SOUTH CAROLINA ACADEMIC STANDARDS FOR MATHEMATICS The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes. Standard EA-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Indicators EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately. EA-1.2 EA-1.3 EA-1.4 EA-1.5 EA-1.6 EA-1.7 Connect algebra with other branches of mathematics. Apply algebraic methods to solve problems in real-world contexts. Judge the reasonableness of mathematical solutions. Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic). Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams. Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs). COMMON CORE STATE STANDARDS FOR MATHEMATICS Indicators A-SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients. A-SSE.1b A-SSE-2 F-IF.9 8.F-5 Interpret complicated expressions by viewing one or more of their parts as a single entity. Use the structure of an expression to identify ways to rewrite it. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Anderson School District Five Page 1 Copyright July 1, 2012
Anderson School District Five Page 2 Copyright July 1, 2012
First Nine Weeks EA-2.1 N-RN.3 EA-2.6 EA-2.5 N-RN.3 Unit 1: Essential Algebra Skills (Daily- 9 days; A/B- 5 days) Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers). Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Carry out a procedure to evaluate an expression by substituting a value for the variable. Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Be able to classify and give examples of integers, rational numbers, irrational numbers, whole, and natural numbers. Be able to write expressions and evaluate. Be able to substitute values for one or more variables. Review Order of Operations (PEMDAS). Be able to recognize and apply commutative, associative, and distributive properties. Review with bellringer daily or weekly. Real numbers Venn diagram Identify the Real Numbers Order of Operation Practice Sheet Expression Bingo Substitute using Literal Equations Properties Quiz Integers and Like Terms Expression and Property Jeopardy Quiz 1 / 0.5 Anderson School District Five Page 3 Copyright July 1, 2012
First Nine Weeks EA 2.7 A-APR.1 EA-2.9 Unit 1: Essential Algebra Skills (Daily- 9 days; A/B- 5 days) Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions. Understand that polynomials form a system analogous to the integers, namely they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication) Be able to add and subtract polynomial expressions and combine like terms. Be able to add and subtract matrices of size no larger than 3 x 3 and multiply matrix by a scalar. Hands on Equations Kit Integers and Like Terms Combining Like Terms Matching Matrix Activity Matrices Fill In Matrices Fill In Completed (Answers) EA-2.10 Represent applied problems by using matrices. Be able to distinguish relevant from irrelevant data. Be able to represent data using matrices and understand the meaning of columns and rows in the applied situation. 1 / 0.5 Unit Test 1 / 1 Anderson School District Five Page 4 Copyright July 1, 2012
First Nine Weeks EA 4.7 A-REI.1 A-REI.3 EA-3.8 EA- 3.7 A-CED.4 Unit 2: Solving Linear Equations (Daily- 20 days; A/B- 10 days) Carry out procedures to solve linear equations for one variable algebraically Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Apply proportional reasoning to solve problems Carry out a procedure to solve literal equations for a specified variable. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Use inverse operations to solve linear equations involving one step, two steps, distributive property, variables on both sides, fractional coefficients, decimals and the collecting of like terms. Solve linear equations that result in one solution, no solution or infinitely many. Be able to solve proportional equations and use proportional reasoning to solve problems in applied situations, including similar figures. Be able to use inverse operations to solve literal equations for a specified variable that may involve multiple steps. Equation Frames Equation Bingo Equation Jeopardy Equation Word Problems Distributive Equations Fractions and Decimals One Step Equations Solving Equations Review Problem Solving Equations Sums and Consecutive Integers Word Problems 12 / 6 Proportions Problems Introduction Proportion Problems Literal Equation Manipulative Substituting and Simplifying Literal Equations EA-2.4 Use dimensional analysis to convert units of measure within a system. Be able to set up and solve unit conversion problems using unit analysis. Be able to recall conversion factors listed in support document. 2 /1 Anderson School District Five Page 5 Copyright July 1, 2012
First Nine Weeks Unit 2: Solving Linear Equations (Daily- 20 days; A/B- 10 days) Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 6 Copyright July 1, 2012
