2016 Mathematics Standards of Learning Algebra I Overview

2016 Mathematics Standards of Learning Algebra I Overview of Revisions from 2009 to 2016 Related documents available on VDOE Mathematics 2016 webpage 1

Purpose • Overview of the 2016 Mathematics Standards of Learning and the Curriculum Framework • Highlight information included in the Essential Knowledge and Skills and the Understanding the Standard sections of the Curriculum Framework 2

Agenda • Overview and Implementation Timeline • Resources Currently Available – Crosswalk (Summary of Revisions) – Standards and Curriculum Frameworks • Comparison of 2009 to 2016 Standards – – Expressions and Operations Equations and Inequalities Functions Statistics 3

Implementation Timeline 2016 -2017 School Year – Curriculum Development VDOE staff provides a summary of the revisions to assist school divisions in incorporating the new standards into local written curricula for inclusion in the taught curricula during the 2017 -2018 school year. 2017 -2018 School Year – Crossover Year 2009 Mathematics Standards of Learning and 2016 Mathematics Standards of Learning are included in the written and taught curricula. Spring 2018 Standards of Learning assessments measure the 2009 Mathematics Standards of Learning and include field test items measuring the 2016 Mathematics Standards of Learning. 2018 -2019 School Year – Full-Implementation Year Written and taught curricula reflect the 2016 Mathematics Standards of Learning assessments measure the 2016 Mathematics Standards of Learning. 4

2016 SOL Revisions • Improve the vertical progression of mathematics content • Ensure developmental appropriateness of student expectations • Increase support for teachers in mathematics content • Clarify expectations for teaching and learning • Improve precision and consistency in mathematical language and format • Ensure proficiency of elementary students in computational skills 5

Support for Teachers • Significant additions to the Understanding the Standard column including – – Definitions Explanations Examples Instructional connections • Improvements in precision, clarity, and consistency in language K-12 • Indicators of SOL sub-bullet added to each bullet within the Essential Knowledge and Skills 6

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Overview of Changes Reporting Category # of Standards (2009) # of Standards (2016) Expressions and Operations 3 3 Equations and Inequalities 3 3 Functions 1 1 Statistics 4 2 11 9 Total 8

Mathematics Process Goals for Students “The content of the mathematics standards is intended to support the five process goals for students” - 2009 and 2016 Mathematics Standards of Learning Communication Connections Problem Solving Representations Mathematical Understanding Reasoning 9

Standards of Learning Curriculum Frameworks Introduction includes: • Mathematical Process Goals for Students • Instructional Technology • Computational Fluency New • Algebra Readiness • Equity 10

2009 2016 11

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EXPRESSIONS AND OPERATIONS 13

2009 SOL 2016 SOL A. 1 The student will represent verbal quantitative A. 1 The student will situations algebraically and evaluate these a) represent verbal quantitative situations expressions for given replacement values of the algebraically; and variables. b) evaluate algebraic expressions for given replacement values of the variables. Revisions: • SOL A. 1 a EKS - Translate between verbal quantitative situations algebraically with expressions and equations (previously included only expressions) is included • SOL A. 1 b EKS - Clarified to evaluate algebraic expressions contain absolute value, square roots, and cube roots without rationalizing denominators 14

2009 SOL A. 2 The student will perform operations on polynomials, including a) applying the laws of exponents to perform operations on expressions; b) adding, subtracting, multiplying, and dividing polynomials; and c) factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations. [Moved to EKS] 2016 SOL A. 2 The student will perform operations on polynomials, including a) applying the laws of exponents to perform operations on expressions; b) adding, subtracting, multiplying, and dividing polynomials; and c) factoring completely first- and second-degree binomials and trinomials in one variable. Revisions: • SOL A. 2 b EKS - Modeling operations of polynomials with concrete objects includes both pictorial and symbolic representations; products of polynomials are limited to five or fewer terms • SOL A. 2 c EKS - Factoring binomials or trinomials is limited to one variable (two variables included in Algebra II) and the leading coefficient is limited to be an integer with no more than four factors after factoring out a greatest common factor; identifying prime polynomials is no longer included • SOL A. 2 c EKS - Graphing calculator used as a tool moved from standard to EKS and referred to as “graphing utility” 15

2009 SOL 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. 2016 SOL A. 3 The student will simplify a) square roots of whole numbers and monomial algebraic expressions; b) cube roots of integers; and c) numerical expressions containing square or cube roots. Revisions: • SOL A. 3 b – Simplify cube roots of all integers (previously limited to whole numbers) • SOL A. 3 c EKS – Includes simplifying numerical expressions containing square or cube roots that may involve addition, subtraction, and multiplication of two monomial radical expressions (limited to a numerical radicand) 16

