Algebra 2 Learning Expectations:

Specific Learning Expectations for this course can be found at: http://www.state.tn.us/education/ci/standards/mathhighschool/algebra2.php

Nine Weeks First	Current Standards for 2008-2009	New Standards Effective 2009-2010	Activities
	Chapter 1 – Approx. Number of Days: 10 Allow extra days for review and assessment Prerequisite Skill Lesson (p. 814) SPI 1.1.A Order a given set of real numbers
	1-1: Expressions and Formulas
	1-2: Properties of Real Numbers SPI 1.1.B Identify the reciprocal of a real number	3103.2.1 Understand that to solve certain problems and equations, the real number system needs to be extended from real numbers to complex numbers. 3103.2.2 Define and give examples of each of the types of numbers in the complex number system.	Classifying Complex Numbers. Use Microsoft Powerpoint to show students how to classify different types of complex numbers. 3103.2.2 http://alex.state.al.us/lesson_view.php?id=11364
	1-3: Solving Equations SPI 2.1.A Translate a verbal sentence into an algebraic equation & vice versa SPI 2.1.C Solve multi-step linear equations (parentheses &/or variables on both sides)
	1-4: Solving Absolute Value Equations
	1-5: Solving Inequalities SPI 2.1.F Identify the graphical representation of the solution to a 1-variable inequality on a number line
	1-6: Solving Compound & Absolute Value Inequalities SPI 2.1.F Identify the graphical representation of the solution to a 1-variable inequality on a number line	3103.3.18 Solve compound inequalities involving disjunction and conjunction and linear inequalities containing absolute values.	Verifying Absolute Value Inequalities with a Graphical Approach. Find the solution sets of absolute value inequalities by graphing on the TI-84. 3103.3.18 http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=7974
	Chapter 2 – Approx. Number of Days: 10 Allow extra days for review and assessment
	2-1: Relations and Functions SPI 2.1.B Select the algebraic equation that generalizes the pattern represented by data in a given table SPI 2.2.E Solve 1-variable linear equations with rational expressions	3103.3.2 Determine the domain of a function represented in either symbolic or graphical form.	Domain Representations. Students will describe the domain of a function with multiple representations. 3103.3.2 http://illuminations.nctm.org/LessonDetail.aspx?id=L621
	2-2: Linear Equations SPI 2.2.A*Select functional notation to generalize a given numeric pattern SPI 5.1.C*Choose the matching linear graph when given a set of ordered pairs representing real-world data	3103.5.1 Collect, represent and describe both linear and nonlinear data developed from contextual situations. 3103.5.2 Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns.	Armstrong Numbers. Students will investigate number patterns using Microsoft Excel to discover Armstrong Numbers smaller than 1000. 3103.5.2 http://illuminations.nctm.org/LessonDetail.aspx?id=L648
	2-3: Slope 3.2.A Predict the graphical transformation that occurs when coefficients &/or constants of given function are changed	3103.3.4 Analyze the effect of changing various parameters on functions and their graphs.
	2-4: Writing Linear Equations SPI 2.1.B Select the algebraic equation that generalizes the pattern represented by data in a given table SPI 2.1.D Select the graph that represents a given linear function expressed in slope-intercept form	3103.5.3 Read and interpret data from a two-way table. 3103.5.9 Use data to detect patterns. 3103.5.2 Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns. 3103.5.1 Collect, represent and describe both linear and nonlinear data developed from contextual situations. 3103.5.6 Use technology to find the appropriate regression equation for both linear and non-linear data. 3103.5.7 Recognize when the correlation coefficient measures goodness of fit and does not imply causation.	Determining Functions Using Regression. Students will investigate data using a TI-84 and determine which model is best to find the regression equation. 3103.5.6 http://illuminations.nctm.org/LessonDetail.aspx?id=U180
