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Algebra II Standard 1 – Mathematical Processes Textbook – Glencoe Algebra 2 (2005)
State of TN Item Sampler
Flipchart
State of TN Practice Test
Flipchart
Algebra
2 EOC Practice Flipchart
EOC Review Warm -ups ( Each review has 5 - 10 questions)
Academic Vocabulary Game (Are You Smarter Than A Fifth Grader?)
CLE 3103.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. CLE 3103.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution. CLE 3103.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition. CLE 3103.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies. CLE 3103.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies. CLE 3103.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world. CLE 3103.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.
Checks for Understanding (Formative/Summative Assessment): ü 3103.1.1 Create and analyze scatter-plots of non-linear and transcendental functions. Constructing Nonlinear Models PowerPoint Regression Analysis – Tutorials, Practice, and Labs The Regression Line and Correlation – Lesson Plan and Applets
ü 3103.1.2 Compare and contrast sampling techniques and identify the best technique for a given situation. The History and Use of Sampling Methods – Lesson Plan and Activity
ü 3103.1.3 Use calculators to identify regression equations for nonlinear data. Finding a Regression Equation (TI-83) (A different set of directions) Video Tutorial – Finding a Regression Equation (TI-84) Video Tutorial – Finding a Regression Equation (TI-nspire) ü 3103.1.4 Identify the weaknesses of calculators and other technologies in representing non-linear data, such as graphs approaching vertical asymptotes, and use alternative techniques to identify these issues and correctly solve problems. ü 3103.1.5 Determine the accuracy and reliability of a mathematical model. ü 3103.1.6 Use graphical representations to perform operations on complex numbers. Lesson and Practice – Performing Operations on Complex Numbers ü 3103.1.7 Use the unit circle to determine the exact value of trigonometric functions for commonly used angles (0°, 30°, 45°, 60°…). Exact Trig Values of Special Angles – Worksheet with Answers Basic Trigonometry Unit Circle Activity ü 3103.1.8 Understand and describe the inverse relationship between exponential and logarithmic functions. ü 3103.1.9 Translate the syntax of technology to appropriate mathematical notation for non-linear and transcendental functions. ü 3103.1.10 Interpret the results of mathematical modeling in various contexts to answer questions.
State Performance Indicators: SPI 3103.1.1 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic) of non-linear and transcendental functions to solve problems, to model mathematical ideas, and to communicate solution strategies. Quadratic Equations Activity, Answers SPI 3103.1.2 Recognize and describe errors in data collection and analysis as well as identifying representations of data as being accurate or misleading. SPI 3103.1.3 Use technology tools to identify and describe patterns in data using non-linear and transcendental functions that approximate data as well as using those functions to solve contextual problems. SPI 3103.1.4 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely to effectively communicate reasoning in the process of solving problems via mathematical modeling with both linear and non-linear functions. Standard 2 – Number & Operations CLE 3103.2.1 Understand the hierarchy of the complex number system and relationships between the elements, properties and operations. CLE 3103.2.2 Connect numeric, analytic, graphical and verbal representations of both real and complex numbers. CLE 3103.2.3 Use appropriate technology (including graphing calculators and computer spreadsheets) to solve problems, recognize patterns and collect and analyze data. CLE 3103.2.4 Understand the capabilities and limitations of technology when performing operations, graphing, and solving equations involving complex numbers.
