Algebra I

Classroom Guide

SkillsTutor

Getting Started ............................................................................................................................................ 1

Algebra I Lessons ................................................................................................................................ 2

Quizzes ..................................................................................................................................................2

Tests ......................................................................................................................................................2

Algebra I Lesson Summaries ...................................................................................................................... 3

Equations, Inequalities, and Polynomials..............................................................................................4

Factoring and Rational Expressions ......................................................................................................6

Functions, Graphing, and Systems of Equations ..................................................................................8

Assignment Sheets .................................................................................................................................... 11

Table of Contents

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SkillsTutor Algebra I is a comprehensive resource for diagnosing and remediating students’basic skills in Algebra I.

The SkillsTutor management system (OTS) provides several important features:

• Tests students’ skills, providing both pretests and posttests to make initial assessments and

gauge student progress

• Makes assignments, based on students’ pretest results

• Monitors student scores and completion of activities

• Produces reports for individual students

• Provides online documentation

This guide outlines the content and activities of SkillsTutor Algebra I. Information on the man-agement system (OTS) is provided under separate cover in the SkillsTutor User’s Guide.

Getting Started

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Algebra I LessonsEach lesson begins with one or more tutorial screens that review a concept. Lessons continuewith a number of multiple-choice questions to reinforce the student’s understanding of the topic,as illustrated below.

These instructions will help the student take full advantage of the features of SkillsTutor lessons:

• Use the mouse to answer questions: click on the correct answer.

• Click Hint for help in answering a question.

• If a question is missed, the student will be told why the answer is wrong. The student

should read the response carefully, and try again. The student cannot move to the next ques-

tion until the current question is answered correctly, so reading and answering carefully will

save time.

• The student may review the instructional material at any time during the lesson by clicking

Review. By clicking Review, students are taken to the first tutorial screen. From there, stu-

dents can go step-by-step through the tutorial screens. To go back to previous tutorial

screens one at a time, click Go Back. Clicking Return allows students to return to the page

where they originally began. After reviewing the tutorial screens, the student returns to the

question that was being answered before the review. The student may return to the question

before completing the review by clicking Resume.

• There may be times when the student needs to exit the program before completing an activity.

To end an activity, close the activity window.

• When the student finishes answering all of the questions in an activity, a score is displayed.

The score, expressed as a percent, is the number of questions answered correctly out of all

the questions attempted.

QuizzesQuizzes operate similarly to lessons. However, quizzes have no introductory instructional material,and they do not require you to answer each question correctly before moving to the next question.Questions are presented in multiple-choice format. Detailed feedback is provided for all questions.

TestsSkillsTutor offers content-area pretests and posttests modeled on standardized tests. Pretests andposttests have no introductory instructional material. Like the questions for quizzes, the testquestions are presented in multiple-choice format to give students practice in answering standardized-test questions. After each test, students have the opportunity to review the ques-tions they missed. Feedback is provided for each missed question.

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Algebra ILesson Summaries

SkillsTutor Algebra I contains 32 lessons, 6 quizzes, and 6 tests in a hierarchical arrangementdesigned to continually reinforce the concepts presented. On the following pages, there is adescription and example for each basic skills lesson. The lessons are arranged in the followingcontent areas:

• Equations, Inequalities, and Polynomials

• Factoring and Rational Expressions

• Functions, Graphing, and Systems of Equations

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LessonNumber

1

2

3

4

5

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Lesson Summary

In this lesson, students will learn how tosolve equations containing one variable byusing inverse operations to isolate the vari-able on one side of the equal sign.

In this lesson, students will learn how towrite an equation that represents the numeri-cal relationships in an application problem.Applications involving numbers, age, con-secutive integers, and geometric figures arediscussed.

In this lesson, students will apply theirknowledge of proportions and equations tosolve various applications of direct andinverse variation.

In this lesson, students will learn to solveequations that express a relationship amongtwo or more variables. They will learn howto use inverse operations to isolate the desig-nated variable on one side of the equal sign.

In this lesson, students will learn to solvemathematical sentences containing inequali-ty signs. They will learn how to use inverseoperations to isolate the variable on oneside of the inequality.

In this lesson, students will learn that com-bined inequalities joined by "and" are con-junctions and those joined by "or" are dis-junctions. They will learn to solve both con-junctions and disjunctions and to identifygraphs of the solution sets.

Examples

Solve.

3m - 15 = 6

Solve the problem by writingand solving an equation.

If 23 is added to three times anumber, the result is 95. Findthe number.

Solve the problem by writingand solving an equation.

If x varies directly as y, and x = 6 when y = 8, find x when y = 38.

Solve the equation for the indicated variable.

Solve C = 2Cr for r

Find the solution set of theinequality.

v - 12 ≥ - 4

Find the solution set of theinequality.

q + 7 < -2 and -4q < 40

Lesson Title

LinearEquations inOne Variable

Applications ofLinearEquations

Direct andInverse Variation

LiteralEquations

LinearInequalities inOne Variable

CombinedInequalities

Equations, Inequalities, and Polynomials

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Equations, Inequalities, and Polynomials

LessonNumber

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8

9

10

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Lesson Summary

In this lesson, students will learn that theabsolute value of a number is its distancefrom zero on the number line. They will usethis knowledge to write a disjunction thatwill produce the solution set of the originalabsolute value equation or inequality.

