solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets; d) solving multistep linear equations algebraically and graphically; f) solving real-world problems involving equations and systems of equations. Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. Essential Questions How are properties related to Algebra? Can equations that appear to be different, be equivalent? How can you solve equations? Prerequisite/Extension SOL Prerequisites: 7.14 a) solve one‐ and two‐step linear equations; b) solve practical problems in one variable 8.15 a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve Extensions: AII.4 solve (alg./graph) equality to justify simplification and solution. multistep linear equations in one variable. Confirm algebraic solutions to linear equations, a graphing calculator. Property, Transitive Property, Properties of Equality, identity, literal equation, and formula. DOE Lesson Textbook Resources Sections 1.4, 1.7, 1.9; 2.1-2.5 Recommended: Concept Byte 2.3, 2.5, & 3.3; and 2.7-.2.9 Resources/Lessons
Extensions: AII.10 ID/create/solve real‐world problems involving inverse/joint variation/combo of direct/inverse variations Graph an equation representing a direct variation, given a set of data. 12 classes Traditional: 24 classes Standard A.6 The student will graph linear equations and linear inequalities in two variables, including a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and b) writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line. Essential Questions What does the slope of a line indicate about the line? What information does the equation of a line give you? What do we know about the slopes of parallel and perpendicular lines? Prerequisite/Extension SOL Prerequisites: 7.15 a) solve one‐step inequalities; b) graph solutions on number line 8.15 b) solve two‐step linear inequalities and graph results on Graph linear equations and inequalities in two variables, including those that arise from a variety of real-world situations. Use the parent function y = x and describe transformations defined by changes in the or y-intercept. Find the slope of the line, given the equation of a linear function. Find the slope of a line, given the coordinates of two points on the line. Find the slope of a line, given the graph of a line. Recognize and describe a line with a slope that is positive, negative, zero, or undefined. Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equation. an equation of a line when given the graph of a line. Key Vocabulary Slope, Rate of Change, slope-intercept form, y-intercept, x-intercept, form, parallel lines, perpendicular lines, opposite reciprocals, horizontal lines, vertical lines, and standard form DOE Lesson Plans Textbook Resources Sections 5.1, 5.3-5.6 Resources/Lessons
How many solutions can a system of linear equations have? What kind of lines have no solutions? Prerequisite/Extension SOL Prerequisites: 7.14 a) solve one‐ and two‐step linear equations; b) solve practical problems in one variable 8.15 a) solve multistep linear equations in one variable (variable on one and two of equations); c) ID properties of operations used to solve Extensions: AII.4 solve (alg./graph) a) abs value equation/inequ.; b) quad equation over complex; c) equation containing rational algebraic expression; d) equation containing radical exp. Determine whether a system of two linear equations has one solution, no solution, or infinite solutions. Write a system of two linear equations that models a real-world situation. Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a situation. Determine if a linear equation in one variable has one, an infinite number, or no solutions.† Textbook Resources Sections 6.1-6.4 Resources/Lessons Exemplars D.J. Dilemma (7-10) Block: 2 classes Traditional: 4 classes Standard A.5 The student will solve multistep linear inequalities in two variables, including c) solving real-world problems involving inequalities; and d) solving systems of inequalities. Essential Questions What is a system of linear inequalities? How do we know whether the graph of an inequality is dotted or solid? multistep linear inequalities in one variable. Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers. Solve real-world problems involving inequalities. Key Vocabulary Linear Inequalities & Systems of Inequalities DOE Lesson Plans Textbook Resources Sections 6.5-6.6 Resources/Lessons
Students determine the problem a mathematician is investigating and the pattern in the solution Sample Performance Tasks: Differences of Reversed Squares (9-12) Fourth 9 Weeks (A.4c; A.3, A.9, A.10, & A.11) 5 classes Traditional: 10 classes Standard A.4c The student will solve multistep linear and quadratic equations in two variables, including c) solving quadratic equations algebraically and graphically. Essential Questions What are the characteristics of a quadratic function? How can you a quadratic equation? Prerequisite/Extension SOL Prerequisites: 7.14 a) solve one‐ and two‐step linear equations; b) solve practical problems in one variable 8.15 a) multistep linear Solve quadratic equations. Identify the roots or zeros of a quadratic function over the real number system as the solution(s) to the quadratic equation that is formed by setting the given quadratic expression equal to zero. Confirm algebraic solutions to linear and quadratic equations, using a graphing calculator. Key Vocabulary Standard form, zero product property, completing the square, quadratic formula, and discriminant DOE Lesson Plans Textbook Resources Sections 9.3-9.6 Resources/Lessons
equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve Extensions: AII.4 solve (alg./graph) a) abs value equation/inequ.; b) quad equation over complex; c) equation containing rational algebraic expression; d) equation containing radical exp. Block: 2 classes Traditional: 4 classes A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form. Essential Questions How are radical expression represented? Prerequisite/Extension SOL Prerequisites: 7.1 d) determine square roots 8.5 a) determine if a number is a perfect square; b) find two consecutive whole numbers between which a square root lies Express square roots of a whole number in simplest form. Express the cube root of a whole number in simplest form. Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values. Key Vocabulary Radical expression, perfect square, radical, and radicand DOE Lesson Plans Textbook Resources Sections 10.2 & VA-1 Resources/Lessons Block: 5 classes Traditional: 10 classes A.9 The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores. Analyze descriptive statistics to determine the implications for the situations from which the data derive. Key Vocabulary Frequency, histogram, mean, median, mode, range, box-and-whisker plot, standard deviation, z-scores, mean absolute deviation, line of best fit,
A. 10 The student will compare and contrast multiple univariate data sets, using plots. A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve problems, using mathematical models. Mathematical models will include linear and quadratic functions. Essential Questions How can analyzing data help you make decisions and predictions? How can you make and interpret different representations of data? Prerequisite/Extension SOL Prerequisites: 5.16 a) describe mean/median/mode; b) describe mean as fair share; c) find the mean/median/mode/range; d) describe as measure of variation 6.15 a) describe mean as balance point; b) decide which measure of center is appropriate 7.11 a) construct/analyze histograms; b) compare/contrast histograms 8.13 a) make data, including data in a context, calculate and interpret the mean absolute deviation of a data set. Given data, including data in a context, calculate variance and standard deviation of a data set and interpret the standard deviation. Given data, including data in a context, calculate and interpret for a data set. Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation. Compare and contrast mean absolute deviation and standard deviation in a real-world context. Compare, contrast, and analyze data, including data from real-world situations displayed in box-and-whisker plots. Write an equation for a curve of best fit, given a set of no more than twenty data points in a table, a graph, or situation. Make predictions about unknown outcomes, using the equation of the curve of best fit. maximum, minimum and curve of best fit. DOE Lesson Plans Textbook Resources Sections 12.2-4, VA-5, VA-6, & VA-7 Resources/Lessons