Checks for Understanding (Formative/Summative Assessment): ü 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. ü 3103.2.2 Define and give examples of each of the types of numbers in the complex number system. ü 3103.2.3 Identify and apply properties of complex numbers (including simplification and standard form). ü 3103.2.4 Add and subtract complex numbers. Introduction to Complex Numbers PowerPoint Complex Numbers Self-Checking Worksheet, Answers ü 3103.2.5 Multiply complex numbers. Introduction to Complex Numbers PowerPoint Complex Numbers Self-Checking Worksheet, Answers ü 3103.2.6 Define and utilize the complex conjugates to write the quotient of two complex numbers in standard form. Introduction to Complex Numbers PowerPoint Complex Numbers Self-Checking Worksheet, Answers ü 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. Graphing and Absolute Value of Complex Numbers PowerPoint Graphing and Absolute Value of Complex Numbers Worksheet, Answers ü 3103.2.8 Solve quadratic equations over the complex number system. Quadratic Equations PowerPoint Introduction to Quadratic Equations Self-Directed Notes Quadratic Equations Worksheet, Answers Quadratic Equations Activity, Answers ü 3103.2.9 Find and describe geometrically the absolute value of a complex number. Graphing and Absolute Value of Complex Numbers PowerPoint Graphing and Absolute Value of Complex Numbers Worksheet, Answers ü 3103.2.10 Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers. ü 3103.2.11 Understand the capabilities and limitations of technology. Make estimations without a calculator to detect potential errors. ü 3103.2.12 Select and use appropriate methods to make estimations without technology when solving contextual problems. ü 3103.2.13 Analyze and evaluate contextual situations involving any type of number from the complex number system. State Performance Indicators: SPI 3103.2.1 Describe any number in the complex number system. Introduction to Complex Numbers PowerPoint
SPI 3103.2.2 Compute with all real and complex numbers. Introduction to Complex Numbers PowerPoint Complex Numbers Self-Checking Worksheet, Answers SPI 3103.2.3 Use the number system, from real to complex, to solve equations and contextual problems. Standard 3 – Algebra CLE 3103.3.1 Understand and apply properties of rational exponents and perform basic operations to simplify algebraic expressions. CLE 3103.3.2 Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations. CLE 3103.3.3 Analyze and apply various methods to solve equations, absolute values, inequalities, and systems of equations over complex numbers. CLE 3103.3.4 Graph and compare equations and inequalities in two variables. Identify and understand the relationships between the algebraic and geometric properties of the graph. CLE 3103.3.5 Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena.
Checks for Understanding (Formative/Summative Assessment) ü 3103.3.1 Perform operations on algebraic expressions and justify the procedures. ü 3103.3.2 Determine the domain of a function represented in either symbolic or graphical form. Find the Domain of the Function (Symbolic Form) ü 3103.3.3 Determine and graph the inverse of a function with and without technology. Graphing Inverse Functions (with a graphing calculator) Graphically Represent the Inverse of a Function – Tutorial and Practice
ü 3103.3.4 Analyze the effect of changing various parameters on functions and their graphs. Match the Translated Function with its Graph - Worksheet Graph the Transformed Functions - Worksheet ü 3103.3.5 Graph piece-wise and step functions. Graphing Piece-wise Functions on a Graphing Calculator Graphing Piece-wise Functions - Worksheet
ü 3103.3.6 Simplify expressions and solve equations containing radicals. Radical Equations Self-directed Notes Radical Equations – Self-checking Worksheet Radical Equations - Application Radical Equations – Tutorial, Practice, and Lab ü 3103.3.7 Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula. Tutorial and Interactive Applet – Graphing Quadratic Functions Proof Without Words – Completing the Square Completing the Square PowerPoint Quadratic Formula Calculator and Solver Quadratic Equations PowerPoint Introduction to Quadratic Equations Self-Directed Notes Quadratic Equations Worksheet, Answers Quadratic Equations Activity, Answers
ü 3103.3.8 Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology. Systems of Equations in Two Variables Self-directed Notes Systems of Equations in Three Variables PowerPoint Tutorial (shows graphs of planes) – Solving Systems of 3 Variable Equation Tutorial – Solving 3x3 System of Linear Equations - Inverse Matrices 3x3 Determinants – Worksheet with answers Matrix Equations (Inverse Required) – Worksheet with answers
ü 3103.3.9 Find an equation for a parabola when given its graph or when given its roots. Tutorial and Interactive Applet – Finding an Equation of a Parabola
ü 3103.3.10 Given a quadratic equation use the discriminant to determine the nature of the roots.
