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BEDFORD COUNTY PUBLIC SCHOOLSAlgebra I Curriculum Guide

First 9 Weeks

Expressions (A.1)Solving Equations (A.4a,b,d,&f)Solving Inequalities (A.5a & b)

Second 9 Weeks

Functions (A.7)Direct and Inverse Variation (A.8)Graphing Equations and Inequalities (A.6)

Third 9 Weeks

Systems of Equations (A.4e)Systems of Inequalities (A.5c&d)Polynomials (A.2)

Fourth 9 Weeks

Solving Quadratic Equations (A.4c)Square Roots and Cube Roots (A.3)Statistics (A.9, A.10, & A.11)

Dates Standards/Essential Questions Essential Knowledge/Skills/Understanding ResourcesBlock:4 classes

Traditional:8 classes

Standard

A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

Essential Questions

What is the difference between an algebraic and a numerical expression?

How can you represent quantities, patterns, and relationships?

Prerequisite/Extension SOL

Prerequisites:7.1b) determine scientific notationfor numbers > zeroc) compare/order fract/dec/%, andscientific notation

7.13 a) write verbal expressions asalgebraic expressions andsentences as equations and vice

Translate verbal quantitative situations into algebraic expressions and vice versa.

Model real-world 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.

Key Vocabulary Quantity, Variable, Algebraic

Expression, Numerical Expression, base, exponent, power, square, cube, radical sign, radicand, absolute value, term, coefficient, like term, and evaluate

DOE Lesson Plans http://www.doe.virginia.gov/testing/

sol/scope_sequence/mathematics_2009/results.php

Textbook Resources Sections 1.1 and 1.2

Resources/Lessons Algebra I County Resources

http://bcpshelpdeskhighschoolmath.weebly.com/algebra-1.html

http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/results.php




versa; b) evaluate algebraicexpressions

8.1 a) simplify numericalexpressions involving positiveexponents, using rational numbers,order of operations, properties; b)compare/order fract/dec/%, andscientific notation

8.4 evaluate algebraic expressionsusing order of operations

Extensions:AII.1 given rational/radical/ polyexpressions a)‐add/sub/mult/div/simplify rationalalg expressions;b) add/sub/mult/div/simplifyradical exp containing rationalnumbers/variables/ expressionscontaining rational exponents; c)write radical exp as exp containingrational exponents; d) factorpolynomials completely

Block:12 classes


Standard

A.4 The student will solve multistep linear and quadratic equations in two variables, including

a) solving literal equations (formulas) for a given variable;

b) justifying steps used in simplifying expressions and

Solve a literal equation (formula) for a specified variable.

Simplify expressions and solve equations, using the field properties of the real numbers and properties of equality to

Key Vocabulary Commutative Properties, Associative

Properties, Identity Properties, Zero Properties or Multiplication, Multiplication Property of -1, like terms, Distributive Property, equation, solution, Reflexive Property, Symmetric


solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;

d) solving multistep linear equations algebraically and graphically;

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.

Essential Questions How are properties related to Algebra? Can equations that appear to be

different, be equivalent? How can you solve equations?

Prerequisite/Extension SOLPrerequisites:7.14 a) solve one and two step‐ ‐linear equations; b) solve practicalproblems in one variable

8.15 a) solve multistep linearequations in one variable (variableon one and two sides ofequations); c) ID properties ofoperations used to solve

Extensions:

justify simplification and solution.

Solve multistep linear equations in one variable.

Confirm algebraic solutions to linear equations, using a graphing calculator.

Property, Transitive Property, Properties of Equality, identity, literal equation, and formula.



Textbook Resources Sections 1.4, 1.7, 1.9; 2.1-2.5

o Recommended: Concept Byte 2.3, 2.5, & 3.3; and 2.7-.2.9







AII.4 solve (alg./graph)a) abs value equation/inequ.; b)quad equation over complex; c)equation containing rationalalgebraic expression; d) equationcontaining radical exp.

Block:5 classes


Standard

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.

Essential Questions How do you represent relationships

between quantities that are not equal? How can you solve inequalities? What do you have to remember to do

when you multiply or divide by a negative number?

