Middle School Algebra 1 Pacing Guide Lynchburg City Schools

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1 Grading Period: 1 st Nine Weeks Days to Teach = 44 SOL & Enabling Objectives: Description Text Recommended Activities Time Frame Begin the school year with relationship building activities continue integrating relationship building throughout the school year Activity Ideas PRE-TEST (for Teacher Evaluation & School Improvement: Interactive Achievement) will be released by the division to be administered at a time TBA Begin teaching the 3 rd day of school. DO NOT FEEL BOUND TO THE TEXT BOOK! PLEASE USE ONLINE RESOURCES, APPLETS, & HANDS-ON ACTIVITIES Algebraic Expressions A.1a Translate verbal quantitative situations into algebraic expressions and vice versa. A.1b Model real-world situations w/ algebraic expressions in a variety of representations (concrete, pictorial, symbolic, verbal). A.1c Evaluate algebraic expressions for a given replacement set to include rational numbers ESS A.1ad Translate & Evaluate ESS A.1c Evaluating Simplifying Expressions ESS A3a Simplifying Square Roots ESS A3.b Simplify Radical ESS A.1ad Translate & Evaluate unit = 13

2 A.3a Express square roots of a whole number in simplest form. 2-7 ESS A4b A Mystery to Solve A.3b Express the cube root of a whole number in simplest form. A.1d Evaluate expressions that contain absolute value, square roots, & cube roots. 2-1 Rest =. A.4b Simplify expressions using the field properties of the real numbers and properties of equality to justify simplification 1-4, 1-5, 1-6, justify = 3-5 Solving Linear Equations A.4b Solve equations using the field properties of the real numbers & properties of equality to justify the solution. (review: 3-1, 3-2, 3-3) ESS A.4b a Mystery to Solve Model solving equations = p.127 ESS A.4e Algebra Tiles & Equation Solving for this unit = 12 A.4e Solve multi-step linear equations in one variable. A.4l Determine if a linear equation in one variable has one, an infinite number, or no solutions. 3-4, 3-5 Model p.141 NLVM Algebra Balance Scales NLVM Algebra Balance Scales Negative A.4f Confirm algebraic solutions to linear ESS A.4f Solving Linear Equations

3 equations using a graphing calculator. Middle School Algebra 1 Pacing Guide A.4a Solve a literal equation (formula) for a specific variable. 3-8 Illuminations Lesson Geology Rocks Equations ESS A.4a solve for Unknown Solving Linear Inequalities A.5a Solve multi-step linear inequalities in one variable A.5b Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers 6-1, 6-2, 6-3 (model p.325) ESS A.5a Inequalities ESS A.5b Greetings Solve inequalities Virtual Lab for this unit = 5 A.5c Solve real-world problems involving inequalities. 6-3 Relations A.7d Represent relations & functions using concrete, verbal, numeric, graphic & algebraic forms. Given one representation, students will be able to represent the relation in another form. 4-3, 4-5 (use set builder notation) ESS A.7d Square Patios for this unit = 10 A.7b Identify the domain, range, zeros & intercepts of a function presented algebraically or graphically. 4-6 ESS A.7b Functions 2 ESS A.7a Functions 1

4 A.7a Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function. A.7c For each x in the domain of f, find f(x). A.7e Detect patterns in data and represent arithmetic and geometric patterns algebraically Domain and Range Using Graphs NLVM Function Machine Illuminations Lesson Do You Notice Sum Thing? NLVM Choosing Patterns Flex /Remediation 3 Grading Period: 2 nd Nine Weeks Days to Teach = 45 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Slope Math Forum Activity Slope of a Line A.6f Recognize and describe a line with a slope that is positive, negative, zero, or undefined. 5-1 Interactive Activity Slop Slider unit = 6 A.6e Find the slope of a line, given the graph of a line. 5-3 ESS A 6d Submarine

