TN Algebra II Standards - 2008-2009 Implementation

Mathematical Processes | Number & Operations | Algebra | Geometry & Measurement | Data Analysis, Statistics, and Probability | Review Help
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Virginia Standards of Learning - Select Algebra II and 10, 20 or 40 questions - Repeat for a new set of questions
SOL Algebra I & II resources - posted by Rockingham County Public Schools
FCAT Sample Test Book - [2008] sample questions and test taking tips
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Mathematical Processes
Mathematics Curriculum Standards 3103 - Algebra II	Internet Resources
Checks for Understanding (Formative/Summative Assessment) 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 | 1.10
Create and analyze scatter-plots of non-linear and transcendental functions. 3103.1.1	Add a Trend Line to a Chart - Mr. Excel has tips for displaying a trend graph Create a Chart - tutorial from Excel Easy Examples of Trend Graphs - presented by Project Feeder Watch, select a species and see trend graphs Excel Trendline - tutorial from Excel Easy Global Temperature Trends from 2500 B.C. to 2040 A.D. - interesting graph at the bottom of this page in the form of a timeline Graphing Data and Curve Fitting - good suggestions on entering data, displaying a trend line and making modifications to the line [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Historical Trend Graphs - several tutorials about using cancer data to make trend graphs Line of Best Fit Line of Best Fit - using graph paper and a strand of spaghetti (uncooked) [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Line of Best Fit - using a graphing calculator [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Line of Best Fit - This activity (from Illuminations) allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit. Line of Best Fit Applet - you can enter up to 10 points in the given chart Line of Best Fit Explanation - [format: discussion between student and mentor] why the line of best fit does not always touch as many points as possible on a scatter plot [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Linear Regression and Excel - suggestions on making graphs displaying linear regression as well as making modifications to the trend lines. [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Regression - Plot a bivariate data set, determine the line of best fit for their data, and then check the accuracy of your line of best fit Scatter Plot and Line of Best Fit - use interactive grid to create your own scatter plot(s) [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Using a Graphing Calculator to Display the Line of Best Fit - specific to the TI-83+/84+ graphing calculator Scatter Plot Creating a Scatter Plot in Excel - a long tutorial (27 pages if printed) on making your own scatter plot Creating an XY (Scatter) Plot in Excel - a seven page tutorial on how to use Excel to make a scatter plot Displaying Data - [designed for 7th grade - use for remediation ] explanation, examples and several interactive practice activities [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Displaying Data - [designed for 8th grade] explanation, examples and several interactive practice activities [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] How to Use Your TI-83 or 84 Calculator to Make a Scatter Plot - provided by MathBits [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Interactive Scatter Plot - from Shodor Interactive Scatterplot - students enter data and make their own scatterplot with this National Library of Virtual Manipulatives page Introduction to Bivariate Data - several good examples of scatter plots are included Line Graphs and Scatter Plots - several good examples Linear Regression - an applet which allows your students to investigate a regression line, also known as a "line of best fit." Pizza Palace - Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data The Regression Line and Correlation - a lesson plan from Illuminations Scatterplots - explanation and several good examples from Canada's National Statistical Agency [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Scatterplots - a lesson plan from North Canton City Schools [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] worksheet to use with the activity above [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Scatter Plot - includes examples of positive association, negative association, and no trend Scatter Plot - links to ten different examples are included with this Engineering Statistics Handbook entry Scatter Plot - the Wikipedia entry Scatter Plot and Line of Best Fit - four interactive applets to experiment with [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Scatter Plots - explanation, examples and several interactive practice activities [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Scatter Plots - from the Business Knowledge Center Scatter Plots - includes examples of perfect correlation, high correlation, and low correlation [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Scatter Plots - from Oswego City School District Regents Exam Prep Center [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Spy Guys Interactive - Understanding and Interpreting Graphs - video lesson Step-by-step Internet4Classrooms module - how to produce a scatter plot using Excel Trend Graph (Weekly Report) - select one of eighteen diseases and create trend graphs [from the Infectious Disease Surveillance Center]
Compare and contrast sampling techniques and identify the best technique for a given situation. 3103.1.2	Marbles - Students learn about sampling with and without replacement by modeling drawing marbles from a bag. Parameters: Number and color of marbles in the bag, replacement rule.