In this lesson, students will learn to use theproperties of exponents when multiplyingand dividing monomials. They will learn toadd exponents when multiplying expressionsthat have the same base and to subtractexponents when dividing expressions thathave the same base.

In this lesson, students will learn how toadd polynomials by adding their like terms.They will also learn to subtract polynomialsby adding the opposite of the polynomialbeing subtracted.

In this lesson, students will learn how tomultiply a polynomial by a monomial. Theywill use the distributive property to multiplyeach term of the polynomial by the monomial.

In this lesson, students will learn how to usethe FOIL method to multiply two binomials.They will also learn that multiplying a poly-nomial by a binomial requires that eachterm in the polynomial be multiplied byeach term in the binomial.

In this lesson, students will learn to divideeach term of a polynomial by a monomialdivisor. They will also learn the long divi-sion method for dividing a polynomial by abinomial.

Examples

Find the solution set of theequation.

| u + 5 | = 8

Click on the simplest form ofthe expression.

(-2x3 y) (10xy)

Find the sum.

Add (5m + 2) and (3 - 2m)

Simplify.

4x(x + 3)

Multiply.

(x + 6) (x - 1)

Divide.

-18y3 + 24y2 - 6y

-6y

Lesson Title

Absolute ValueEquations andInequalities

Monomials andProperties ofExponents

Adding andSubtractingPolynomials

Multiplying aPolynomial by aMonomial

Multiplying aPolynomial by aBinomial

DividingPolynomials

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LessonNumber

1

2

3

4

5

6

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Lesson Summary

In this lesson, students will learn how tofactor an expression by finding the greatestcommon factor (GCF) of its terms.

In this lesson, students will learn how to fac-tor a trinomial by expressing it as the prod-uct of two binomials.

In this lesson, students will learn how tofactor an expression completely by lookingfirst for the greatest common factor of theterms and then factoring the remaining tri-nomial or difference of squares.

In this lesson, students will learn that if aproduct is zero, then at least one of the fac-tors must be zero. They will learn to solveequations by factoring and then setting eachof the factors equal to zero.

In this lesson, students will learn how tosimplify a rational expression by dividingits numerator and denominator by theirgreatest common factor (GCF).

In this lesson, students will learn how tomultiply rational expressions by multiplyingthe numerators and multiplying the denomi-nators. They will also learn to divide ration-al expressions by changing to multiplicationby the reciprocal of the divisor.

In this lesson, students will learn how toadd and subtract rational expressions withlike denominators. They will learn to com-bine the numerators and write that sum ordifference over the common denominator.

Examples

Factor the expression completely.

9x - 3

Factor the trinomial.

x2 - 18x + 81

Factor the expression.

y2 - 36

Find all solutions of the equation.

b2 - 9b = 0

Find the simplest form.

7c3

Find the product in simplestform.

4a2 b2

b 2

Find the sum in the simplestform.

12m2 3n2

21mn 21mn

Lesson Title

CommonMonomialFactors

FactoringTrinomials

FactoringCompletely

SolvingEquations byFactoring

SimplifyingRationalExpressions

Multiplying andDividingRationalExpressions

Adding andSubtractingRationalExpressions I

Factoring and Rational Expressions

21cd

•

•

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LessonNumber

8

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Lesson Summary

In this lesson, students will learn how toadd and subtract rational expressions withunlike denominators by first renaming theexpressions with their least commondenominator (LCD).

In this lesson, students will learn how tosolve equations containing one or morerational expressions by first multiplying bothsides of the equation by the least commondenominator (LCD). Resulting equations inthis lesson are linear equations.

In this lesson, students will learn how tosolve equations containing one or morerational expressions. Resulting equations inthis lesson are quadratic equations. Studentswill also solve word problems by creatingand solving simple rational equations. In thiscase, resulting equations are linear equations.

Examples

Find equivalent expressions withthe LCD.

9v2 4v

3v + 1 5

Solve the equation.

2a 1

8 4

Find all solutions of the rational equation.

6 12

n – 1 n2 – 1

Lesson Title

Adding andSubtractingRationalExpressions II

Solving RationalEquations

Solving RationalEquations II

Factoring and Rational Expressions

and

=

= –2–

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LessonNumber

1

2

3

4

5

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Lesson Summary

In this lesson, students will learn that a rela-tion can be represented by a graph, a map-ping, a table, a set of ordered pairs, or anequation in two variables. They will alsolearn that a function is a relation in whicheach element of the domain is associatedwith exactly one element of the range.

In this lesson, students will learn to evaluatefunctions and to read functional notation.Given a function, students will learn to sub-stitute the given input value and then com-pute the output value.

In this lesson, students will learn that a lin-ear equation is an equation whose graph is astraight line. They will learn to graph linearequations by graphing values of x and y thatsatisfy the equation.