How can you confirm a solution to an inequality?

Prerequisite/Extension SOLPrerequisites:7.15 a) solve one step inequalities;‐b) graph solutions on number line

8.15 b) solve two step linear‐inequalities and graph results on

Solve multistep linear inequalities in one variable.

Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers.

Key Vocabulary Solution of an inequality, inequality,

open sentence, closed sentence, greater than, less than, greater than or equal to, and less than or equal to



Textbook Resources Sections 3.1-3.4







number line; c) ID properties ofoperations used to solve

Extensions:AFDA.5 determine opt values inproblem situations by identifyingconstraints/using linearprogrogramming techniques

AII.5 solve nonlinear systems(alg/graph)

Performance Task must be completed and graded on rubric by the end of Quarter 1

Sample Performance Tasks: Table Hopping (7-10) Reach Out and Touch Someone (9-12)

Block:7 classes


Standard

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; andf) making connections between and

among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

Essential Questions

Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function.

Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

For each x in the domain of f, find f(x).

Represent relations and functions using concrete, verbal, numeric, graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form.

Detect patterns in data and represent arithmetic and geometric patterns

Key Vocabulary Function, input, output, linear function,

nonlinear function, domain, range, independent variable, dependent variable, function rule, x-intercept, y-intercept, and zeros of functions.



Textbook Resources Sections 4.1 – 4.6







How do you use the vertical line test to identify a function?

What is the difference between a relation and a function?

How can you represent and describe a function?

What types of real world situations could a function represent?

Prerequisite/Extension SOLPrerequisites:7.12 represent relationships withtables, graphs, rules, and words

8.17 ID domain, range, indep/depVariable

8.14 make connections betweenany two representations (tables,graphs, words, rules)

Extensions:AFDA.1 investigate/analyzefunction (linear/quad/exp/log)families/characteristics a)‐continuity; b) local/abs max/min; c)domain/range;d) zeros; e) intercepts; f) intervalsinc/dec; g) end behaviors; h)asymptotes

AFDA.4 transfer between/analyzemult representations of functions(alg formulas/graphs/tables/words)

algebraically.


AII.7 investigate/analyze functions(alg/graph)a) domain/range; b) zeros;c) x and y intercepts; d) intervals‐ ‐inc/dec; e) asymptotes; f) endbehavior;g) inverse of a function; h)composition of multiple functions

Block:3 classes


Standard

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.

Essential Questions What is the difference between

inverse and direct variation?

Prerequisite/Extension SOLExtensions:AII.10 ID/create/solve real world‐problems involving inverse/jointvariation/combo of direct/inversevariations

Given a situation, including a real-world situation, determine whether a direct variation exists.

Given a situation, including a real-world situation, determine whether an inverse variation exists.

Write an equation for a direct variation, given a set of data.

Write an equation for an inverse variation, given a set of data.

Graph an equation representing a direct variation, given a set of data.

Key Vocabulary Direct variation, constant of variation,

inverse variation, and rate of change



Textbook Resources Sections 5.2 & 11.6


Block:12 classes


Standard

A.6 The student will graph linear equations and linear inequalities in two variables, including

Graph linear equations and inequalities in two variables, including those that arise from a variety of real-world situations.

Use the parent function y = x and describe

Key Vocabulary Slope, Rate of Change, slope-intercept

form, y-intercept, x-intercept, point-slope form, parallel lines, perpendicular lines, opposite






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.

Essential Questions What does the slope of a line indicate

about the line? What information does the equation

of a line give you? What do we know about the slopes of

parallel and perpendicular lines?


8.15 b) solve two step linear‐inequalities and graph results onnumber line; c) ID properties ofoperations used to solve

Extensions:AFDA.2 use transformations towrite equations, given graph offunction (linear/quad/exp/log)

transformations defined by changes in the slope or y-intercept.

Find the slope of the line, given the equation of a linear function.

Find the slope of a line, given the coordinates of two points on the line.

Find the slope of a line, given the graph of a line.

Recognize and describe a line with a slope that is positive, negative, zero, or undefined.

Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equation.