Use calculators to identify regression equations for nonlinear data. 3103.1.3	16 function Scientific Calculator - includes instructions on calculator conventions Coolmath's Graphing Calculator - scroll down for instructions on using the graphing calculator Excel Order of Operations - understanding how Excel worksheets handle order of operations [BEDMAS] Math Open Reference Scientific Calculator - scientific calculator similar to those from TI, Casio, HP - extensive explanation of conventions used Mathematical Operators in Excel Spreadsheets - screen shots and a listing of symbols used in Excel spreadsheets to indicate math operators Spreadsheet Math Fundamentals - protocols to be used when writing math formulas and functions in spreadsheets
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. 3103.1.4	Graphing Linear Equations: Making a T-chart (finding plot points) - four pages of instructions with several examples and illustrations Graphing Non-Linear Functions - two examples with explanations of each Nonlinear Functions and their Graphs - a 14 slide show [you might want to delete the two assignment slides, they probably don't match your textbook] Lesson on Non-Linear Functions - session 7 of Patterns, Functions, and Algebra from Annenberg Linear and Non Linear Functions - handout to print with explanation, example and practice problems Using Linear Algebra to solve systems of non-linear equations - a discussion posted at the Physics Forum
Determine the accuracy and reliability of a mathematical model. 3103.1.5	�
Use graphical representations to perform operations on complex numbers. 3103.1.6	Roots, Radicals, and Complex Numbers - a fifty-nine slide PowerPoint show
Use the unit circle to determine the exact value of trigonometric functions for commonly used angles (0�, 30�, 45�, 60��). 3103.1.7	�
Understand and describe the inverse relationship between exponential and logarithmic functions. 3103.1.8	�
Translate the syntax of technology to appropriate mathematical notation for non-linear and transcendental functions. 3103.1.9	�
Interpret the results of mathematical modeling in various contexts to answer questions. 3103.1.10	�
State Performance Indicators 1.1 | 1.2 | 1.3 | 1.4
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. SPI 3103.1.1	�
Recognize and describe errors in data collection and analysis as well as identifying representations of data as being accurate or misleading. SPI 3103.1.2	�
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 3103.1.3	�
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. SPI 3103.1.4	�
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Number & Operations
Mathematics Curriculum Standards 3103 - Algebra II	Internet Resources
Checks for Understanding (Formative/Summative Assessment) 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 | 2.10 | 2.11 | 2.12 | 2.13
Understand that to solve certain problems and equations, the real number system needs to be extended from real numbers to complex numbers. 3103.2.1	�
Define and give examples of each of the types of numbers in the complex number system. 3103.2.2	�
Identify and apply properties of complex numbers (including simplification and standard form). 3103.2.3	�
Add and subtract complex numbers. 3103.2.4	Roots, Radicals, and Complex Numbers - a fifty-nine slide PowerPoint show
Multiply complex numbers. 3103.2.5	Roots, Radicals, and Complex Numbers - a fifty-nine slide PowerPoint show
Define and utilize the complex conjugates to write the quotient of two complex numbers in standard form. 3103.2.6	�
Graph complex numbers in the complex plane and recognize differences and similarities with the graphical representations of real numbers graphed on the number line. 3103.2.7	�
Solve quadratic equations over the complex number system. 3103.2.8	�
Find and describe geometrically the absolute value of a complex number. 3103.2.9	Absolute Value lesson from Purple Math Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball Solving Absolute Value Equations - a lesson from Purple Math
Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers. 3103.2.10	�
Understand the capabilities and limitations of technology. Make estimations without a calculator to detect potential errors. 3103.2.11	�
Select and use appropriate methods to make estimations without technology when solving contextual problems. 3103.2.12	�
Analyze and evaluate contextual situations involving any type of number from the complex number system. 3103.2.13	�
State Performance Indicators 2.1 | 2.2 | 2.3
Describe any number in the complex number system. SPI 3103.2.1	�
Compute with all real and complex numbers. SPI 3103.2.2	�
Use the number system, from real to complex, to solve equations and contextual problems. SPI 3103.2.3	�
National Library of Virtual Manipulatives	Number & Operations [Grades 9-12]
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Algebra
Mathematics Curriculum Standards 3103 - Algebra II	Internet Resources
Checks for Understanding (Formative/Summative Assessment) 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.11 | 3.12 | 3.13 | 3.14 | 3.15 | 3.16 | 3.17 | 3.18 | 3.19 | 3.20 | 3.21 | 3.22 | 3.23
Perform operations on algebraic expressions and justify the procedures. 3103.3.1	�
