SkillsTutor Algebra I Classroom Guide
Table of Contents 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 2001 Achievement Technologies, Inc. All rights reserved. All trademarks are the property of their respective owners.
Getting Started 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 management system (OTS) is provided under separate cover in the SkillsTutor User s Guide. 6 1 6
Algebra I Lessons Each lesson begins with one or more tutorial screens that review a concept. Lessons continue with 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 question 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, students 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. Quizzes Quizzes 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. Tests SkillsTutor offers content-area pretests and posttests modeled on standardized tests. Pretests and posttests have no introductory instructional material. Like the questions for quizzes, the test questions 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 questions they missed. Feedback is provided for each missed question. 6 2 6
Algebra I Lesson Summaries SkillsTutor Algebra I contains 32 lessons, 6 quizzes, and 6 tests in a hierarchical arrangement designed to continually reinforce the concepts presented. On the following pages, there is a description and example for each basic skills lesson. The lessons are arranged in the following content areas: Equations, Inequalities, and Polynomials Factoring and Rational Expressions Functions, Graphing, and Systems of Equations 6 3 6
Equations, Inequalities, and Polynomials Lesson Number Lesson Title Lesson Summary Examples 1 Linear Equations in One Variable solve equations containing one variable by using inverse operations to isolate the variable on one side of the equal sign. Solve. 3m - 15 = 6 2 Applications of Linear Equations write an equation that represents the numerical relationships in an application problem. Applications involving numbers, age, consecutive integers, and geometric figures are discussed. Solve the problem by writing and solving an equation. If 23 is added to three times a number, the result is 95. Find the number. 3 Direct and Inverse Variation In this lesson, students will apply their knowledge of proportions and equations to solve various applications of direct and inverse variation. Solve the problem by writing and solving an equation. If x varies directly as y, and x = 6 when y = 8, find x when y = 38. 4 Literal Equations In this lesson, students will learn to solve equations that express a relationship among two or more variables. They will learn how to use inverse operations to isolate the designated variable on one side of the equal sign. Solve the equation for the indicated variable. Solve C = 2ϖr for r 5 Linear Inequalities in One Variable In this lesson, students will learn to solve mathematical sentences containing inequality signs. They will learn how to use inverse operations to isolate the variable on one side of the inequality. Find the solution set of the inequality. v - 12-4 6 Combined Inequalities In this lesson, students will learn that combined inequalities joined by "and" are conjunctions and those joined by "or" are disjunctions. They will learn to solve both conjunctions and disjunctions and to identify graphs of the solution sets. Find the solution set of the inequality. q + 7 < -2 and -4q < 40 6 4 6
Equations, Inequalities, and Polynomials Lesson Number Lesson Title Lesson Summary Examples 7 Absolute Value Equations and Inequalities In this lesson, students will learn that the absolute value of a number is its distance from zero on the number line. They will use this knowledge to write a disjunction that will produce the solution set of the original absolute value equation or inequality. Find the solution set of the equation. u + 5 = 8 8 Monomials and Properties of Exponents In this lesson, students will learn to use the properties of exponents when multiplying and dividing monomials. They will learn to add exponents when multiplying expressions that have the same base and to subtract exponents when dividing expressions that have the same base. Click on the simplest form of the expression. (-2x 3 y) (10xy) 9 Adding and Subtracting Polynomials add polynomials by adding their like terms. They will also learn to subtract polynomials by adding the opposite of the polynomial being subtracted. Find the sum. Add (5m + 2) and (3-2m) 10 Multiplying a Polynomial by a Monomial multiply a polynomial by a monomial. They will use the distributive property to multiply each term of the polynomial by the monomial. Simplify. 4x(x + 3) 11 Multiplying a Polynomial by a Binomial use the FOIL method to multiply two binomials. They will also learn that multiplying a polynomial by a binomial requires that each term in the polynomial be multiplied by each term in the binomial. Multiply. (x + 6) (x - 1) 12 Dividing Polynomials In this lesson, students will learn to divide each term of a polynomial by a monomial divisor. They will also learn the long division method for dividing a polynomial by a binomial. Divide. -18y 3 + 24y 2-6y -6y 6 5 6
