# Virginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning

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1 BUI L T F O VIR R G INIA Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning

3 Grade 6 Virginia -Specific Learning Pathway Number and Operations in Base Ten Number and Operations - Fractions The Number System VA SOL -Specific Standards-Aligned Pathways Adding and Subtracting Decimals 6.7 The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals. Adding and Subtracting Decimals in Real-World Situations 6.7 The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals. Using Reasoning and Estimation to Calculate with Decimals 6.7 The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals. Calculating with Decimals 6.7 The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals. Adding Fractions - Estimation Strategies 6.6.b estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions Subtracting Fractions - Estimation Strategies 6.6.b estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions Multiplying Fractions by Whole Numbers Multiplying Fractions by Whole Numbers Solving Word Problems with Multiplication of Fractions by Whole Numbers Multiplying Fractions by Whole Numbers to Solve Multistep Problems Dividing Fractions by Whole Numbers Dividing Whole Numbers by Fractions Using the Relationship Between Multiplication and Division to Divide Fractions Dividing Fractions by Fractions Using Division of Fractions to Represent and Solve Problems 6.6.b estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions Operations with Fractions - Mixed Practice 6.6.b estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions Integer Concepts 6.3.a identify and represent integers 6.3.b order and compare integers Integer Concepts with a Number Line 6.3.a identify and represent integers 6.3.b order and compare integers 3

4 Grade 6 Virginia -Specific Learning Pathway The Number System (continued) Ratios and Proportional Relationships Absolute Value I 6.3.c identify and describe absolute value of integers Absolute Value II 6.3.c identify and describe absolute value of integers Comparing Rational Numbers I 6.2.d compare and order fractions, decimals, and percents 6.3.b order and compare integers Comparing Rational Numbers II 6.2.d compare and order fractions, decimals, and percents 6.3.b order and compare integers Classifying and Ordering Real Numbers 6.2.d compare and order fractions, decimals, and percents 6.3.b order and compare integers Integers in the Coordinate Plane I Integers in the Coordinate Plane II Rational Numbers in the Coordinate Plane I Rational Numbers in the Coordinate Plane II Distance on the Coordinate Plane II Identifying Ratios 6.1 The student will describe and compare data, using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Ratios 6.1 The student will describe and compare data, using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Percent Concepts 6.2.a investigate and describe fractions, decimals, and percents as ratios 6.2.b identify a given fraction, decimal, or percent from a representation 6.2.d compare and order fractions, decimals, and percents Reasoning with Percents 6.2.d compare and order fractions, decimals, and percents Calculations with Percent 6.2.d compare and order fractions, decimals, and percents VA SOL -Specific Standards-Aligned Pathways 4

5 Grade 6 Virginia -Specific Learning Pathway Expressions and Equations Geometry Measurement and Data Statistics and Probability Fraction, Decimal, and Percent Equivalents 6.2.c demonstrate equivalent relationships among fractions, decimals, and percents Evaluating Simple Expressions 6.8 The student will evaluate whole number numerical expressions, using the order of operations. Reasoning About One-Step Equations 6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions. Writing and Solving One-Step Equations 6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions. Understanding Exponents 6.5 The student will investigate and describe concepts of positive exponents and perfect squares. Concept of Inequalities I 6.20 The student will graph inequalities on a number line. Area of Parallelograms 6.10.c solve practical problems involving area and perimeter Area of Triangles 6.10.c solve practical problems involving area and perimeter Area of Trapezoids and Composite Figures 6.10.c solve practical problems involving area and perimeter Circumference 6.10.a define pi as the ratio of the circumference of a circle to its diameter 6.10.b solve practical problems involving circumference and area of a circle, given the diameter or radius Area of Circles 6.10.b solve practical problems involving circumference and area of a circle, given the diameter or radius Surface Area and Volume of Rectangular Prisms 6.10.d describe and determine the volume and surface area of a rectangular prism Introduction to the Coordinate Plane Representing Real-World Quantities in the First Quadrant Distance on the Coordinate Plane I Volume of Rectangular Prisms I 6.10.d describe and determine the volume and surface area of a rectangular prism Volume of Rectangular Prisms II 6.10.d describe and determine the volume and surface area of a rectangular prism Circle Graphs 6.14.a construct circle graphs 6.14.b draw conclusions and make predictions, using circle graphs Simple Probability 6.16.b determine probabilities for dependent and independent events VA SOL -Specific Standards-Aligned Pathways 5