Determine the domain of a function represented in either symbolic or graphical form. 3103.3.2	�
Determine and graph the inverse of a function with and without technology. 3103.3.3	�
Analyze the effect of changing various parameters on functions and their graphs. 3103.3.4	�
Graph piece-wise and step functions. 3103.3.5	�
Simplify expressions and solve equations containing radicals. 3103.3.6	Roots, Radicals, and Complex Numbers - a fifty-nine slide PowerPoint show Simplifying Radical Expressions - Intermediate Algebra tutorial Simplifying Radicals - basic information about perfect square numbers [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.] Simplifying Radicals - explanation and practice problems
Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula. 3103.3.7	Exponential Functions - lesson plan for two class periods, the document includes links to worksheets Identify Linear, Quadratic, and Exponential Functions - a four slide show Linear Equations - lesson plan for two or three class periods, the document includes links to worksheets Math Unit 10 - Graphing Quadratic and Exponential Functions - [designed for 8th grade] assessment review, 23 questions Patterns with Linear, Quadratic, and Exponential Functions - lesson plan for two or three class periods, the document includes links to worksheets Quadratic Equations and Patterns - lesson plan for two class periods, the document includes links to worksheets A Quick Guide to Recognizing Linear, Quadratic, and Exponential Functions - a four page .pdf document Solving Quadratic Equations by Factoring - a fifteen slide show with examples and a chance for student response - an Interactive Chalkboard show
Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology. 3103.3.8	�
Find an equation for a parabola when given its graph or when given its roots. 3103.3.9	�
Given a quadratic equation use the discriminant to determine the nature of the roots. 3103.3.10	�
Describe and articulate the characteristics and parameters of a parent function. 3103.3.11	�
Understand the relationship between real zeros of a function and the x-intercepts of its graph. 3103.3.12	�
Solve problems using exponential functions requiring the use of logarithms for their solutions. 3103.3.13	Basic Log Rules from Purple Math College Algebra - a tutorial on Logarithmic Properties with several examples and practice problems Exponential functions - a review of logarithms from SOS Math Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes Properties of Logarithms from SOS Math
Define and use arithmetic and geometric sequences and series including using sigma and pi notation. 3103.3.14	�
Find the sum of an geometric series whose common ratio, r, is in the interval (-1,1). 3103.3.15	�
Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems. 3103.3.16	Exponential functions - a review of logarithms from SOS Math Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes
Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems. 3103.3.17	�
Solve compound inequalities involving disjunction and conjunction and linear inequalities containing absolute values. 3103.3.18	Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball
Solve linear programming problems. 3103.3.19	�
Understand the relationships between the equations of conic sections and their graphs. 3103.3.20	�
Factor polynomials using a variety of methods including the factor theorem, synthetic division, long division, sums and differences of cubes, and grouping. 3103.3.21	�
Determine the number and possible types of zeros for a polynomial function and find the rational roots. 3103.3.22	�
Understand the connection between the roots, zeros, x-intercepts, factors of polynomials, and solutions of polynomial equations. 3103.3.23	�
State Performance Indicators 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 | 3.10 | 3.11 | 3.12 | 3.13 | 3.14
Add, subtract and multiply polynomials; divide a polynomial by a lower degree polynomial. SPI 3103.3.1	�
Solve quadratic equations and systems, and determine roots of a higher order polynomial. SPI 3103.3.2	�
Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents. SPI 3103.3.3	�
Use the formulas for the general term and summation of finite arithmetic and both finite and infinite geometric series. SPI 3103.3.4	�
Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent. SPI 3103.3.5	�
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. SPI 3103.3.6	Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball
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. SPI 3103.3.7	�
Solve systems of three linear equations in three variables. SPI 3103.3.8	Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball
Graph the solution set of two or three linear or quadratic inequalities. SPI 3103.3.9	�
Identify and/or graph a variety of functions and their transformations. SPI 3103.3.10	�
Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph. SPI 3103.3.11	�
Interpret graphs that depict real-world phenomena. SPI 3103.3.12	�
Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations. SPI 3103.3.13	�
Solve problems involving the binomial theorem and its connection to Pascal�s Triangle, combinatorics, and probability. SPI 3103.3.14	�
