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# Fractions and Mixed Numbers

1 Teaching objective(s)
The students will write fractions as mixed numbers and mixed numbers as
fractions.

2 Instructional Activities
On each side of the gym there are nine seats in a row. When 13 fifth graders
were being seated to watch the game, they needed more than one row. How
can a fraction represent the rows they needed.
Teacher explains: A mixed number is a number written as a whole number
and a fraction.
An improper fraction is a fraction in which the numerator is greater than or
equal
to the denominator.13/9
The teacher will model on the dry erase board an example of a mixed number
and an improper fraction.

Example 1:
Write 13/9 as a mixed number:
Since 13/9 means 13 divided by 9, use division to change an improper
fraction to a mixed number. Write the remainder as a fraction.

Example 2:
Write as an improper fraction.
Multiply the denominator by the whole number and add the numerator.
Write the sum over the denominator.

The teacher will call students randomly to practice on the dry erase board
writing mixed number as improper fractions. The students will then write
each proper fraction as a mixed number.

.
The students will work in groups of four to complete the following problems
in 10 minutes. The teacher will say write each mixed number as an improper
fraction. Write each improper fraction as a mixed number. The teacher will
observe and monitor students working in groups.

3 Materials and Resources
Textbook: Silver Burdett Ginn Mathematics:
The Path to Math Success. Copyright 2001
Dry eraser
Board
Paper
Pencil

4 Assessment
Teacher will observe students working problems.
Teacher will call students randomly to work problems on the board.
Teacher will give students a worksheet to complete and receive a grade. See
Attachment

Write each mixed number as in improper fraction. Write each improper
fraction as a mixed number.

# Beginning Algebra I

1) Welcome to MATH 097 – Beginning Algebra I

Math 097 is a beginning
course in algebra. Topics include: algebraic expressions ,
solving linear equations and inequalities, ratios and proportions, graphing and
determining linear equations, exponents and polynomials. A graphing calculator is
required
. Prerequisite: Math 096 with a grade of C or higher or equivalent math
placement score.

If you do not have the class prerequisite (Math 96 or equivalent) or are unsure about
your willingness to devote the time (15 hours per week minimum) and energy
required for this class I suggest you reconsider your educational choices. During the
term please COMMUNICATE with me whenever you have a problem or question.

I am looking forward to working with you and hope that this class will be an
interesting, challenging, useful, and productive experience.

2) Required Textbook

 Beginning and Intermediate Algebra & MyMathLab, 3/E K. Elayn Martin-Gay Prentice Hall Value-Pack ISBN# 0132201054 NOTE: this textbook is used for Math 97, 98, and 99

3) Calculator

You are required to have a graphing calculator. The mathematics department
recommends the TI-83, TI-83 Plus, TI-83 Silver Edition, TI-84, TI-84 Plus, or TI-84
Silver Edition.

4) Exams

Online exams count for 80% of your grade. When taking the exams you may use
your calculator, notes, and textbook. You will not be able to take an exam until you
have completed the appropriate homework with a score of 80% or better. You may
take each exam as many times as you wish; however, you must complete the exam
on or before the due date. The highest score will be the one that counts. There is a
two (2) hour time limit on all exams. Please see the on-line Course Calendar for due
dates.

• Exam 01 – Chapter 1: Review of Real Numbers
• Exam 02 – Chapter 2: Equations, Inequalities, and Problem Solving
• Exam 03 – Chapter 3: Graphing
• Exam 04 – Chapter 4: Systems of Linear Equations
• Exam 05 – Chapters 1-5: Chapters 1-4 and Chapter 5: Exponents and
Polynomials

# Course Syllabus for Algebra II

COURSE DESCRIPTION

Description:
Expands upon the topics of Algebra I including rational expressions, radicals and
exponents, quadratic equations, systems of equations, and applications. Develops the
mathematical proficiency necessary for selected curriculum entrance. Credits not
applicable toward graduation. Prerequisites: a placement recommendation for MTH 04
and Algebra I or equivalent.

 Credits: 5 – Graded as S (satisfactory) and U (unsatisfactory) Submissions: Certifications (and Tests) through Software provided with the Textbook Assessments: 8 Proctored Assessments: 0 Online Activities: Required

COURSE MATERIALS

Textbook:

Introductory and Intermediate Algebra , by D. Franklin Wright.
Hawkes Publishing, 2006. ISBN: 0-918091-98-5.
Bundled with the Hawkes Learning System (HLS) Software CD and license.