6 Grade 7 Virginia -Specific Learning Pathway Expressions and Equations Introduction to the Language of Algebra 7.13.a write verbal expressions as algebraic expressions and sentences as equations and vice versa Evaluating Expressions with Two Operations 7.13.b evaluate algebraic expressions for given replacement values of the variables Evaluating Expressions with Real Numbers I 7.16.a The student will apply the following properties of operations with real numbers: a. the commutative and associative properties for addition and multiplication 7.16.b The student will apply the following properties of operations with real numbers: b. the distributive property 7.16.c The student will apply the following properties of operations with real numbers: c. the additive and multiplicative identity properties 7.16.d The student will apply the following properties of operations with real numbers: d. the additive and multiplicative inverse properties 7.16.e The student will apply the following properties of operations with real numbers: e. the multiplicative property of zero Evaluating Expressions with the Distributive Property 7.16.b The student will apply the following properties of operations with real numbers: b. the distributive property Using the Distributive Property to Represent Real-World Situations 7.16.b The student will apply the following properties of operations with real numbers: b. the distributive property Solving and Modeling Two-Step Problems 7.14.a solve one- and two-step linear equations in one variable 7.14.b solve practical problems requiring the solution of one- and two-step linear equations Solving Equations with the Distributive Property 7.16.b The student will apply the following properties of operations with real numbers: b. the distributive property Solving Equations with the Distributive Property in Context 7.16.b The student will apply the following properties of operations with real numbers: b. the distributive property Solving Two-Step Equations 7.14.a solve one- and two-step linear equations in one variable 7.14.b solve practical problems requiring the solution of one- and two-step linear equations Solving Word Problems with Algebra 7.12 The student will represent relationships with tables, graphs, rules, and words b solve practical problems requiring the solution of one- and two-step linear equations Interpreting Slope 7.12 The student will represent relationships with tables, graphs, rules, and words. Understanding Square and Cube Roots 7.1.d determine square roots Interpreting Numbers Written in Scientific Notation 7.1.b determine scientific notation for numbers greater than zero 7.1.c compare and order fractions, decimals, percents, and numbers written in scientific notation Concept of Inequalities II 7.15.a solve one-step inequalities in one variable 7.15.b graph solutions to inequalities on the number line VA SOL -Specific Standards-Aligned Pathways 6

7 Grade 7 Virginia -Specific Learning Pathway Ratios and Proportional Relationships The Number System Interpreting Rates on Graphs 7.12 The student will represent relationships with tables, graphs, rules, and words. Proportion Concepts 7.12 The student will represent relationships with tables, graphs, rules, and words. Proportional Relationships in Tables and Equations 7.12 The student will represent relationships with tables, graphs, rules, and words. Interpreting Points on Graphs of Proportional Relationships 7.12 The student will represent relationships with tables, graphs, rules, and words. Distance, Rate, and Time 7.14.b solve practical problems requiring the solution of one- and two-step linear equations Introduction to Similar Figures 7.6 The student will determine whether plane figures quadrilaterals and triangles are similar and write proportions to express the relationships between corresponding sides of similar figures. Using Similar Figures to Solve Problems 7.6 The student will determine whether plane figures quadrilaterals and triangles are similar and write proportions to express the relationships between corresponding sides of similar figures. Adding and Subtracting Rational Numbers I 7.3.a model addition, subtraction, multiplication, and division of integers 7.3.b add, subtract, multiply, and divide integers Adding and Subtracting Rational Numbers II 7.3.a model addition, subtraction, multiplication, and division of integers 7.3.b add, subtract, multiply, and divide integers Multiplying and Dividing Rational Numbers 7.3.a model addition, subtraction, multiplication, and division of integers 7.3.b add, subtract, multiply, and divide integers Writing and Interpreting Expressions with Rational Numbers 7.3.a model addition, subtraction, multiplication, and division of integers 7.3.b add, subtract, multiply, and divide integers Operations with Rational Numbers I 7.3.a model addition, subtraction, multiplication, and division of integers 7.3.b add, subtract, multiply, and divide integers Operations with Rational Numbers II 7.3.a model addition, subtraction, multiplication, and division of integers 7.3.b add, subtract, multiply, and divide integers VA SOL -Specific Standards-Aligned Pathways 7