	2-5: Modeling Real-World Data: Using Scatter Plots SPI 2.1.B Select the algebraic equation that generalizes the pattern represented by data in a given table SPI 5.1.A Make a prediction from the graph of a real-world data set SPI 5.1.C***Choose the matching linear graph when given a set of ordered pairs representing real-world data SPI 5.2.A Categorize the correlation of a scatterplot using real-world data (ie, positive, negative, strong, weak) SPI 5.3.A Find the equation for the line of best fit given a scatterplot depicting real-world data		Exploring Linear Data. Students use linear data from a variety of settings to construct scatterplots and investigate the notion of line of best fit. 3103.5.2 http://illuminations.nctm.org/LessonDetail.aspx?id=L298 Graphing Calculator Investigation. Students use a TI-84 to find the non-linear regression line given a set of real world data. 3103.5.6 Pg. 539 in Glencoe Algebra 2 book.
	2-6: Special Functions SPI 1.2.B Select a graph that represents an absolute value equation on a coordinate plane SPI 3.2.A Predict the graphical transformation that occurs when coefficients &/or constants of given function are changed SPI 3.3.A Describe the transformation that has changed a "parent function" to the given related function (eg, shifts, reflection)	3103.3.5 Graph piece-wise and step functions. 3103.3.11 Describe and articulate the characteristics and parameters of a parent function. 3103.3.4 Analyze the effect of changing various parameters on functions and their graphs.	Creating piece wise functions using CBR system. Students use a TI-84 and CBR to generate a piece wise function, then use algebra to identify the three equations and restrict the domains. 3103.3.5 http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=7469
	2-7: Graphing Inequalities SPI 2.2.C Select the graph of a 2-variable inequality
	Chapter 3 – Approx. Number of Days: 8 Allow extra days for review and assessment
	3-1: Solving Systems of Equations by Graphing SPI 2.2.F Solve a system of linear equations with 2 variables
	3-2: Solving Systems of Equations Algebraically SPI 2.2.F Solve a system of linear equations with 2 variables
	3-3: Solving Systems of Inequalities by Graphing
	3-4: Linear Programming	3103.3.19 Solve linear programming problems.	Dirt Bike Dilemma. Students use a TI-84 to set up and solve a linear programming problem. 3103.3.19 http://illuminations.nctm.org/LessonDetail.aspx?id=L685
	3-5: Solving Systems of Equations in 3 Variables	3103.3.8 Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology.	Hanging Chains. Students will find the equation of a parabola by algebraically solving a three by three system of linear equations. 3103.3.8 http://illuminations.nctm.org/LessonDetail.aspx?id=L628
	Chapter 4 – Approx. Number of Days: 13 Allow extra days for review and assessment
	4-1: Introduction to Matrices SPI 2.2.H Identify matrices that model given real-world situations
	4-2: Operations with Matrices SPI 2.2.H Identify matrices that model given real-world situations
	4-3: Multiplying Matrices SPI 2.2.H Identify matrices that model given real-world situations
	4-4: Transformations with Matrices
	4-5: Determinants
	4-6: Cramer's Rule SPI 2.2.F Solve a system of linear equations with 2 variables	3103.3.8 Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology.
	4-7: Identity and Inverse Matrices
	4-8: Using Matrices to Solve Systems of Equations SPI 2.2.F Solve a system of linear equations with 2 variables	3103.3.8 Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology.

