ALGEBRA I (Created 2014) Amherst County Public Schools

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1 ALGEBRA I (Created 2014) Amherst County Public Schools The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity the content that all teachers should teach and all students should learn. Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for each standard. The Curriculum Framework is divided into two columns: Essential Understandings and Essential Knowledge and Skills. The purpose of each column is explained below. The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise. Virginia Department of Education (http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/) Textbook Overview Course Text: Algebra I, Holt McDougal, 2012

2 Suggested Sequence of Instruction and Pacing First Nine Weeks SOL Chapter/Sections/Topic Time Frame (Tentative) Pre-Requisite Skills Numbers / Number Sense 2 Days A.1 Verbal Expressions 3 Days A.1, A.4b, A.5b Properties, Simplifying Expressions 8 Days A.4d Solving Equations 10 Days A.5a Solving Inequalities 3 Days A.4a Literal Equations 3 Days A.4f, A.5c Word Problems 4 Days A.4a Linear Equations (solving for y)* 3 Days A.7b Graphing Point on Coordinate Plane/Domain and Range* 3 Days Review/Testing 6-8 Days 45 Days *Due to threat of inclement weather, linear equations (solving for y), graphing points, and domain and range should be covered in the first nine weeks, but will be assessed on the 2 nd Nine Weeks.

3 Second Nine Weeks SOL Chapter/Sections/Topic Time Frame (Tentative) A.7 Functions 3-4 Days A.7 (e) Graphing Lines from a Table 4 Days A.6 (a) Slope 4-5 Days A.6 (a) Graphing Lines from Slope and Intercept 4 Days A.6 (b) Writing the Equation of a Line 5 Days A.8 Direct & Inverse Variation 3 Days A.6 (a,b) Linear Inequalities 4 Days A.4 (e) Systems of Equations, Intro and Solve by Graphing # 4 Days A.4 (e) Systems of Equations by Substitution # 4 Days Review and Testing 8 Days 45 Days # = Because of typical inclement weather in the third nine weeks, these items will be presented in the 2 nd nine weeks but tested in the 3 rd.

4 Third Nine Weeks SOL Chapter/Sections/Topic Time Frame (Tentative) A.4 (e) Systems of Equations by Elimination 6-7 Days A.5 (d) Systems of Inequalities 4 Days A.2 (a) Exponent Rules 10 Days A.2 (b) Operations with Polynomials 10 Days A.2 (c) Factoring numbers, expressions of the form x 2 + bx + c 3 Days Review / Testing (less total days because of typical inclement weather during this time) 4-6 Days 40 Days

5 Fourth Nine Weeks SOL Chapter/Sections/Topic Time Frame (Tentative) A.2 (c) Factoring Expression of the form ax 2 + bx + c 5 days A.3 Simplifying Square Roots and Cube Roots 4 6 days A.4 (c) Quadratic Equations 5 7 days A.9, A.10, A.11 Statistics 7 10 days Practice SOL Exam (Most Recent Released Exam) Review for SOL Exam Remediation / Extra Topics as Determined by Teacher 2 Days 7-10 Days 5-8 Days 45 Days

6 First Nine Weeks Instruction SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary 1.2, 1.3, 1.4, 1.5, 1.6 Glencoe Student Workbook Sec. 1-2 Rational number Integer All Real Numbers Order of Operations A.1 The student will represent verbal 1.1 Glencoe Student Write the following verbal expression as Expression quantitative situations algebraically Workbook Sec 1-1 algebraic. Quantitative Write the following algebraic expression Representation as verbal. Absolute value Variable A.1 and evaluate these Glencoe Student What is the value of the following Replacement value expressions for given replacement Workbook Sec 1-5 expression when? Square root values of the variables. Find the value of three more than twice Cube root a number when the number is 2. A.4 (b) The student will solve multistep 1.7 Glencoe Student Name each property used to simplify the Associative Property linear and quadratic equations in two Workbook Sec 1-3 expression. Commutative Property variables, including justifying steps used Which property is shown from line 3 to Distributive Property