First Nine Weeks EA-4.8 A-REI.3 Unit 3: Inequalities (Daily- 5 days; A/B- 2.5 days) Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Be able to solve linear inequalities involving one step, two steps, distributive property, variables on both sides, fractional coefficients, decimals and the collecting of like terms. Be able to graph inequalities on a number line. Graphing Inequalities Nutrition Activity EA- 5.12 A-CED.1 Analyze given information to write a linear inequality in one variable that models a given problem situation. Create equations an inequalities in one variable and use them to solve problems. Be able to assign a variable, assign restrictions to the variable, and solve an inequality. Test 1 / 0.5 Anderson School District Five Page 7 Copyright July 1, 2012
First Nine Weeks Anderson School District Five Page 8 Copyright July 1, 2012
Second Nine Weeks EA -3.1 F-IF.1 8.F-1 Unit 4: Functions (Daily- 11 days; A/B- 5 days) Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Be able to classify a set of ordered pairs in a table, or mapping, as a function or not a function. Be able to use the vertical line test to classify the graph as a function or not a function. Guess My Rule Function Bridge Function Flow Chart What s Your Function Card Game Quiz 1 / 0.5 EA-3.2 F-IF.2 Use function notation to represent functional relationships. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Be able to use function notation to represent functions given as an equation, graph, or described in words. Function Web Linear Function Application Problems 1 / 0.5 Anderson School District Five Page 9 Copyright July 1, 2012
Second Nine Weeks EA-3.3 F-IF.2 Unit 4: Functions (Daily- 11 days; A/B- 5 days) Carry out a procedure to evaluate a function for a given element in the domain. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Be able to substitute a given value for the independent variable and use the order of operations to evaluate the function for the given element. Function Notation 1 / 0.5 EA -3.4 F-IF.5 Analyze the graph of a continuous function to determine the domain and range of the function. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Be able to determine and describe the set of x- and y- coordinates using words or mathematical expressions to specify the domain and range of a continuous function. 1 / 0.5 EA-3.5 F-IF.7b F-IF.7a F-BF.3 Carry out a procedure to graph parent functions 2 1 (including y x, y x, y x, y x, and y x Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b. ). Identify the effect on the graph of replacing f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Be able to graph parent functions. Be able to understand how the value of slope affects the steepness and direction of the line. Be able to understand how the value of the y- intercept affects where the line crosses the y-axis. Algebra Aerobics Transformations Linear Function Project Anderson School District Five Page 10 Copyright July 1, 2012
Second Nine Weeks EA 3.6 Unit 4: Functions (Daily- 11 days; A/B- 5 days) Classify a variation as either direct or inverse. Be able to understand and classify a variation as inverse or direct. Direct Variation Practice Test 1 / 0.5 Anderson School District Five Page 11 Copyright July 1, 2012
Second Nine Weeks EA-5.1 F-IF-7a EA-5.6 F-IF.6 EA-5.7 Unit 5: Writing and Graphing Linear Equations Part 1 (Daily- 15 days; A/B- 8 days) Carry out a procedure to graph a line when given the equation of the line. Graph linear and quadratic functions and show intercepts, maxima, and minima. Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Apply the concept of slope as a rate of change to solve problems. Review plotting points. Be able to graph a given equation by making a table and identifying rate of change. Be able to find the slope of a line from a table and graph. Be able to find the slope of a line from two points using the formulas for slope. Cookie Cutter Activity Create a Foldable for Equations of Lines Ski Slope Design Linear Function Application Problems Spaghetti Linear Lab S-ID.7 F-IF.6 F-LE.1b Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Be able to identify and use slope as a rate of change in applied problems. Anderson School District Five Page 12 Copyright July 1, 2012
Second Nine Weeks EA-4.1 Unit 5: Writing and Graphing Linear Equations Part 1 (Daily- 15 days; A/B- 8 days) Carry out a procedure to write an equation of a line with a given slope and a y-intercept. 8.F-4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Be able to find the slope of a line from a graph or table. Be able to recognize and use the slope intercept form of a linear equation. EA-5.3 F-IF.7a Carry out a procedure to graph the line with a given slope and a y-intercept. Graph linear and quadratic functions and show intercepts, maxima, and minima. Be able to use the slope intercept form of a line to identify and plot the y- intercept and use slope to plot additional points of a line. Be able to graph and recognize horizontal and vertical lines. Using slope-intercept form to graph Equations Graphs Card Match Game Stained Glass Activity 1 / 0.5 Quiz 1 / 0.5 Anderson School District Five Page 13 Copyright July 1, 2012