Nine Weeks Second	Current Standards for 2008-2009	New Standards Effective 2009-2010	Activities
	Chapter 5 – Approx. Number of Days: 17 Allow extra days for review and assessment
	5-1: Monomials SPI 1.2.D Simplify expressions with rational & negative exponents	SPI 3103.3.3 Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents.
	5-2: Polynomials SPI 1.1.C Multiply 2 polynomials with each factor having no more than 2 terms SPI 1.2.E Add, subtract, & multiply algebraic expressions SPI 4.1.A Select the area representation for a given product of 2 binomials	3103.3.1 Perform operations on algebraic expressions and justify the procedures. 3103.3.21 Factor polynomials using a variety of methods including the factor theorem, synthetic division, long division, sums and differences of cubes, and grouping.
	5-3: Dividing Polynomials
	5-4: Factoring Polynomials
	5-5: Roots of Real Numbers
	5-6: Radical Expressions	3103.3.6 Simplify expressions and solve equations containing radicals. SPI 3103.3.3 Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents.
	5-7: Rational Exponents SPI 1.2.D Simplify expressions with rational & negative exponents
	5-8: Radical Equations and Inequalities
	5-9: Complex Numbers SPI 1.2.A Perform basic operations using complex numbers (+,-,x) SPI 1.3.A Determine the conjugate of a complex number	3103.2.7 Graph complex numbers in the complex plane and recognize differences and similarities with the graphical representations of real numbers graphed on the number line. 3103.2.9 Find and describe geometrically the absolute value of a complex number. 3103.2.3 Identify and apply properties of complex numbers (including simplification and standard form). 3103.2.4 Add and subtract complex numbers. 3103.2.5 Multiply complex numbers. 3103.2.6 Define and utilize the complex conjugates to write the quotient of two complex numbers in standard form. 3103.2.13 Analyze and evaluate contextual situations involving any type of number from the complex number system. 3103.2.10 Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers.	Lesson Plan: Complex Number Properties. Students experiment with complex numbers to see which properties apply to the system of complex numbers. 3103.2.10 http://dnet01.ode.state.oh.us/IMS.ItemDetails/LessonDetail.aspx?id=0907f84c8053191c Complex Numbers. Students use the TI-84 to compute basic operations over complex numbers. 3103.2.4 http://www.mathbits.com/MathBits/TISection/Algebra2/complexgc.htm Algebra Activity. Short explanation/example of finding the absolute value of a complex number. 3103.2.9 Pg. 272 in Glencoe Algebra 2 book.
	Chapter 6 – Approx. Number of Days: 14 Allow extra days for review and assessment
	6-1: Graphing Quadratic Functions	3103.3.4 Analyze the effect of changing various parameters on functions and their graphs.	Graphing Families of Quadratic Functions. Students will use the Transfrm app on the TI-84 to explore changing parameters on different kinds of functions. 3103.3.4 http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=7529
	6-2: Solving Quadratic Equations by Graphing	3103.3.7 Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula. 3103.3.10 Given a quadratic equation use the discriminant to determine the nature of the roots. 3103.3.22 Determine the number and possible types of zeros for a polynomial function and find the rational roots. 3103.3.23 Understand the connection between the roots, zeros, x-intercepts, factors of polynomials, and solutions of polynomial equations. 3103.2.10 Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers. 3103.2.8 Solve quadratic equations over the complex number system. 3103.2.11 Understand the capabilities and limitations of technology. Make estimations without a calculator to detect potential errors. 3103.2.12 Select and use appropriate methods to make estimations without technology when solving contextual problems.	Solving Quadratic Equations. Students use a TI-84 to find the solutions (roots) of a quadratic equation by graphing. 3103.3.7 http://mrsroberts.com/MathBits/TISection/Algebra2/quadraticequations.htm
	6-3: Solving Quadratic Equations by Factoring
	6-4: Completing the Square
	6-5: The Quadratic Formula and the Discriminant		Building Connections. Students make connections between the x-intercepts of the graph of a polynomial and the polynomial's linear factors. 3103.3.23 http://illuminations.nctm.org/LessonDetail.aspx?id=L282
	6-6: Analyzing Graphs of Quadratic Functions SPI 3.2.A Predict the graphical transformation that occurs when coefficients &/or constants of given function are changed SPI 3.3.A Describe the transformation that has changed a "parent function" to the given related function (eg, shifts, reflection)	3103.3.4 Analyze the effect of changing various parameters on functions and their graphs. 3103.3.11 Describe and articulate the characteristics and parameters of a parent function. 3103.5.2 Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns. 3103.5.1 Collect, represent and describe both linear and nonlinear data developed from contextual situations. 3103.5.6 Use technology to find the appropriate regression equation for both linear and non-linear data.	Ball Bounce. Students will use TI-84 and CBR to collect both linear and non-linear data, and analyze results. 3103.5.1 http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=7650
	6-7: Graphing and Solving Quadratic Inequalities
	Chapter 7 – Approx. Number of Days: 9 Allow extra days for review and assessment
	7-1: Polynomial Functions
	7-2: Graphing Polynomial Functions SPI 5.1.A Make a prediction from the graph of a real-world data set SPI 5.3.A Find the equation for the line of best fit given a scatterplot depicting real-world data	3103.5.2 Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns. 3103.5.1 Collect, represent and describe both linear and nonlinear data developed from contextual situations. 3103.5.6 Use technology to find the appropriate regression equation for both linear and non-linear data. 3103.5.7 Recognize when the correlation coefficient measures goodness of fit and does not imply causation.	How to weigh an alligator. Students will use a TI-84 to explore real data and determine which type of regression is appropriate. 3103.5.6 http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=7682 Line of Best Fit. Students use NBA stats and explore the changes in the regression equation and the correlation coefficient, r. Could be done with TI-84. 3103.5.7 http://illuminations.nctm.org/ActivityDetail.aspx?ID=146 Correlation Does Not Equal Causation. Student use a TI-84 and are given a real world setting to evaluate. 3103.5.7 http://mrsroberts.com/MathBits/TISection/Statistics2/correlationcausation.htm
	7-3: Solving Equations Using Quadratic Techniques
	7-4: The Remainder and Factor Theorems	3103.3.21 Factor polynomials using a variety of methods including the factor theorem, synthetic division, long division, sums and differences of cubes, and grouping.