7 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary in simplifying expressions and solving line 4? Equality Properties equations, using field properties and Name each property used to solve the Identity Properties axioms of equality that are valid for the equation. Inverse Properties set of real numbers and its subsets Simplify the Expression Simplify Which expression is in simplified form? Combine Like Terms A.5 (b) The student will solve multistep What would be the next line if the Division Property of linear inequalities in two variables, Division Property of Inequality is used? Inequality including 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; A.4 (d) The student will solve multistep 2-1, 2-2, 2- Glencoe Student Find the solution to the equation. Solve linear and quadratic equations in two 3, 2-4, 2-7 Workbook Sec 2- Which is the solution for? Solution variables, including solving multistep 2, 2-3, and 2-4 linear equations algebraically and graphically A.5 (a) The student will solve multistep 3-2, 3-3, 3- Glencoe Student Find the solution to the inequality. Inequality linear inequalities in two variables, 4, 3-5 Workbook Sec 5-1, Which is the solution for? Linear Inequality including solving multistep linear 5-2, and 5-3

8 SOL Covered inequalities algebraically and graphically; Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.4 (a) The student will solve multistep 2-5 Glencoe Workbook Solve the equation for. Literal linear and quadratic equations in two Sec 2-8 Rewrite the following formula in terms of Formula variables, including solving literal. equations (formulas) for a given variable A.4 (f) The student will solve multistep linear and quadratic equations in two variables, including solving real-world problems involving equations and systems of equations. A.5 (c) The student will solve multistep linear inequalities in two variables, including solving real-world problems involving inequalities; 2-1, 2-2, 2-3, 2-4, and , 3-3, 3-4, and 3-5 Glencoe Workbook Sec 2-2, 2-3, and 2-4 Teacher created materials Glencoe Workbook Sec 5-1, 5-2, and 5-3

9 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.4 (a) The student will solve multistep Solving for y Teacher created Solve for y Slope Intercept Form linear and quadratic equations in two materials and Put the equation into slope-intercept variables, including solving literal Infinite Algebra form. equations (formulas) for a given variable Software. A.7 (b) The student will investigate and 4-1 and 4-2 Glencoe Workbook What is the domain/range of the Domain analyze function (linear and quadratic) Sec 1-6 function? Range families and their characteristics both Given the domain x={.}, find the Dependent variable algebraically and graphically, including range of the function. Independent variable domain and range.

10 Second Nine Weeks Instruction SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.7 The student will investigate and 4-3 Glencoe Workbook Which is/is not a function? Function analyze function (linear and quadratic) Sec 1-7 and 3-1 Given f(x), find f(n). Function notation families and their characteristics both algebraically and graphically A.7 (e) The student will investigate and 4-4 Glencoe Workbook Graph the function using a table. Table of values analyze function (linear and quadratic) Sec 1-7 and 3-1 Given the following domain, find the families and their characteristics both range to draw the line. algebraically and graphically, including Plot three points that would lie on the finding the values of a function for function y =.. elements in its domain A.6 (a) The student will graph linear 5-3 and 5-4 Glencoe Workbook Find the slope of the line. Slope equations and linear inequalities in two Sec 3-3 Which graph(s) have Rise over Run variables, including determining the positive/negative/zero/undefined Rate of Change

11 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary 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 A.6 (a) The student will graph linear equations and linear inequalities in two variables, including 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 A.6 (b) The student will graph linear equations and linear inequalities in two variables, including 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. slope(s) Given the slope m = a/b, which point would lie on the line with (x, y) Use the slope and y-intercept to graph the line. Which line shows y = Which line has a slope of and goes through the point (0, y)? Write the equation of the line that goes through (x, y) and has a slope of m = - a/b. Write the equation of the line that contains the points (x 1, y 1 ) and (x 2, y 2 ) Change in y over Change in x Undefined slope Positive/negative slope y-intercept Slope intercept form Point slope form

12 SOL Covered 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. Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.6 (a, b) The student will graph linear equations and linear inequalities in two variables, including 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 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. Which graph has the correct region shaded? Graph the following inequality. Dashed line greater than, less than Solid line greater/less than or equal to