8 Grade 7 Virginia -Specific Learning Pathway Geometry Statistics and Probability Building Functions Classifying Quadrilaterals II 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. Surface Area and Volume of Rectangular Prisms 7.5.b solve practical problems involving the volume and surface area of rectangular prisms and cylinders Surface Area of Cylinders 7.5.b solve practical problems involving the volume and surface area of rectangular prisms and cylinders Volume of Cylinders 7.5.a describe volume and surface area of cylinders 7.5.b solve practical problems involving the volume and surface area of rectangular prisms and cylinders Translations 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. Reflections 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. Rotations 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. Dilations 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. Bar Graphs and Histograms 7.11.a construct and analyze histograms Compound Probability 7.10 The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle. Direct Variation 7.12 The student will represent relationships with tables, graphs, rules, and words. VA SOL -Specific Standards-Aligned Pathways 8

9 Grade 8 Virginia -Specific Learning Pathway Ratios and Proportional Relationships Expressions and Equations Functions Concept of Ratios and Rates Using Ratios to Solve Problems Identifying Rates Solving Problems with Rates Converting s of Measure I Converting s of Measure II Using Proportions to Solve Problems Proportions in Scale Drawings Percent and Percent Change 8.3.b determine the percent increase or decrease for a given situation Percent and Percent Error Simple Interest Evaluating Expressions and Equations with Exponents 8.1.a simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers Analyzing Solution Sets to Linear Equations with the Variable on Both Sides 8.15.a solve multistep linear equations in one variable with the variable on one and two sides of the equation Solving Equations with the Variable on Both Sides 8.15.a solve multistep linear equations in one variable with the variable on one and two sides of the equation Understanding Square and Cube Roots 8.5.b find the two consecutive whole numbers between which a square root lies Approximating Values of Irrational Numbers 8.5.b find the two consecutive whole numbers between which a square root lies Interpreting Numbers Written in Scientific Notation 8.1.b compare and order decimals, fractions, percents, and numbers written in scientific notation Interpreting Graphs of Real-World Situations 8.14 The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship. Introduction to Sketching Graphs of Real-World Situations 8.14 The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship. VA SOL -Specific Standards-Aligned Pathways 9

10 Grade 8 Virginia -Specific Learning Pathway Geometry Statistics and Probability Area of Complex Composite Figures 8.11 The student will solve practical area and perimeter problems involving composite plane figures. Surface Area of Pyramids 8.7.a investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids Surface Area of Cones 8.7.a investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids Volume of Cylinders 8.7.a investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids Volume of Pyramids and Cones 8.7.a investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids Angle Pairs 8.6.a verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles Parallel Lines and Transversals 8.6.a verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles Pythagorean Theorem - Hypotenuse 8.10.b apply the Pythagorean Theorem Pythagorean Theorem - Legs 8.10.b apply the Pythagorean Theorem Pythagorean Theorem - Mixed Problems 8.10.b apply the Pythagorean Theorem Pythagorean Theorem - Distance Formula 8.10.b apply the Pythagorean Theorem Translations 8.8.a apply transformations to plane figures Reflections 8.8.a apply transformations to plane figures Rotations 8.8.a apply transformations to plane figures Composition of Transformations 8.8.a apply transformations to plane figures Dilations 8.8.a apply transformations to plane figures Quartiles 8.13.a make comparisons, predictions, and inferences, using information displayed in graphs Box Plots 8.13.a make comparisons, predictions, and inferences, using information displayed in graphs Compound Probability 8.12 The student will determine the probability of independent and dependent events with and without replacement. VA SOL -Specific Standards-Aligned Pathways 10

11 Algebra I Virginia -Specific Learning Pathway Expressions and Equations Language of Algebra A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. Solving Rational and Radical Equations I 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. Slope A.6.a 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. Graphing Inequalities and Systems of Inequalities in Real-World Situations A.5.d The student will solve multistep linear inequalities in two variables, including d. solving systems of inequalities. A.6.a 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. Understanding Properties of Integer Exponents A.2.a The student will perform operations on polynomials, including a. applying the laws of exponents to perform operations on expressions. Applying Properties of Integer Exponents A.2.a The student will perform operations on polynomials, including a. applying the laws of exponents to perform operations on expressions. Factoring Expressions A.2.c The student will perform operations on polynomials, including c. factoring completely first- and second-degree binomials and trinomials in one or two variables. A.4.b The student will solve multistep linear and quadratic equations in two variables, including b. justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets. Simplifying Monomials A.2.c The student will perform operations on polynomials, including c. factoring completely first- and second-degree binomials and trinomials in one or two variables. Using Rational Exponents to Rewrite Expressions A.2.c The student will perform operations on polynomials, including c. factoring completely first- and second-degree binomials and trinomials in one or two variables. Common Factors in Polynomials A.2.c The student will perform operations on polynomials, including c. factoring completely first- and second-degree binomials and trinomials in one or two variables. VA SOL -Specific Standards-Aligned Pathways 11