ü 3103.3.11 Describe and articulate the characteristics and parameters of a parent function. Tutorial – Transformations of Parent Functions ü 3103.3.12 Understand the relationship between real zeros of a function and the x-intercepts of its graph. ü 3103.3.13 Solve problems using exponential functions requiring the use of logarithms for their solutions. Applications of Exponential and Logarithmic Functions Solving Exponential Equations with Logarithms – Worksheet with Answers
ü 3103.3.14 Define and use arithmetic and geometric sequences and series including using sigma and pi notation. Arithmetic and Geometric Sequences and Series Review Worksheet/Puzzle Practice with Arithmetic and Geometric Sequences and Series
ü 3103.3.15 Find the sum of an geometric series whose common ratio, r, is in the interval (-1,1). Tutorial – Sum of Geometric Series
ü 3103.3.16 Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems. Introduction to Logarithms PowerPoint Properties of Logarithms PowerPoint Logarithms Review Worksheet, Answers
ü 3103.3.17 Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems. Earthquake Log Worksheet, Answers
ü 3103.3.18 Solve compound inequalities involving disjunction and conjunction and linear inequalities containing absolute values. Compound Inequalities – Worksheet with Answers Absolute Value Inequalities – Tutorial, Practice, and Activity Absolute Value Inequalities – Worksheet with Answers
ü 3103.3.19 Solve linear programming problems. Applications of Linear Programming
ü 3103.3.20 Understand the relationships between the equations of conic sections and their graphs. Table – Graphs and Properties of Conic Sections Activities – Circles and Parabolas Applications of Conics (each is a different link) – Parabolas, Ellipses, Hyperbolas
ü 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. Factoring Around the Room Activity Factoring Quadratic Expressions – Worksheet with Answers The Remainder and Factor Theorem PowerPoint
ü 3103.3.22 Determine the number and possible types of zeros for a polynomial function and find the rational roots. Solving & Graphing Polynomials of Higher Degree – Tutorial and Practice Descartes’ Rule of Signs – Worksheet with Answers ü 3103.3.23 Understand the connection between the roots, zeros, x-intercepts, factors of polynomials, and solutions of polynomial equations. State Performance Indicators SPI 3103.3.1 Add, subtract and multiply polynomials; divide a polynomial by a lower degree polynomial.
SPI 3103.3.2 Solve quadratic equations and systems, and determine roots of a higher order polynomial. Completing the Square PowerPoint Quadratic Equations PowerPoint Introduction to Quadratic Equations Self-Directed Notes Quadratic Equations Worksheet, Answers Quadratic Equations Activity, Answers
SPI 3103.3.3 Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents. Tutorial and Interactive Applet – Graphing Rational Functions Multiplying and Dividing Rational Expressions – Worksheet with Answers Adding and Subtracting Rational Expressions – Worksheet with Answers
Adding and Subtracting Rational Numbers
SPI 3103.3.4 Use the formulas for the general term and summation of finite arithmetic and both finite and infinite geometric series. 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. Tutorial and Interactive Applet – Graphs of Common 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. Composition of Functions Relay Operations on Functions Worksheet, Answers
SPI 3103.3.7 Identify whether a function has an inverse, whether two functions are inverses of each other, and/or explain why their graphs are reflections over the line y = x. Tutorial and Interactive Applet – Inverse Functions Inverse Functions – Worksheet with Answers
SPI 3103.3.8 Solve systems of three linear equations in three variables. Systems of Equations in Two Variables Self-directed Notes Systems of Equations in Three Variables PowerPoint Systems of Equations in Three Variables – Worksheet with Answers
SPI 3103.3.9 Graph the solution set of two or three linear or quadratic inequalities. Interactive Applet – Graphing Systems of Linear Inequalities Graphing Quadratic Inequalities – Worksheet with Answers SPI 3103.3.10 Identify and/or graph a variety of functions and their translations. SPI 3103.3.11 Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph. Tutorial and Interactive Applet – Finding the Equation of a Circle Tutorial and Interactive Applet – Equation of an Ellipse Tutorial and Interactive Applet – Equation of a Hyperbola
SPI 3103.3.12 Interpret graphs that depict real-world phenomena.
SPI 3103.3.13 Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations.
Solving
Rational Equations Flipchart
Contextual Problems – Quadratic Functions M & M’s Lab – Rate of Growth, Rate of Decay, Calculator Review Sheet
SPI 3103.3.14 Solve problems involving the binomial theorem and its connection to Pascal’s Triangle, combinatorics, and probability. Binomial Theorem – Tutorial and Practice Standard 4 – Geometry & Measurement CLE 3103.4.1 Understand the trigonometric functions and their relationship to the unit circle. Demonstration of the Unit Circle Formula and Graph CLE 3103.4.2 Know and use the basic identities of sine, cosine, and tangent as well as their reciprocals. CLE 3103.4.3 Graph all six trigonometric functions and identify their key characteristics. Graphing Trigonometric Functions on a Graphing Calculator PowerPoint Tutorial – Graphing Trigonometric Functions CLE 3103.4.4 Know and use the Law of Sines to find missing sides and angles of a triangle, including the ambiguous case. Law of Sines – Applet and Application Law of Sines – Worksheet with Answers CLE 3103.4.5 Use trigonometric concepts, properties and graphs to solve problems.