13 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.4 (e) The student will solve multistep linear and quadratic equations in two variables, including solving systems of two linear equations in two variables algebraically and graphically A.4 (e) The student will solve multistep linear and quadratic equations in two variables, including solving systems of two linear equations in two variables algebraically and graphically Find the solution to the system of equations by graphing them. Use substitution to find the solution to the system of equations System of Equations Point of Intersection No Solution Infinite Solutions

14 Third Nine Weeks Instruction SOL Covered A.4 (e) The student will solve multistep linear and quadratic equations in two variables, including solving systems of two linear equations in two variables algebraically and graphically A.5 (d) The student will solve multistep linear inequalities in two variables, including solving systems of inequalities Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary Use elimination to find the solution to the system of equations. Find the solution to the system of inequalities. Shade the region that contains the solutions to the system of inequalities. A.2 (a) The student will perform operations on polynomials, including applying the laws of exponents to perform operations on expressions; A.2 (b) The student will perform operations on polynomials, including adding, subtracting, multiplying, and dividing polynomials Simplify the expression. Which is equivalent to.? Which is the (sum/difference/ product/quotient) of and? Multiplication Rule Division Rule Power Rule Negative Exponent Monomial Polynomial Binomial Trinomial

15 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary FOIL Difference of Squares Perfect Square Trinomial A.2 (c) The student will perform operations on polynomials, including factoring completely first- and seconddegree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations Factor completely. Find all of the factors of.

16 Fourth Nine Weeks Instruction SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.2 (c) The student will perform operations on polynomials, including factoring completely first- and seconddegree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations 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. Factor completely. Find all of the factors of. Which is the simplified form of? Find the simplest form of.. Greatest Common Factor Simplest radical form Simplified Cube Root

17 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary A.4 (c) The student will solve multistep linear and quadratic equations in two variables, including solving quadratic equations algebraically and graphically Find the solution(s) for the equation Quadratic Equation Roots Zeros Solutions x-intercepts Vertex 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 Find the mean/variance/standard deviation/mean absolute deviation for the following set of data. Which data set is the most varied? Which person did better relative to their own class? Mean Standard deviation Variance Mean Absolute Deviation z-score Standardize A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots Which group has a smallest/largest median/iqr/range/lower quartile/upper quartile? If the point (x) were added to the data set, what would happen to the Interquartile range Minimum Value Lower Quartile Median Upper Quartile

18 SOL Covered Textbook Chapter and Section Resources Essential Questions / Skills Vocabulary median/iqr/? Maximum Value Range 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 real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions Find the line or curve of best fit using the calculator. Use your line/curve to estimate the value of y when given some x. Line of Best Fit Curve of Best Fit Predict Estimate

19 Instructional Example Questions A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. A.2 The student will perform operations on polynomials, including a) applying the laws of exponents to perform operations on expressions A.2 The student will perform operations on polynomials, including b) adding, subtracting, multiplying, and dividing polynomials

20 A.2 The student will perform operations on polynomials, including 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. 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

21 A.4 The student will solve multistep linear and quadratic equations in two variables, including a) solving literal equations (formulas) for a given variable; A.4 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

22 A.4 The student will solve multistep linear and quadratic equations in two variables, including c) solving quadratic equations algebraically and graphically A.4 The student will solve multistep linear and quadratic equations in two variables, including d) solving multistep linear equations algebraically and graphically; A.4 The student will solve multistep linear and quadratic equations in two variables, including e) solving systems of two linear equations in two variables algebraically and graphically;

23 A.4 The student will solve multistep linear and quadratic equations in two variables, including f) solving real-world problems involving equations and systems of equations A.5 The student will solve multistep linear inequalities in two variables, including a) solving multistep linear inequalities algebraically and graphically A.5 The student will solve multistep linear inequalities in two variables, including 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

24 A.5 The student will solve multistep linear inequalities in two variables, including c) solving real-world problems involving inequalities A.5 The student will solve multistep linear inequalities in two variables, including d) solving systems of inequalities

25 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 A.6 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 Write the equation of the line for each example.

26 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 A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including b) domain and range;

27 A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including c) zeros of a function; A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including d) x- and y-intercepts;

28 A.7 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 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

29 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 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

30 A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots

31 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 real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions

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