Factoring and Rational Expressions Lesson Number Lesson Title Lesson Summary Examples 1 Common Monomial Factors factor an expression by finding the greatest common factor (GCF) of its terms. Factor the expression completely. 9x - 3 2 Factoring Trinomials factor a trinomial by expressing it as the product of two binomials. Factor the trinomial. x 2-18x + 81 3 Factoring Completely factor an expression completely by looking first for the greatest common factor of the terms and then factoring the remaining trinomial or difference of squares. Factor the expression. y 2-36 4 Solving Equations by Factoring In this lesson, students will learn that if a product is zero, then at least one of the factors must be zero. They will learn to solve equations by factoring and then setting each of the factors equal to zero. Find all solutions of the equation. b 2-9b = 0 5 Simplifying Rational Expressions simplify a rational expression by dividing its numerator and denominator by their greatest common factor (GCF). Find the simplest form. 7c 3 21cd 6 Multiplying and Dividing Rational Expressions multiply rational expressions by multiplying the numerators and multiplying the denominators. They will also learn to divide rational expressions by changing to multiplication by the reciprocal of the divisor. Find the product in simplest form. 4a 2 b 2 b 2 7 Adding and Subtracting Rational Expressions I add and subtract rational expressions with like denominators. They will learn to combine the numerators and write that sum or difference over the common denominator. Find the sum in the simplest form. 12m 2 3n 2 21mn 21mn 6 6 6
Factoring and Rational Expressions Lesson Number Lesson Title Lesson Summary Examples 8 Adding and Subtracting Rational Expressions II add and subtract rational expressions with unlike denominators by first renaming the expressions with their least common denominator (LCD). Find equivalent expressions with the LCD. 9v 2 4v and 3v + 1 5 9 Solving Rational Equations solve equations containing one or more rational expressions by first multiplying both sides of the equation by the least common denominator (LCD). Resulting equations in this lesson are linear equations. Solve the equation. 2a = 1 8 4 10 Solving Rational Equations II solve equations containing one or more rational expressions. Resulting equations in this lesson are quadratic equations. Students will also solve word problems by creating and solving simple rational equations. In this case, resulting equations are linear equations. Find all solutions of the rational equation. 6 12 n 1 n 2 1 = 2 6 7 6
Functions, Graphing, and Systems of Equations Lesson Number Lesson Title Lesson Summary Examples 1 Relations and Functions In this lesson, students will learn that a relation can be represented by a graph, a mapping, a table, a set of ordered pairs, or an equation in two variables. They will also learn that a function is a relation in which each element of the domain is associated with exactly one element of the range. Which set represents the set of ordered pairs for the relation? x y 5 2.5 1 0 0 0.5 2 Evaluating Functions In this lesson, students will learn to evaluate functions and to read functional notation. Given a function, students will learn to substitute the given input value and then compute the output value. Evaluate the function for the given value. Evaluate y = 9(x) - 25 for x = 8 3 Graphing Linear Equations In this lesson, students will learn that a linear equation is an equation whose graph is a straight line. They will learn to graph linear equations by graphing values of x and y that satisfy the equation. Which ordered pair is a solution of the equation? 2 x + y = 6 3 4 Slope of a Line In this lesson, students will learn that the slope of a line is the ratio of vertical change to horizontal change. They will learn to find the slope given the graph of a line, two points on the line, or the equation of the line. Find the slope of the given line. 5 Equations of Lines In this lesson, students will use their knowledge of the slope-intercept form of a linear equation to write equations of lines. They will write equations of lines given the slope and y-intercept, the slope and one point on the line, the y-intercept and one point on the line, or two points on the line. Write an equation in standard form of the line with the given slope and y-intercept. 2 slope =, y-intercept = -5 3 6 Graphing Linear Inequalities graph linear inequalities by graphing the boundary line of an open or closed halfplane. Click on the correct answer. Which of the following is the inequality whose graph is shown here? 6 8 6
Functions, Graphing, and Systems of Equations Lesson Number Lesson Title Lesson Summary Examples 7 Systems of Linear Equations: Graphing solve systems of linear equations by graphing the equations. If the graphs intersect at a point, the solution of the system is the point of intersection. Use the graph to solve this system of equations. -x + y = 2 x + y = -4 8 Systems of Linear Equations: Substitution solve systems of linear equations by solving one of the equations for one of the variables and then substituting for that variable in the other equation. Use the substitution method to solve the system for x. { 6x - 4y = 6 2x + y = -5 9 Systems of Linear Equations: Linear Combination solve systems of linear equations by adding the equations together to eliminate one of the variables. Solve the system using the linear combination method. { -4x + y = 2 4x - 3y = -8 10 Applications of Systems of Equations In this lesson, students will learn that systems of equations can be used to solve many different types of application problems. Applications involving ages, mixtures of two different components, and motion (time/rate/distance) are discussed. Solve by using a system of equations. Tony is 4 years younger than Ben. Seven years ago, the sum of their ages was 48. How old is Tony now? 11 Systems of Linear Inequalities In this lesson, students will learn to solve systems of linear inequalities by graphing the inequalities in the same coordinate plane and finding the overlap of their solution sets. Which of the following is the system of inequalities whose graph is shown here? 6 9 6
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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