given a graph of a function or relation, write the equation. Given the graph of a conic, write the equation.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11F	Identify whether systems of equations and inequalities are consistent or inconsistent.	Graph a system of linear equations. Indicate the number of solutions to a system. Classify a system as consistent and independent, consistent and dependent, or inconsistent. Classify a system without graphing.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11G	Analyze and explain systems of equations, systems of inequalities and matrices.	Given a real world situation, write a system of equations and inequalities. Solve a system of equations by graphing, elimination, substitution, Cramer’s Rule, or other matrix procedures. Interpret the solution to a system.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11H	Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators.	Solve a system of linear or quadratic equations (or inequalities) by graphing. Use both a graphing calculator and its utilities and graphing by hand to find the solution. Solve a system of equations by applying Cramer’s Rule or using the matrix function and utilities found on a graphing calculator.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11I	Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication.	Solve a system of equations in two or three variables using Cramer’s Rule or matrices. Perform operations on matrices (add, subtract, multiply, and scalar multiplication). Calculate and use the identity and inverse matrices. Solve augmented matrices by hand and by using a graphing calculator.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11J	Demonstrate the connections between algebraic equations and inequalities and the geometry of relations in the coordinate plane.	Use equations to help draw linear, greatest integer, absolute value, and quadratic functions or relations. Use intercepts to help graph functions or solve related equations. Use conic equations to draw the graphs for the conic section. Solve systems of inequalities involving quadratics and conics graphically.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11K	Select, justify and apply appropriate techniques to graph a linear function in two variables, including slope-intercept, x-and y-intercepts, graphing by transformations and the use of a graphing calculator.	Write linear equations in standard form, and then graph using intercepts. Write equations in slope-intercept form, and then graph using slope and y-intercept Use graphing calculators to explore linear transformations. Graph linear equations by applying concepts of transformations. Given a linear equation, choose a method to graph and justify the chosen method.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11L	Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line.	Given a graph, two points, or one point and the slope, write the equation of the line using point-slope form and/or slope-intercept form.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11M	Given a set of data points, write an equation for a line of best fit.	Draw a scatter plot and a line of best fit. Write a prediction equation.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11N	Solve linear and quadratic equations both symbolically and graphically.	Solve a linear equation by making a table of ordered pairs. Solve a linear equation by graphing the related function. Solve a quadratic equation by graphing the related function and/or by using algebraic techniques. Solve non-quadratic equations using quadratic techniques. Solve rational equations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11O	Determine the domain and range of a relation, given a graph or set of ordered pairs.	State the domain and range of a relation when given a graph, a set of ordered pairs, or a mapping.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11P	Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically.	Identify the best graphical representation of a relation of direct, inverse, or joint variation. Represent a relation of direct or inverse variation using an algebraic equation.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11Q	Represent functional relationships in tables, charts and graphs.	Graph a relation and determine if the relation is a function. Use a table to identify ordered pairs for a function. Write equations for parallel and perpendicular lines. Determine slope and intercepts from tables, graphs, and equations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11R	Create and interpret functional models.	Use linear programming procedures to solve problems. Use graphs to represent real life situations and to help find solutions to questions about those situations. Use equations to represent situations and to help find solutions to questions about those situations. Collect data from a problem situation, and construct a scatter plot which can be used to find the equation that represents the data.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11S	Analyze properties and relationships of functions.	Graph linear, quadratic (including conic relations), absolute value, and greatest integer functions. Identify distinguishing characteristics of linear and quadratic functions. Identify relationships between variables in linear and quadratic functions. Graph conic sections and identify distinguishing characteristics.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11T	Analyze and categorize functions by their characteristics.	Given a graph of a function, identify it as linear, quadratic (including conic relations), absolute value, or greatest integer. Given an equation, identify it as linear, quadratic, absolute value, or greatest integer function. Identify type of conic section from its equation or graph.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.11 Standard: Concepts of Calculus Course: Advanced Algebra II
	Course Objectives	Performance Indicators	Assessment Options
2.11.11A	Determine maximum and minimum values of a function over a specified interval.	Find the maximum and minimum values of a function defined for a polygonal convex set.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.11.11B	Interpret maximum and minimum values in problem situations.	Solve linear programming problems that involve maximum and minimum values.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.11.11D	Determine sums of finite sequences of numbers and infinite geometric series.	Find sums of arithmetic series. Find sums of geometric series. Find the sum of an infinite geometric series. Use sigma notation to express the sum.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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District Recommended Instructional Approaches For the Course

To Drive Teacher’s Instructional Activities

Whole group instruction
Small group instruction
Projects
Class discussion
Peer evaluation
Teacher and peer conferencing
Oral presentations
Individual instruction
Research
Dramatization
Role playing
Independent reading
Read aloud
Directed reading-thinking activities
Modeling process
Games
Self-reflection
Self-evaluation
Independent study
Guest speaker
Guest reading
Writing activities
Thematic units
Notebooks
Study guides
Computer technology

Planned Instruction