Second Nine Weeks EA-4.2 8.F-4 EA-5.4 F-IF.7a EA-4.3 Unit 5: Writing and Graphing Linear Equations Part 1 (Daily- 15 days; A/B- 8 days) Carry out a procedure to write an equation of a line with a given slope passing through a given point. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Carry out a procedure to graph the line with a given slope passing through a given point. Graph linear and quadratic functions and show intercepts, maxima, and minima. Carry out a procedure to write an equation of a line passing through two given points Be able to write the equation of a line in slope intercept form and pointslope form given the slope and one point. Be able to plot a point and use the slope to determine additional points. Be able to graph a line using slope intercept form and pointslope form. 8.F-4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Be able to find the slope of a line given two points and write the equation of a line in slope intercept form or point-slope form. Review and Test 1 / 0.5 Anderson School District Five Page 14 Copyright July 1, 2012
Second Nine Weeks EA-4.6 Unit 6: Writing and Graphing Linear Equations Part 2 (Daily- 14 days; A/B- 7 days) Represent linear equations in multiple forms (including point-slope, slopeintercept, and standard). 8.F-4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Be able to write the equation of a line in standard form. Be able to use algebraic techniques to translate linear equations from one form to another. (standard, pointslope, slope-intercept) 4 / 2 EA-5.5 S-ID-7 Carry out a procedure to determine the x- intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Be able to recognize the x and y-intercepts as the points where a line intersects each axis and recognize the x and y-intercepts from a table of values. Be able to substitute zero for x or y to find the y or x- intercept. EA-5.8 Analyze the equations of two lines to determine whether the lines are perpendicular or parallel. Be able to know the relationship between the slopes of parallel and perpendicular lines. It is not essential for students to write the equation of these lines at this time. Parallel and Perpendicular Race Anderson School District Five Page 15 Copyright July 1, 2012
Second Nine Weeks Unit 6: Writing and Graphing Linear Equations Part 2 (Daily- 14 days; A/B- 7 days) EA-5.9 A-CED.2 EA-5.10 EA-4.4 S-ID.6c EA 4.5 S-ID.6a 8.SP-3 Analyze given information to write a linear function that models a given problem situation Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Analyze given information to determine the domain and range of a linear function in a problem situation. Use a procedure to write an equation of a trend line from a given scatterplot. Fit a linear function for a scatter plot that suggests a linear association. Analyze a scatterplot to make predictions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Be able to recognize a linear relationship from a word problem. Be able to assign variables and write the linear equation for the applied problem. Be able to determine the domain and range within an applied problem. Be able to specify between continuous and non-continuous domains. Be able to graph a scatter plot and recognize the correlation of the data. Be able to write an equation of a trend line. Be able to use the concept of slope as a rate of change to make predictions. Be able to determine the meaning of the slope, y-intercept, and coordinates in a contextual problem. Be able to determine which axis represents the independent and dependent variables. Bucket Brigade Tying Knots 1 / 0.5 1 / 0.5 Anderson School District Five Page 16 Copyright July 1, 2012
Second Nine Weeks Unit 6: Writing and Graphing Linear Equations Part 2 (Daily- 14 days; A/B- 7 days) Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 17 Copyright July 1, 2012
Second Nine Weeks Anderson School District Five Page 18 Copyright July 1, 2012
Third Nine Weeks EA-4.9 Unit 7: Systems of Equations (Daily - 10 days; A/B - 5 days) Carry out a procedure to solve systems of two linear equations graphically. Carnegie Investigation Graphing Systems PowerPoint A-REI.5 A-REI.6 8.EE-8a Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Be able to determine the point of intersection of the graph of the two linear equations. Be able to graphically recognize and understand when a system has exactly one solution (consistent and independent), infinitely many solutions (consistent and dependent) or no solution (inconsistent). 8.EE-8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Anderson School District Five Page 19 Copyright July 1, 2012
Third Nine Weeks EA- 4.10 A-REI.5 A-REI.6 8.EE-8a 8.EE-8b Unit 7: Systems of Equations (Daily - 10 days; A/B - 5 days) Carry out a procedure to solve systems of two linear equations algebraically. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Be able to apply the substitution and elimination method to solve a system. Be able to algebraically recognize and understand when a system has exactly one solution (consistent and independent), infinitely many solutions (consistent and dependent) or no solution (inconsistent). System Worksheets Fund Raiser Activity Game Memory Systems of Equations 4 / 2 Anderson School District Five Page 20 Copyright July 1, 2012