EQUATIONS AND INEQUALITIES 17

2009 SOL 2016 SOL A. 4 The student will solve multistep linear and quadratic A. 4 The student will solve equations in two variables, including a) multistep linear equations in one variable a) solving literal equations (formulas) for a given variable; algebraically; b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality b) quadratic equations in one variable algebraically; that are valid for the set of real numbers and its subsets; c) solving quadratic equations algebraically and graphically; c) literal equations for a specified variable; d) systems of two linear equations in two variables d) solving multistep linear equations algebraically and graphically; and e) solving systems of two linear equations in two variables e) practical problems involving equations and algebraically and graphically; and systems of equations. 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. [Moved to EKS] Revisions: • SOL A. 4 a EKS - Includes determining if a linear equation has one solution, no solution, or an infinite number of solutions • SOL A. 4 a, b EKS - Includes applying properties of real numbers and properties of equality when solving linear and quadratic equations • SOL A. 4 b EKS - Clarifies that solving quadratic equations includes those with both rational and irrational solutions • SOL A. 4 e - Real-world problems are now referred to as practical problems in the 2016 standards 18

2009 SOL 2016 SOL A. 5 The student will solve multistep linear inequalities in two variables, including a) solving multistep 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; [Moved to EKS] c) solving real-world problems involving inequalities; and d) solving systems of inequalities. A. 5 The student will a) solve multistep linear inequalities in one variable algebraically and represent the solution graphically; b) represent the solution of linear inequalities in two variables graphically; c) solve practical problems involving inequalities; and d) represent the solution to a system of inequalities graphically. Revisions: • SOL A. 5 a-d EKS - Includes determine and verify algebraic solutions using a graphing utility • SOL A. 5 a EKS - clarifies that students will solve multistep linear inequalities in one variable algebraically and represent the solution graphically; includes apply properties of real numbers and properties of inequality • SOL A. 5 c - Real-world problems are now referred to as practical problems in the 2016 standards; A. 5 c EKS includes determine if a coordinate pair is a solution of an inequality or system of inequalities • SOL A. 5 d EKS - Clarified that solutions to systems of inequalities should be represented graphically 19

2009 SOL 2016 SOL 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. A. 6 The student will a) determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line; b) 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; and c) graph linear equations in two variables. Revisions: • SOL A. 6 - Includes linear equations in two variables only (graphing linear inequalities in two variables is now included in A. 5) • SOL A. 6 b EKS - Includes writing the equation of a line parallel or perpendicular to a given line through a given point 20

FUNCTIONS 21

2009 SOL 2016 SOL A. 7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including a) determining whether a relation is a function; 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 between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. A. 7 The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including a) determining whether a relation is a function; b) domain and range; c) zeros; d) intercepts; e) values of a function for elements in its domain; and f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. Revisions: • SOL A. 7 EKS - No longer includes detect patterns in data and represent arithmetic and geometric patterns algebraically [Included in AFDA. 1 and AII. 5] SOL A. 7 EKS - Includes investigate and analyze characteristics and multiple representations of linear and quadratic functions using a graphing utility SOL A. 7 a EKS - Includes determine whether a relation represented by a mapping is a function SOL A. 7 d EKS - Includes the use of x-intercepts from the graphical representation of a quadratic function to determine and confirm its factors 22

Middle School Revisions Leading to Algebra I 23

STATISTICS 24

2009 SOL 2016 SOL A. 8 The student, given a situation in a real-world A. 8 The student, given a data set or practical context, will analyze a relation to determine situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically. Revisions: • Replace “given a situation” in the 2009 standard with “given a data set or practical situation” in the 2016 standard 25

2009 SOL 2016 SOL 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. [Included in AFDA. 7 and AII. 11] A. 10 The student will compare and contrast multiple univariate data sets, using box- and-whisker plots. [Moved to 8. 12] Revisions: • Interpret variation in real-world contexts and calculate and interpret standard deviation, and z-scores now included in AFDA. 7 and AII. 11 • Calculate and interpret mean absolute deviation removed • Compare and contrast multiple univariate data sets, using box-and-whisker plots moved to 8. 12 26

2009 SOL 2016 SOL A. 11 The student will collect and analyze data, A. 9 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world order to make predictions, and solve practical problems, using mathematical models of linear Mathematical models will include linear and quadratic functions. Revisions: • Design experiments and collect data to address specific, real-world questions was removed [Included in AFDA. 8] • Determine the equation of best fit was clarified to be performed with the use of a graphing utility • Real-world problems are now referred to as practical problems in the 2016 standards 27

Questions? Please contact the VDOE Mathematics Team Mathematics@doe. virginia. gov 28