Checks for Understanding (Formative/Summative Assessment): ü 3103.4.1 Convert between radians and degrees and vice versa. Tutorial – Converting Radians to Degrees (and vice versa) Worksheet – Converting Radians to Degrees (and vice versa) Basic Trigonometry Unit Circle Activity
ü 3103.4.2 Determine the period and the amplitude of a periodic function. Tutorial and Interactive Applet – Period Functions ü 3103.4.3 Extend the trigonometric functions to periodic functions on the real line by defining them as functions on the unit circle. ü 3103.4.4 Understand the relationship between the radius, the central angle, and radian measure. ü 3103.4.5 Determine the domain and range of the six trigonometric functions given a graph. Chart of Properties of Trigonometric Functions
ü 3103.4.6 Know and be able to use the fundamental trigonometric identities, including the Pythagorean identities, reciprocal identities, sum of sine and cosine, and odd and even identities. Angle Sum/Difference Identities – Worksheet with Answers Double- and Half-Angle Identities – Worksheet with Answers
State Performance Indicators: SPI 3103.4.1 Exhibit knowledge of unit circle trigonometry. Tutorial and Interactive Applet – Unit Circle and the Trigonometric Functions Basic Trigonometry Unit Circle Activity
SPI 3103.4.2 Match graphs of basic trigonometric functions with their equations. Interactive Applet – Graphs of Basic Trigonometric Functions Mini-Quiz – Graphs of Trigonometric Functions Interactive Applet – Trigonometric Functions
SPI 3103.4.3 Describe and articulate the characteristics and parameters of parent trigonometric functions to solve contextual problems. Chart of Properties of Trigonometric Functions
Standard 5 – Data Analysis, Statistics, & Probability
CLE 3103.5.1 Describe, interpret, and apply quantitative data. CLE 3103.5.2 Evaluate and critique various ways of collecting data and using information based on data published in the media. CLE 3103.5.3 Use data and statistical thinking to draw inferences, make predictions, justify conclusions and identify and explain misleading uses of data. CLE 3103.5.4 Develop an understanding of probability concepts in order to make informed decisions.
Checks for Understanding (Formative/Summative Assessment): ü 3103.5.1 Collect, represent and describe both linear and non-linear data developed from contextual situations. ü 3103.5.2 Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns. ü 3103.5.3 Read and interpret data from a two-way table. ü 3103.5.4 Understand the impact of various sampling methods and use them to draw valid conclusions. ü 3103.5.5 Calculate measures of central tendency and spread (variance and standard deviation). ü 3103.5.6 Use technology to find the appropriate regression equation for both linear and non-linear data. ü 3103.5.7 Recognize when the correlation coefficient measures goodness of fit and does not imply causation. ü 3103.5.8 Know the Empirical Rule for one, two and three standard deviations for a normal distribution. ü 3103.5.9 Use data to detect patterns. ü 3103.5.10 Design simple experiments to collect data to answer questions of interest. ü 3103.5.11 Evaluate published data by considering the source, the design of the study and the analysis and representation (or misrepresentation) of the data. ü 3103.5.12 Investigate bias and the phrasing of questions during data acquisition to formulate reasonable conclusions. ü 3103.5.13 Apply both theoretical and experimental probability to analyze the likelihood of an event. Random Drawing Tool – Individual Events Random Drawing Tool – Sampling Distribution Theoretical and Empirical Probabilities – Tutorial, Practice, and Activity State Performance Indicators: SPI 3103.5.1 Compute, compare and explain summary statistics for distributions of data including measures of center and spread. Measures of Central Tendency and Dispersion - PowerPoint Measures of Central Tendency and Spread - PowerPoint SPI 3103.5.2 Compare data sets using graphs and summary statistics. SPI 3103.5.3 Analyze patterns in a scatter-plot and describe relationships in both linear and non-linear data. Regression Analysis – Tutorials, Practice, and Labs
SPI 3103.5.4 Apply the characteristics of the normal distribution. Normal Distribution – Tutorial, Practice, and Activity
SPI 3103.5.5 Determine differences between randomized experiments and observational studies. Experiments and Observational Studies – Notes/Tutorial Experiments and Observational Studies - PowerPoint
SPI 3103.5.6 Find the regression curve that best fits both linear and non-linear data (using technology such as a graphing calculator) and use it to make predictions. Interactive Applet – Line of Best Fit SPI 3103.5.7 Determine/recognize when the correlation coefficient measures goodness of fit. SPI 3103.5.8 Apply probability concepts such as conditional probability and independent events to calculate simple probability. Conditional Probability – Tutorial and Practice Conditional Probability and Probability of Simultaneous Events - Activities Independent Events – Tutorial and Practice
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