5 A.6c Find the slope of a line, given the equation of a linear function. A.6d Find the slope of a line, given the coordinates of two points on the line. 5-1 Illuminations Lesson Movement with f(x)s Illuminations Lesson Rise Run Triangles Graphing Linear Equations A.6a Graph linear equations in two variables, including those that arise from a variety of realworld problems. A.6b Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept. A.6h Write an equation of a line when given the graph of a line. pp (incomplete) 5-3 NLVM Line Plotter Line Grapher y=mx + b ESS A.6b Transformationally Speaking Interactive Activity Graphit Illuminations Lesson Trout Pond equation of line unit = 12 A.6g Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equations. 5-3 ESS A.6g Transformation Investigation Seeing math Activity Linear Transformer A.6j Write an equation of a line given the slope and a point on the line whose coordinates are integers. 5-4 ESS A.6i Equations of Lines

6 A.6i Write an equation of a line when given two points on the line whose coordinates are integers. p. 273 (5-3) ESS A.6i Slippery Slope A.6k Write an equation of a vertical line as x = a ESS A.6k slope 2 slope A.6l Write an equation of a horizontal line as y = c p. 273 (5-3) & p. 287 (5-5) Direct & Inverse Variation A.8a Given a situation, including a real-world situation, determine whether a direct variation exists. A.8c Write an equation for a direct variation, give a set of data. 5-2 ESS a.8a Direct Variation Illuminations Lesson Mow Whole Thing? Interactive Activity Graphit unit = 6 A.8e Graph an equation representing a direct variation, given a set of data. ESS A.8b Inverse Variation A.8b Given a situation, including a real-world situation, determine whether an inverse variation exists A.8d Write an equation for an inverse variation, given a set of data. Exam Review/Semester Exam unit = 6

7 Solving Systems of Linear Equations A.4h Given a system of two linear equations in two variables that has a unique solution, solve the system graphically by identifying the point of intersection. 7-1 ESS A.4h Spring Fling Carnival unit =9 A.4g Given a system of two linear equations in two variables that has a unique solution, solve the system by substitution of elimination to find the ordered pair which satisfies both equations. A.4i Determine whether a system of two linear equations has one solutions, no solution, or infinite solutions. 7-2, , 7-2, 7-3 ESS A4.g All.c How Much is that Tune Illuminations Lesson Supply & Demand ESS A.4i Road Trip ESS A.4j2 Exercise Fields A.4j Write a system of two linear equations that models a real-world situation. 7-1, 7-2, 7-3, 7-4 ESS A.5d Graphing System Inequalities A.4k Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a real-world situation. 7-1, 7-2, 7-3, 7-4 Interactive Activity Linear Inequalities Solving Systems of Linear Inequalities Solve systems inequalities lesson plan

8 A.5d Solve systems of linear inequalities algebraically and graphically. 7-6 Henrico systems of inequalities resources unit = 4 Flex /Remediation: 4 Grading Period: 3 rd Nine Weeks Days to Teach = 48 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Polynomials (For 8-1) ESS A2a Exponents A.2a Simplify monomial expressions & ratios of monomial expressions in which the exponents are integers, using the laws of exponents. 8-1, 8-2, 8-3 (for 8-2) ESS A2 a Scientifically Speaking (sci. not.) unit = 18 A.2b Model sum & difference of polynomials w/ concrete objects & their related pictorial representations. Sums/Dif = pp Algebra Tiles (see A.2d, A.2e, A.2f) Virtual Algebra Tiles A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2d Find sums & differences of polynomials. 8-5 ESS A2.d Add Subtract Polynomials Alg Tiles (Algebra Tiles (see A.2d, A.2e, A.2f)

9 A.2b Model products of polynomials w/ concrete objects & their related pictorial representations. pp NLVM Algebra Tiles A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2e Find the products of polynomials. The factors will have no more that five total terms. 8-6, 8-7 ESS A.2e Multiply Poly With Alg Tiles A.2b Model quotients of polynomials w/ concrete objects & related pictorial representations. pp. 416, 667 ESS A2.f Divide Poly with Alg. Tiles A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2f Find the quotient of polynomials, using a monomial or binomial divisor, or a complete factored divisor.. Factoring Polynomials A.2g Factor completely first-and second-degree polynomials w/ integral coefficients A.2h Identify prime polynomials 9-1, 9-2, 9-3, 9-4, 9-5, 9-6 ESS A.2g Factoring NLVM Algebra Tiles unit = 13