National Library of Virtual Manipulatives	Algebra [Grades 9-12]
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Geometry & Measurement
Mathematics Curriculum Standards 3103 - Algebra II	Internet Resources
Checks for Understanding (Formative/Summative Assessment) 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6
Convert between radians and degrees and vice versa. 3103.4.1	�
Determine the period and the amplitude of a periodic function. 3103.4.2	�
Extend the trigonometric functions to periodic functions on the real line by defining them as functions on the unit circle. 3103.4.3	�
Understand the relationship between the radius, the central angle, and radian measure. 3103.4.4	�
Determine the domain and range of the six trigonometric functions given a graph. 3103.4.5	�
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. 3103.4.6	Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
State Performance Indicators 4.1 | 4.2 | 4.3
Exhibit knowledge of unit circle trigonometry. SPI 3103.4.1	�
Match graphs of basic trigonometric functions with their equations. SPI 3103.4.2	�
Describe and articulate the characteristics and parameters of parent trigonometric functions to solve contextual problems. SPI 3103.4.3	�
National Library of Virtual Manipulatives	Geometry [Grades 9-12] Measurement [Grades 9-12]
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Data Analysis, Statistics, & Probability
Mathematics Curriculum Standards 3103 - Algebra II	Internet Resources
Checks for Understanding (Formative/Summative Assessment) 5.1 | 5.2 | 5.3 | 5.4 | 5.5 | 5.6 | 5.7 | 5.8 | 5.9 | 5.10 | 5.11 | 5.12 | 5.13
Collect, represent and describe both linear and non-linear data developed from contextual situations. 3103.5.1	�
Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns. 3103.5.2	�
Read and interpret data from a two-way table. 3103.5.3	�
Understand the impact of various sampling methods and use them to draw valid conclusions. 3103.5.4	�
Calculate measures of central tendency and spread (variance and standard deviation). 3103.5.5	�
Use technology to find the appropriate regression equation for both linear and non-linear data. 3103.5.6	�
Recognize when the correlation coefficient measures goodness of fit and does not imply causation. 3103.5.7	�
Know the Empirical Rule for one, two and three standard deviations for a normal distribution. 3103.5.8	�
Use data to detect patterns. 3103.5.9	�
Design simple experiments to collect data to answer questions of interest. 3103.5.10	�
Evaluate published data by considering the source, the design of the study and the analysis and representation (or misrepresentation) of the data. 3103.5.11	�
Investigate bias and the phrasing of questions during data acquisition to formulate reasonable conclusions. 3103.5.12	�
Apply both theoretical and experimental probability to analyze the likelihood of an event. 3103.5.13	�
State Performance Indicators 5.1 | 5.2 | 5.3 | 5.4 | 5.5 | 5.6 | 5.7 | 5.8
Compute, compare and explain summary statistics for distributions of data including measures of center and spread. SPI 3103.5.1	�
Compare data sets using graphs and summary statistics. SPI 3103.5.2	�
Analyze patterns in a scatter-plot and describe relationships in both linear and non-linear data. SPI 3103.5.3	�
Apply the characteristics of the normal distribution. SPI 3103.5.4	�
Determine differences between randomized experiments and observational studies. SPI 3103.5.5	�
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. SPI 3103.5.6	�
Determine/recognize when the correlation coefficient measures goodness of fit. SPI 3103.5.7	�
Apply probability concepts such as conditional probability and independent events to calculate simple probability. SPI 3103.5.8	�
National Library of Virtual Manipulatives	Data Analysis & Probability [Grades 9-12]

Review Help
Practice Tests	Howe-Two Online Gateway Skills Assessment - Quiz questions based on a quiz prepared by Anderson County Teachers based on Gateway Performance Objectives modified by Leslie Howe, a Farragut High School math teacher. (Note: the results page offers software for sale, but students may take this test as many times as needed without a purchase.) Practice Tests from Virginia State Standards of Learning - Select Algebra I or II, and then select 10, 20, or 40 questions. Take a Gateway Practice Test - (close the test to come back to this list) This nine-page test was prepared by Anderson County teachers
Multiple Review Activities	28 E-Lab Activities for eighth grade level mathematics from Harcourt School Publishers Algebra Help - in-depth algebra help through algebra history, an online textbook, and various articles covering everything from basic algebra fundamentals to the latest-and-greatest algebra software help available AAAMath offers a large number of math review topics, each one supported by an interactive practice page (8th grade level) Interactive online End of Course Algebra Review National Library of Virtual Manipulatives - Virtual manipulatives related to the NCTM Number & Operations standard. (9-12 at the bottom of the page) Practical Algebra Lessons from PurpleMath - The lessons give practical tips, hints, and examples, and point out common mistakes. SOS Mathematics - Algebra lessons