In this lesson, students will learn that theslope of a line is the ratio of vertical changeto horizontal change. They will learn to findthe slope given the graph of a line, twopoints on the line, or the equation of the line.

In this lesson, students will use their knowl-edge of the slope-intercept form of a linearequation to write equations of lines. Theywill write equations of lines given the slopeand y-intercept, the slope and one point onthe line, the y-intercept and one point on theline, or two points on the line.

In this lesson, students will learn how tograph linear inequalities by graphing theboundary line of an open or closed half-plane.

Examples

Which set represents the set ofordered pairs for the relation?

x y5 2.5

1 0

0 0.5

Evaluate the function for thegiven value.

Evaluate y = 9(x) - 25 for x = 8

Which ordered pair is a solutionof the equation?

– x + y = 6

Find the slope of the given line.

Write an equation in standardform of the line with the givenslope and y-intercept.

slope = , y-intercept = -5

Click on the correct answer.Which of the following is theinequality whose graph isshown here?

Lesson Title

Relations andFunctions

EvaluatingFunctions

Graphing LinearEquations

Slope of a Line

Equations ofLines

Graphing LinearInequalities

Functions, Graphing, and Systems of Equations

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23

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LessonNumber

7

8

9

10

11

Lesson Summary

In this lesson, students will learn how tosolve systems of linear equations by graph-ing the equations. If the graphs intersect at apoint, the solution of the system is the pointof intersection.

In this lesson, students will learn how tosolve systems of linear equations by solvingone of the equations for one of the variablesand then substituting for that variable in theother equation.

In this lesson, students will learn how tosolve systems of linear equations by addingthe equations together to eliminate one ofthe variables.

In this lesson, students will learn that sys-tems of equations can be used to solvemany different types of application prob-lems. Applications involving ages, mixturesof two different components, and motion(time/rate/distance) are discussed.

In this lesson, students will learn to solvesystems of linear inequalities by graphingthe inequalities in the same coordinate planeand finding the overlap of their solutionsets.

Examples

Use the graph to solve this sys-tem of equations.

-x + y = 2x + y = -4

Use the substitution method tosolve the system for x.

6x - 4y = 6

2x + y = -5

Solve the system using the linearcombination method.

-4x + y = 2

4x - 3y = -8

Solve by using a system ofequations.

Tony is 4 years younger thanBen. Seven years ago, the sumof their ages was 48. How old isTony now?

Which of the following is thesystem of inequalities whosegraph is shown here?

Lesson Title

Systems ofLinearEquations:Graphing

Systems ofLinearEquations:Substitution

Systems ofLinearEquations: LinearCombination

Applications ofSystems ofEquations

Systems ofLinearInequalities

Functions, Graphing, and Systems of Equations

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Assignment Sheets: Algebra I

A c t i v i t y Date A s s i g n e d Date Completed S c o re / P ro g re s s

Equations, Inequalities, and Polynominals

• Pretest on Equations, Inequalities, and Polynominals

1 Linear Equations in One Variable

2 Applications of Linear Equations

3 Direct and Inverse Variation

4 Literal Equations

5 Linear Inequalities in One Variable

6 Combined Inequalities

7 Absolute Value Equations and Inequalities

Q1 Quiz on Lessons 1 through 7

8 Monomials and Properties of Exponents

9 Adding and Subtracting Polynomials

10 Multiplying a Polynomial by a Monomial

11 Multiplying a Polynomial by a Binomial

12 Dividing Polynomials

Q2 Quiz on Lessons 8 through 12

• Posttest on Equations, Inequalities, and Polynominals

Using Factoring and Rational Expressions

• Pretest on Using Factoring and Rational Expressions

1 Common Monomial Factors

2 Factoring Trinomials

3 Factoring Completely

4 Solving Equations by Factoring

Q1 Quiz on Lessons 1 through 4

5 Simplifying Rational Expressions

6 Multiplying and Dividing Rational Expressions

7 Adding and Subtracting Rational Expressions I

8 Adding and Subtracting Rational Expressions II

9 Solving Rational Equations

10 Solving Rational Equations II

Q2 Quiz on Lessons 5 and 10

• Posttest on Using Factoring and Rational Expressions

Assignment Sheets: Algebra I

A c t i v i t y Date A s s i g n e d Date Completed S c o re / P ro g re s s

Functions, Graphing, and Systems of Equations

• Pretest on Functions, Graphing, and Systems of Equations

1 Relations and Functions

2 Evaluating Functions

3 Graphing Linear Equations

4 Slope of a Line

5 Equations of Lines

6 Graphing Linear Inequalities

Q1 Quiz on Lessons 1 through 6

7 Systems of Linear Equations: Graphing

8 Systems of Linear Equations: Substitution

9 Systems of Linear Equations: Linear Combination

10 Applications of Systems of Equations

11 Systems of Linear Inequalities

Q2 Quiz on Lessons 7 through 11

• Posttest on Functions, Graphing, and Systems of Equations