Algebra 1 Prince William County Schools Pacing Guide (Crosswalk)

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1 Algebra 1 Prince William County Schools Pacing Guide (Crosswalk) Teacher focus groups have assigned a given number of days to each unit based on their experiences and knowledge of the curriculum. It is recommended that teachers stay as close as possible to the pacing guidelines to ensure that all of the have been taught prior to the SOL Test, and that, as students move within the Division, their math instruction remains consistent. Ongoing review should occur throughout the year. Teachers may find the full wording of the objectives, along with the essential knowledge and skills to be learned, in the Unit Plans. These documents are available on the Math Web site at Unit plans created by the Teacher Focus Groups provide suggestions for learning experiences as well as resources to support instruction. (6 days/3 blocks) Unit 1: Expressions Translate verbal quantitative situations into algebraic expressions and equations and vice versa, orally and in writing. A.1 Model practical situations with algebraic expressions in a variety of representations (concrete, pictorial, symbolic, verbal). Evaluate algebraic expressions for a given replacement set to include rational numbers. Evaluate expressions that contain absolute value, square roots, and cube roots. (16 days/8 Blocks) Unit 2: Literal Equations and One-Variable Equations and Inequalities Solve multi-step linear equations in one variable, including: a. solving literal equations (formulas) for a given variable; b. justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality d. solving multi-step linear equations algebraically and graphically; f. solving practical problems involving equations. Solve multi-step linear inequalities in one variable, including: a. solving multi-step linear inequalities algebraically and graphically; b. justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets; c. solving practical problems involving inequalities. Determine and verify algebraic solutions using a graphing utility. A A.5

2 (10 days/5 blocks) Unit 3: Relations and Functions Investigate and analyze function (linear) families and their characteristics both algebraically and graphically, including: a. determining whether a relation is a function, given ordered pairs, a mapping, a table or a graph; b. identifying domain and range; c. finding zeros of a function e. finding the values of a function for elements in its domain; and f. representing functions using concrete, verbal, numeric, graphic and algebraic forms. A.7 Represent arithmetic and geometric patterns algebraically using function notation. Determine whether a relation, represented by a set of ordered pairs, a table, a mapping, or a graph is a function A.7 Solve multi-step linear equations in one variable. (10 days/5 blocks) Unit 4: Graphing Linear Functions Solve practical problems involving equations. Graph linear equations in two variables, including those that arise from a variety of practical situations. A.6 Determine the slope of a line given an equation of the line, the graph of the line, or two points on the line. Recognize slope as rate of change. Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equation. Identify x- and y-intercepts. A.7 Make connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. Investigate and analyze characteristics and multiple representations of functions with a graphing utility A.7

3 Solve practical problems involving equations. (12 days/6 blocks) Unit 5: Linear Functions Write 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. A.6b Convert between alternative forms of linear equations, including slopeintercept, standard, and point-slope form. Make connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic Given a data set or practical situation, determine whether a direct or inverse variation exists. A.7f A.8 Write an equation for a direct or an inverse variation Graph a direct variation. Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems using linear mathematical models. Write the equation of a line parallel or perpendicular to a given line through a given point. A A.6 Recognize and describe a line with a slope or rate of change that is positive, negative, zero, or undefined. Convert between alternative forms of linear equations including slopeintercept, standard, and point-slope form.

4 Solve practical problems involving inequalities. (10 days/5 blocks) Unit 6: Linear Inequalities A.5 Determine whether an ordered pair is a solution to the inequality given the inequality or graph. Graph linear inequalities in two variables, including those that arise from a variety of practical situations. A.6 Graph linear inequalities given slope-intercept, standard, horizontal, or vertical form. Write the inequality to represent the graph. Identify the intercepts of a function presented algebraically or graphically. Determine and verify algebraic solutions using a graphing utility. A A.5 (14 days/7 blocks) Unit 7: Systems of Equations and Inequalities Solve systems of linear equations graphically and algebraically by substitution and elimination. Solve practical problems involving systems of equations. e,f Solve systems of linear inequalities graphically and verify solutions algebraically. A.5 Solve practical problems using systems of inequalities. Determine whether a coordinate pair is a solution of a linear inequality or a system of linear equations A.5 Determine and verify algebraic solutions using a graphing utility.

5 (14 days/7 blocks) Unit 8: Exponents and Polynomials Simplify monomial expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents. A.2 Express numbers using scientific notation, and perform operations involving scientific notation using the laws of exponents. Add, subtract and multiply polynomials (14 days/7 blocks) Unit 9: Factoring and Polynomial Division Factor completely first- and second-degree polynomials with integral coefficients and identify prime polynomials. use the x-intercepts from the graphical representation of the polynomial to determine and confirm its factors. Simplify the quotient of polynomials using a monomial or binomial divisor, or a completely factored divisor. A.2 (16 days/8 blocks) Unit 10: Quadratic Functions Solve quadratic equations algebraically and graphically. Investigate and analyze quadratic function algebraically and graphically, including: b. domain and range c. zeros of a function d,. x- and y-intercepts e. finding the values of a function for elements in its domain, and f. making connections among multiple representations of functions including concrete, verbal, numeric, graphic and algebraic Collect and analyze data, and determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models. Investigate and analyze characteristics and multiple representations of functions with a graphing utility. A A.7

6 (8 days/4 blocks) Unit 11: Radicals Represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. Express the square roots of whole numbers and the square root of a monomial in simplest radical form. A.1 A.3 Express cube roots of integers in simplest radical form Simplify numerical expressions containing square or cube roots. Simplify cube roots of integers 2016 A.3 Add, subtract, and multiply two monomial expressions limited to a numerical radicand. (20 days/10 blocks) Unit 12: Statistics and Data Analysis Given a set of data, interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores. Construct, compare, contrast, and analyze data, including data from practical situations displayed in box-and-whisker plots. Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using linear and quadratic mathematical models. A.9 A.10 A.11

Equations and Inequalities

Equations and Inequalities Algebra I SOL Expanded Test Blueprint Summary Table Blue Hyperlinks link to Understanding the Standards and Essential Knowledge, Skills, and Processes Reporting Category Algebra I Standards of Learning