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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
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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
1
2
3
4
5
6
Lesson Title
Lesson Summary
Examples
Linear
Equations in
One Variable
In this lesson, students will learn how to
solve equations containing one variable by
using inverse operations to isolate the variable on one side of the equal sign.
Solve.
Applications of
Linear
Equations
In this lesson, students will learn how to
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.
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.
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.
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.
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.
Literal
Equations
6 4 6
3m - 15 = 6
If 23 is added to three times a
number, the result is 95. Find
the number.
If x varies directly as y, and
x = 6 when y = 8, find x when
y = 38.
Solve C = 2Cr for r
v - 12 ≥ - 4
q + 7 < -2 and -4q < 40
Equations, Inequalities, and Polynomials
Lesson
Number
7
8
9
10
11
12
Lesson Title
Lesson Summary
Examples
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.
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.
Adding and
Subtracting
Polynomials
In this lesson, students will learn how to
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.
Multiplying a
Polynomial by a
Monomial
In this lesson, students will learn how to
multiply a polynomial by a monomial. They
will use the distributive property to multiply
each term of the polynomial by the
monomial.
Simplify.
Multiplying a
Polynomial by a
Binomial
In this lesson, students will learn how to 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.
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.
6 5 6
|u+5|=8
(-2x3 y) (10xy)
Add (5m + 2) and (3 - 2m)
4x(x + 3)
(x + 6) (x - 1)
-18y3 + 24y2 - 6y
-6y
Factoring and Rational Expressions
Lesson
Number
1
2
3
4
5
6
7
Lesson Title
Lesson Summary
Examples
Common
Monomial
Factors
In this lesson, students will learn how to
factor an expression by finding the greatest
common factor (GCF) of its terms.
Factor the expression completely.
Factoring
Trinomials
In this lesson, students will learn how to factor a trinomial by expressing it as the product of two binomials.
Factor the trinomial.
Factoring
Completely
In this lesson, students will learn how to
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.
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.
Simplifying
Rational
Expressions
In this lesson, students will learn how to
simplify a rational expression by dividing
its numerator and denominator by their
greatest common factor (GCF).
Find the simplest form.
In this lesson, students will learn how to
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.
In this lesson, students will learn how to
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.
Multiplying and
Dividing
Rational
Expressions
Adding and
Subtracting
Rational
Expressions I
6 6 6
9x - 3
x2 - 18x + 81
y2 - 36
b2 - 9b = 0
7c3
21cd
4a2
b
•
12m2
21mn
b2
2
3n2
• 21mn
Factoring and Rational Expressions
Lesson
Number
8
9
10
Lesson Title
Lesson Summary
Examples
Adding and
Subtracting
Rational
Expressions II
In this lesson, students will learn how to
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.
In this lesson, students will learn how to
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.
In this lesson, students will learn how to
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.
Solving Rational
Equations
Solving Rational
Equations II
6 7 6
9v2
and
3v + 1
4v
5
2a
1
=
8
6
n–1
4
–
12
n2 – 1
= –2
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.
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?
3
Graphing Linear
Equations
Evaluate y = 9(x) - 25 for x = 8
– 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.
In this lesson, students will learn how to
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
Graphing Linear
Inequalities
6 8 6
slope =
2
, y-intercept = -5
3
Functions, Graphing, and Systems of Equations
Lesson
Number
7
8
9
Lesson Title
Lesson Summary
Examples
Systems of
Linear
Equations:
Graphing
In this lesson, students will learn how to
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.
Systems of
Linear
Equations:
Substitution
In this lesson, students will learn how to
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.
Systems of
Linear
Equations: Linear
Combination
In this lesson, students will learn how to
solve systems of linear equations by adding
the equations together to eliminate one of
the variables.
-x + y = 2
x + y = -4
{
6x - 4y = 6
2x + y = -5
Solve the system using the linear
combination method.
{
-4x + y = 2
4x - 3y = -8
10
11
Applications of
Systems of
Equations
Systems of
Linear
Inequalities
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.
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
Tony is 4 years younger than
Ben. Seven years ago, the sum
of their ages was 48. How old is
Tony now?
6 10 6
Assignment Sheets: Algebra I
Activity
Date Assigned
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
Date Completed
Score/Progress
Assignment Sheets: Algebra I
Activity
Date Assigned
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
Date Completed
Score/Progress