Write an equation of a line when given the graph of a line.

Write an equation of a line when given two points on the line whose coordinates are integers.

Write an equation of a line when given the slope and a point on the line whose coordinates are integers.

Write an equation of a vertical line as x = a.

Write the equation of a horizontal line as y = c.

reciprocals, horizontal lines, vertical lines, and standard form



Textbook Resources Sections 5.1, 5.3-5.6







AII.6 recognize general shape offunction (abs val/sq root/ cuberoot/rational/poly/exp/ log)families/convert between graphicand symbolic forms of functions ‐transformational approach tographing


Sample Performance Tasks: Bridges (7-10) Display Dilemma (7-10)

Block:8 classes


Standard

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; and

Essential Questions What is a system of linear equations? What is a solution to a system of linear

equations? How many solutions can a system of

linear equations have? What kind of lines have no solutions?


8.15 a) solve multistep linear

Given a system of two linear equations in two variables that has a unique solution, solve the system by substitution or elimination to find the ordered pair which satisfies both equations.

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.

Determine whether a system of two linear equations has one solution, no solution, or infinite solutions.

Write a system of two linear equations that models a real-world situation.

Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a real-world

Key Vocabulary Substitute, Eliminate, System of

Equations, Solution to a System of Equations, Infinitely Many Solution, No Solution, and Parallel Lines





Exemplars D.J. Dilemma (7-10)






equations in one variable (variableon one and two sides ofequations); c) ID properties ofoperations used to solve

Extensions:AII.4 solve (alg./graph)a) abs value equation/inequ.; b)quad equation over complex; c)equation containing rationalalgebraic expression; d) equationcontaining radical exp.

situation.

Determine if a linear equation in one variable has one, an infinite number, or no solutions.†

Block:2 classes


Standard

A.5 The student will solve multistep linear inequalities in two variables, including

c) solving real-world problems involving inequalities; and

d) solving systems of inequalities.

Essential Questions What is a system of linear inequalities? How do we know whether the graph of

an inequality is dotted or solid? How do we know whether to shade

above or below the graph of an inequality?


8.15 b) solve two step linear‐inequalities and graph results on

Solve multistep linear inequalities in one variable.

Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers.

Solve real-world problems involving inequalities.

Solve systems of linear inequalities algebraically and graphically.

Key Vocabulary Linear Inequalities & Systems of

Inequalities










number line; c) ID properties ofoperations used to solve

Extensions:AFDA.5 determine opt values inproblem situations by identifyingconstraints/using linearprogrogramming techniques

AII.5 solve nonlinear systems(alg/graph)

Block:12 classes


Standard

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.

Essential Questions How can you represent very large and

very small numbers? How can you simplify expressions

involving exponents? Can two algebraic expressions that

appear to be different be equivalent?

Simplify monomial expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents.

Model sums, differences, products, and quotients of polynomials with concrete objects and their related pictorial representations.

Relate concrete and pictorial manipulations that model polynomial operations to their corresponding symbolic representations.

Find sums and differences of polynomials.

Find products of polynomials. The factors will have no more than five total terms (i.e. (4x+2)(3x+5) represents four terms and (x+1)(2x2 +x+3) represents five terms).

Find the quotient of polynomials, using a monomial or binomial divisor, or a

Key Vocabulary Exponent, power, base, coefficient,

monomial, binomial, trinomial, degree, polynomial, factor, and standard form



Textbook Resources Sections 7.1-7.5 & 8.1-8.8







How are the properties of real numbers related to polynomials?

Prerequisite/Extension SOLPrerequisites:7.16 apply properties w/ realnumbers: a) commutative andassociative properties foradd/mult; b) distrib property; c)add/mult identity properties; d)add/mult inverse properties; e)mult property of zero

8.15 c) ID properties of operationsused to solve equations

Extensions:AII.3 perform operations oncomplex numbers/express resultsin simplest form using patterns ofthe powers of i/ID field propertiesfor complex numbers

completely factored divisor.

Factor completely first- and second-degree polynomials with integral coefficients.

Identify prime polynomials.