10 A.2i Use the x-intercepts from the graphical representation of the polynomial to determine & confirm its factors Finding Roots of Expressions & Quadratic Equations A.3c Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values Cutting Corners solving quadratic equations lesson unit = 8 A.4c Solve quadratic equations. A.4d Identify the roots or zeros of a quadratic function over the real number system as the solutions to the quadratic equation that is formed by setting the given quadratic expression equal to zero Solving quadratic equation practice ESS A4.d Factoring for Zeros A.4f Confirm algebraic solutions to quadratic equations, using a graphing calculator. 10-1, 10-2 Statistics Curve of Best Fit Optional Line of best fit A.11a Write an equation for a curve of best fit, given a set of no more that twenty data points 5-7 pp ESS A.11d Line of Best Fit ESS A11a Linear Curve Best Fit unit = 6

11 in a table, a graph, or real-world situation. A.11b Make predictions about unknown outcomes, using the equation of the curve of best fit. A.11c Design experiments and collect data to address specific, real-world questions. A.11d Evaluate the reasonableness of a mathematical model of a real-world situation Interactive Activity Regression ESS A.11b Quadratic Curve Best Fit ESS A4c A11c How Much is that Tune Get a Half Life curve of best fit lesson plan Flex /Remediation 3 Grading Period: 4 th Nine Weeks Days to Teach = 43 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Statistics ESS A.9a Analyzing Interpreting Stats A.9a Analyze descriptive statistics to determine the implications for the real-world situations from which the data drive. Interactive Activity Measures Interactive Activity Normal Distribution unit = 17 A.9b Given data, including data in a real-world context, calculate & interpret the mean absolute deviation of a data set. ESS A9.b Exploring Stats ESS A.9c Calculating Measures Dispersion

12 A.9c Given data, including data in a real-world context, calculate variance & standard deviation of a data set & interpret the standard deviation. TI z-score activity ESS A9.d Z-scores Z-score worksheet Z-score video A.9d Given data, including data in a real-world context, calculate & interpret z-score for a data set. A.9e Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation. A.9f Compare & contrast mean absolute deviation & standard deviation in real-world context. A.10 Compare, contrast,& analyze data, including data from real-world situations displayed in box-and-whisker plots Z scores activity PA mean absolute deviation lesson plan Atlanta Schools mean absolute deviation SAD to MAD Annenberg Media mean absolute deviation ESS A10 Box-and Whisker Plots Illuminations Activity Box Plotter Illuminations lesson plan_nba & box plots POST-TEST (for Teacher Evaluation & School Improvement use same test as PRE-TEST 1 day SOL Review & Testing: 23 Days Final Exam Review & Testing 2

13 RECOMMENDED WEBSITES for additional lesson plans, activities, virtual manipulatives, and applets: Illuminatinos_NCTM Henrico Algebra Resources Algebra 1 resources Algebra Bits Project interactive Suffolk Algebra Resources Texas Instruments Activities National Library of Virtual Manipulatives NVLM Florida lesson plans Jefferson Lab Sol Review Algebra 1: Math Cross Walk 2001 and 2009 SOLs Changes to the reporting categories for Algebra 1 sol test: Now there are 3 reporting categories instead of 4. Relations & functions and statistics have been combined into 1 strand. Also, the Algebra 1 Formula Sheet has been revised Reporting Category 2009 SOL # items % of test # of items % of test Expressions & A.1, A.2a-c, A % 12 24% Operations Equations & A.4a-f, A.5a-d, A6 a % 18 36% Inequalities b Functions & Statistics A.7a-f, A.8, A.9, A.10, A % 20 40%

14 Middle School Alg. 1: SOL CONCEPT OVERVIEW 1 st 9 weeks = 44 Algebraic Expressions Solving Linear Equations Solving Linear Inequalities Relations nd 9 weeks = 45 Slope Graphing Linear Equations Direct & Inverse Variation Solving Systems of Linear Equations Solving Systems of Linear Inequalities

15 3 rd 9 weeks = 48 Polynomials Factoring Polynomials Find Roots of Expressions & Quadratic Equations Statistics Curve of Best Fit th 9 weeks = 43 Statistics SOL Review & Testing 17 23