12 Algebra I Virginia -Specific Learning Pathway Interpreting Functions Seeing Structure in Expressions Graphs of Real-World Functions I A.7.f The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including f. making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. Sketching Graphs of Real-World Situations A.7.f The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including f. making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. Graphs of Real-World Functions II A.7.f The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including f. making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. Graphing Linear Equations A.6 The student will graph linear equations and linear inequalities in two variables. Slope and Rate of Change A.6.a 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. Equations in Slope Form A.6.b The student will graph linear equations and linear inequalities in two variables, including 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. Evaluating Expressions with Real Numbers II A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. A.4.b The student will solve multistep linear and quadratic equations in two variables, including b. justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets. Simplifying Algebraic Expressions A.4.b The student will solve multistep linear and quadratic equations in two variables, including b. justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets. Factoring Polynomials A.2.c The student will perform operations on polynomials, including c. factoring completely first- and second-degree binomials and trinomials in one or two variables. VA SOL -Specific Standards-Aligned Pathways 12

13 Algebra I Virginia -Specific Learning Pathway Reasoning with Equations and Inequalities Creating Equations Functions Building Functions Solving Multistep Equations A.4.b The student will solve multistep linear and quadratic equations in two variables, including b. justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets. Inequalities A.5.a The student will solve multistep linear inequalities in two variables, including a. solving multistep linear inequalities algebraically and graphically. A.5.c The student will solve multistep linear inequalities in two variables, including c. solving real-world problems involving inequalities. Graphing Inequalities A.6.a 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. Using the Quadratic Formula A.4.c The student will solve multistep linear and quadratic equations in two variables, including c. solving quadratic equations algebraically and graphically. Solving Quadratics - Completing the Square A.4.c The student will solve multistep linear and quadratic equations in two variables, including c. solving quadratic equations algebraically and graphically. Complex Numbers and Complex Solutions A.4.c The student will solve multistep linear and quadratic equations in two variables, including c. solving quadratic equations algebraically and graphically. Solving Literal Equations A.4.a The student will solve multistep linear and quadratic equations in two variables, including a. solving literal equations (formulas) for a given variable Slope-Intercept Form A.6.b The student will graph linear equations and linear inequalities in two variables, including 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. Point-Slope Form A.6.b The student will graph linear equations and linear inequalities in two variables, including 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. Direct Variation A.8 The student, given a situation in a real-world context, 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. VA SOL -Specific Standards-Aligned Pathways 13

14 Algebra I Virginia -Specific Learning Pathway Arithmetic with Polynomials and Rational Expressions Linear, Quadratic, and Exponential Models Statistics and Probability Adding and Subtracting Polynomials A.2.a The student will perform operations on polynomials, including a. applying the laws of exponents to perform operations on expressions. A.2.b The student will perform operations on polynomials, including b. adding, subtracting, multiplying, and dividing polynomials. Multiplying and Dividing Monomials A.2.a The student will perform operations on polynomials, including a. applying the laws of exponents to perform operations on expressions. A.2.b The student will perform operations on polynomials, including b. adding, subtracting, multiplying, and dividing polynomials. Multiplying Polynomials A.2.a The student will perform operations on polynomials, including a. applying the laws of exponents to perform operations on expressions. A.2.b The student will perform operations on polynomials, including b. adding, subtracting, multiplying, and dividing polynomials. Graphs of Quadratic Functions A.7.a 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. A.7.d The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including d. x- and y-intercepts. A.7.e The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including e. finding the values of a function for elements in its domain. A.7.f The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including f. making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. Problem Solving with Quadratic Functions A.4.c The student will solve multistep linear and quadratic equations in two variables, including c. solving quadratic equations algebraically and graphically. Quartiles A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots. Box Plots A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots. Comparing Data A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots. Standard Deviation 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. VA SOL -Specific Standards-Aligned Pathways 14

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