Use the x-intercepts from the graphical representation of the polynomial to determine and confirm its factors.


Sample Performance Tasks: D.J. Dilemma (7-10) Differences of Reversed Squares (9-12)

Block:5 classes

Standard

A.4c The student will solve multistep linear and quadratic equations in two variables,

Solve quadratic equations.

Identify the roots or zeros of a quadratic

Key Vocabulary Standard form, zero product property,

completing the square, quadratic



includingc) solving quadratic equations

algebraically and graphically.

Essential Questions What are the characteristics of a

quadratic function? How can you solve a quadratic

equation?


8.15 a) solve multistep linearequations in one variable (variableon one and two sides ofequations); c) ID properties ofoperations used to solve

Extensions:AII.4 solve (alg./graph)a) abs value equation/inequ.; b)quad equation over complex; c)equation containing rationalalgebraic expression; d) equationcontaining radical exp.

function over the real number system as the solution(s) to the quadratic equation that is formed by setting the given quadratic expression equal to zero.

Confirm algebraic solutions to linear and quadratic equations, using a graphing calculator.

formula, and discriminant





Block:2 classes

Traditional:

A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic

Express square roots of a whole number in simplest form.

Express the cube root of a whole number

Key Vocabulary Radical expression, perfect square,

radical, and radicand






4 classes expression in simplest radical form.

Essential Questions How are radical expression

represented?

Prerequisite/Extension SOLPrerequisites:7.1 d) determine square roots

8.5 a) determine if a number is aperfect square; b) find twoconsecutive whole numbersbetween which a square root lies

in simplest form.

Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values.



Textbook Resources Sections 10.2 & VA-1


Block:5 classes


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.

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

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.

Essential Questions How can analyzing data help you make

decisions and predictions? How can you make and interpret

Analyze descriptive statistics to determine the implications for the real-world situations from which the data derive.

Given data, including data in a real-world context, calculate and interpret the mean absolute deviation of a data set.

Given data, including data in a real-world context, calculate variance and standard deviation of a data set and interpret the standard deviation.

Given data, including data in a real-world context, calculate and interpret z-scores for a data set.

Explain ways in which standard deviation addresses dispersion by examining the

Key Vocabulary Frequency, histogram, mean, median,

mode, range, box-and-whisker plot, standard deviation, z-scores, mean absolute deviation, line of best fit, maximum, minimum and curve of best fit.



Textbook Resources Sections 12.2-4, VA-5, VA-6, & VA-7











different representations of data?

Prerequisite/Extension SOLPrerequisites:5.16 a) describemean/median/mode; b) describemean as fair share; c) find themean/median/mode/range; d)describe range as measure ofvariation

6.15 a) describe mean as balancepoint; b) decide which measure ofcenter is appropriate

7.11 a) construct/analyzehistograms; b) compare/contrasthistograms

8.13 a) makecomparisons/predictions/inferences, using information displayed ingraphs; b) construct/analyzescatterplots

Extensions:AFDA.3 collect data/generate equfor curve (linear/quad/ exp/log) ofbest fit/use best fit equ tointerpolate function values/makedecisions/justify conclusions(alg/graph models)

AFDA.7 analyze norm distrib ‐a) characteristics of normally

formula for standard deviation.

Compare and contrast mean absolute deviation and standard deviation in a real-world context.

Compare, contrast, and analyze data, including data from real-world situations displayed in box-and-whisker plots.

Write an equation for a curve of best fit, given a set of no more than twenty data points in a table, a graph, or real-world situation.

Make predictions about unknown outcomes, using the equation of the curve of best fit.

Design experiments and collect data to address specific, real-world questions.

Evaluate the reasonableness of a mathematical model of a real-world situation.


distrib data; b) percentiles;c) normalizing data, using z scores;‐d) area under std normcurve/probability

AII.9 collect/analyze data/determine equ of the curve of bestfit/make predictions/ solve realworldproblems, using models(poly/exp/log)

AII.11 ID properties of normdistrib/apply properties todetermine probabilities associatedwith areas under the standardnormal curve


Sample Performance Tasks: Batter, Batter, Batter (9-12)

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