Nine Weeks Third	Current Standards for 2008-2009	New Standards Effective 2009-2010	Activities
	Chapter 7(Cont.) – Approx. Number of Days: 10 Allow extra days for review and assessment
	7-5: Roots and Zeros
	7-6: Rational Zero Theorem
	7-7: Operations on functions	SPI 3103.3.6 Combine functions (such as polynomial, rational, radical and absolute value expressions) by addition, subtraction, multiplication, division, or by composition and evaluate at specified values of their variables.
	7-8: Inverse Functions and Relations	3103.3.3 Determine and graph the inverse of a function with and without technology.	What is the Inverse of a Function? Students will find the inverse of a function algebraically, then check their answer on the TI-84. 3103.3.3 http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=8211
	7-9: Square Root Functions and Inequalities SPI 2.2.D Determine the domain of polynomial, rational, square root, exponential and logarithmic functions 2.2.E Determine the range of a wide variety of functions given a graph	SPI 3103.3.5 Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent.
	Chapter 8 – Approx. Number of Days: 14 Allow extra days for review and assessment
	8-1: Midpoint and Distance and Formulas
	8-2: Parabolas	3103.3.9 Find an equation for a parabola when given its graph or when given its roots. 3103.3.12 Understand the relationship between real zeros of a function and the x-intercepts of its graph.
	8-3: Circles	3103.3.20 Understand the relationships between the equations of conic sections and their graphs.
	8-4: Ellipses
	8-5: Hyperbolas
	8-6: Conic Sections
	8-7: Solving Quadratic Systems
	Chapter 9 – Approx. Number of Days: 11 Allow extra days for review and assessment
	9-1: Multiplying and Dividing Rational Expressions
	9-2: Adding and Subtracting Rational Expressions
	9-3: Graphing Rational Functions SPI 2.2.D Determine the domain of polynomial, rational, square root, exponential and logarithmic functions	SPI 3103.3.5 Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent.
	9-4: Direct, Joint, & Inverse Variation
	9-5: Classes of Functions SPI 1.2.B Select a graph that represents an absolute value equation on a coordinate plane SPI 2.1.B Select the algebraic equation that generalizes the pattern represented by data in a given table SPI 2.1.E Select the graph that models a given real-world situation (linear & non-linear)	SPI 3103.3.12 Interpret graphs that depict real-world phenomena.
	9-6: Solving Rational Equations and Inequalities SPI 2.2.B Solve 1-variable linear equation with rational expressions
	Chapter 10 – Approx. Number of Days: 6 Allow extra days for review and assessment
	10-1: Exponential Functions SPI 2.2.D Determine the domain of polynomial, rational, square root, exponential and logarithmic functions SPI 2.2.E Determine the range of a wide variety of functions given a graph SPI 4.3.A Solve real-world problems given logarithmic and exponential formulas (e.g., pH scale, Richter scale)	SPI 3103.3.5 Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent. 3103.3.3 Determine and graph the inverse of a function with and without technology. 3103.3.13 Solve problems using exponential functions requiring the use of logarithms for their solutions. 3103.3.16 Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems. 3103.3.17 Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems.	Inverse Functions. Students use the TI-84 to find the inverse of a function. 3103.3.3 http://www.mathbits.com/MathBits/TISection/Algebra2/inverse.htm
	10-2: Logarithms and Logarithmic Functions SPI 1.2.C Identify the exponential form of a logarithmic expression & vice versa SPI 2.2.D Determine the domain of polynomial, rational, square root, exponential and logarithmic functions SPI 2.2.E Determine the range of a wide variety of functions given a graph SPI 2.3.A Determine the inverse of a logarithmic function given its graph SPI 4.3.A Solve real-world problems given logarithmic and exponential formulas (e.g., pH scale, Richter scale SPI 5.1.A Make a prediction from the graph of a real-world data set SPI 5.3.A Find the equation for the line of best fit given a scatter plot depicting real-world data
	10-3: Properties of Logarithms SPI 2.2.G Apply properties of logarithms to simplify a logarithmic expression SPI 4.3.A Solve real-world problems given logarithmic and exponential formulas (eg pH scale, Richter scale

Nine Weeks

Fourth

Current Standards for

2008-2009

New Standards Effective

2009-2010

Activities

Chapter 10(Cont.) – Approx. Number of Days: 6

Allow extra days for review and assessment

10-4: Common Logarithms

SPI 4.3.A Solve real-world problems given logarithmic and exponential formulas (e.g., pH scale, Richter scale)

3103.3.17 Know that the logarithm and exponential functions are inverses and use

this information to solve real-world problems.

Algebra 2 Learning Expectations:

First