Third Nine Weeks EA- 5.11 Unit 7: Systems of Equations (Daily - 10 days; A/B - 5 days) Analyze given information to write a system of linear equations that models a given problem situation Systems short response System word problems Systems Trashketball A-CED.3 8.EE-8c Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Be able to write a system of linear equations given two linear relationships between two variables. Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 21 Copyright July 1, 2012
Third Nine Weeks Unit 8: Laws of Exponents (Daily 20 days; A/B - 10 days) EA-2.2 Apply the laws of exponents and roots to solve problems Be able to evaluate and simplify expressions using the laws of exponents. 6 / 3 EA-2.3 Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation. Be able to carry out a procedure to multiply and divide numbers written in scientific notation. EA-2.7 A-APR-1 EA-2.2 Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions. Understand that polynomials form a system analogous to the integers, namely they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Apply the laws of exponents and roots to solve problems. Be able to add, subtract, and/or multiply polynomial expressions. Be able to divide a polynomial by a monomial. Write polynomials in standard form, naming by degree and number of terms. Simplify rational expressions containing integers including Pythagorean Theorem. Polynomial Bullseye Mix and Match Polynomials Matching Polynomials Exponent Bingo Algebra Tiles 6 / 3 4 / 2 Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 22 Copyright July 1, 2012
Third Nine Weeks EA-2.8 A-SSE.1a A-SSE.1b A-SSE.2 Unit 9: Factoring (Daily - 14 days; A/B - 7 days) Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials). Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. Use the structure of an expression to identify ways to rewrite it. Be able recognize greatest common factors. Be able to factor quadratic trinomials by using difference of squares, trial-and-error method, or another suitable method. Jeopardy Factor Review Factor Dominoes GCF Color by Number 12 / 6 Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 23 Copyright July 1, 2012
Fourth Nine Weeks EA-5.2 Unit 10: Quadratic Graphing (Daily -8 days; A/B - 4 days) Graph linear and quadratic functions and show intercepts, maxima, and minima. Axis of Symmetry x = -b/2a 4 / 2 EA-6.1 Analyze the effects of changing the leading coefficient a on the graph of y ax 2 Transformations with Functions PowerPoint Transformation PowerPoint F-BF.3 Identify the effect on the graph of replacing f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Be able to determine the graphical effect of changing the sign and magnitude of the leading coefficient (y = ax 2 ). 1 / 0.5 EA-6.2 Analyze the effects of changing the constant c on the graph of y x 2 c. F-BF.3 Identify the effect on the graph of replacing f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Be able to determine the graphical effect of increasing or decreasing the constant (y = ax 2 + c). 1 / 0.5 Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 24 Copyright July 1, 2012
Fourth Nine Weeks Unit 11: Quadratics and Factoring (Daily - 12 days; A/B 6 days) EA-6.4 Carry out a procedure to solve quadratic equations by factoring. A-SSE.3a A-REI-4b Factor a quadratic expression to reveal the zeros of the function it defines. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Be able to put a quadratic 2 equation in ax bx c 0 form and solve using factoring. EA-6.3 F-IF.7a Analyze the graph of a quadratic function to determine its equation. Graph linear and quadratic functions and show intercepts, maxima, and minima. Be able to associate the features of a graph with the lead coefficient or constant tem of equation. Be able to associate the x-intercepts of the graph with the factored form of the equation. EA-6.5 F-IF-7a Carry out a graphic procedure to approximate the solutions of quadratic equations. Graph linear and quadratic functions and show intercepts, maxima, and minima. Be able to graph a quadratic function and estimate the zeros from the graph. Anderson School District Five Page 25 Copyright July 1, 2012
Fourth Nine Weeks EA-6.6 Unit 11: Quadratics and Factoring (Daily - 12 days; A/B 6 days) Analyze given information to determine the domain of a quadratic function in a problem situation. Be able to determine the meaningful domain of a quadratic function for an applied problem (may require finding the zeros of a quadratic function). Application of Quadratics Chutes and Ladders Review for Quadratics Golf Ball Toss Hole in Bottle Quadratics Pass the Ball Activity Quadratic Project Review 1 / 0.5 Test 1 / 0.5 Anderson School District Five Page 26 Copyright July 1, 2012