Other Materials:
Calculator: A scientific calculator is suggested ;
either a TI-36X (basic) or a TI-83, (graphing).
Notebook and graph paper
Computer storage device (recommended): Floppy disk or flash drive

COURSE INFORMATION

Approved By: Carol Hurst

I. INTRODUCTION

This is a Distance Education course designed specifically for those students whose learning
styles are best served by providing instructional opportunities beyond the traditional classroom
setting. The student will be working with a textbook and computer software. The computer
software is not Internet based. The software must be installed on the student’s home
computer. The learning components of the software are available without Internet access;
however, Internet access is required for registering Certification Codes and for testing, as
explained in the sections on Course Materials and Procedures. Installation and use of the
software is fully explained in the Course Documents in Blackboard.

II. COURSE OBJECTIVES

Upon the successful completion of this course, the student will have a strong base of
algebra skills. This course is intended to help you learn "how to learn" mathematics. It is
With the understanding of mathematics and the study skills you will develop in Math 04, you
should be able to move to the next mathematics course with increased confidence and a
higher expectation of success.

III. COURSE COMMUNICATION

Additional information regarding the structure of the course is posted in Blackboard.

Communications throughout the semester will be through announcements in Blackboard, via
email, or telephone. Responses to email and questions will be posted in the Discussion Board
in Blackboard. You are encouraged to use the Discussion Board for information exchange with

IV. COURSE CONTENT

Chapter 6 Factoring Polynomials and Solving Quadratic Equations
6.1 Greatest Common Factor and Factoring by Grouping
6.2 Special Factoring Techniques I
6.3 Special Factoring Techniques II
6.4 Solving Quadratic Equations by Factoring
6.7 Using a Graphing Calculator to Solve Equations and Absolute Values

Chapter 7 Rational Expressions
7.1 Multiplication and Division with Rational Expressions
7.2 Addition and Subtraction with Rational Expressions
7.3 Complex Fractions
7.4 Equations and Inequalities with Rational Expressions
7.5 Applications

Chapter 9 Systems of Linear Equations I
9.1 Systems of Equations: Solutions by Graphing
9.2 Systems of Equations: Solutions by Substitution
9.3 Systems of Equations: Solutions by Addition
9.4 Applications: Distance-Rate-Time, Number Problems, Amounts and Costs
9.5 Applications: Interest and Mixture

Chapter 10 Roots, Radicals, and Complex Numbers
10.2 Rational Exponents

11.1 Quadratic Equations: Completing the Square
11.3 Applications

Chapter 12 Quadratic Functions and Conic Sections
12.3 f(x) Notation (don’t do Translations)

# LCM and GCF

In Topic 1.2, the Least Common Multiple and Greatest Common Factor are presented. Use this worksheet to help you remember how to find each of these and how to tell the difference!

GCF: factors, in general, are small numbers because they must divide INTO a given number. Factors of 12, for example, are the numbers 1, 2, 3, 4, 6, and 12. All of the numbers listed divide INTO 12 evenly (so there is no remainder).

LCM: multiples, in general, are large numbers because a multiple must be divided BY a given number. Multiples of 12, for example, are 12, 24, 36, 48, and so on. All of the numbers listed can be divided BY 12 evenly (so there is no remainder).

Using the PRIME FACTORIZATION of two or more numbers is a great way to find both the GCFactor and the LCMultiple . Use the example below to help you understand how to find both the GCF and LCM.

Say you are asked to find the GCFactor and the LCMultiple of the numbers 12, 30 and 54. Begin by finding the prime factorization of each of the numbers (using a factor tree is a good way to do this).

12 = 2•2•3
30 = 2•3•5
54 = 2•3•3•3

To find the GCFactor, ask yourself -
how many 2's are in the prime factorization of 12? _______
how many 2's are in the prime factorization of 30? _______
how many 2's are in the prime factorization of 54? _______

What is the FEWEST (F for Fewest and F for Factor) number of 2's in any one of the numbers? _______ So this is how many 2's are in your GCFactor.

how many 3's are in the prime factorization of 12? _______
how many 3's are in the prime factorization of 30? _______
how many 3's are in the prime factorization of 54? _______

What is the FEWEST (F for Fewest and F for Factor) number of 3's in any one of the numbers? _______ So this is how many 3's are in your GCFactor.

how many 5's are in the prime factorization of 12? _______
how many 5's are in the prime factorization of 30? _______
how many 5's are in the prime factorization of 54? _______

What is the FEWEST (F for Fewest and F for Factor) number of 5's in any one of the numbers? _______ So this is how many 5's are in your GCFactor. BE CAREFUL!!

The GCF then is: ___ • ____ or _____

To find the LCMultiple, ask yourself -
how many 2's are in the prime factorization of 12? _______
how many 2's are in the prime factorization of 30? _______
how many 2's are in the prime factorization of 54? _______

What is the MOST (M for Most and M for Multiple) number of 2's in any one of the numbers? _______ So this is how many 2's are in your LCMultiple.

how many 3's are in the prime factorization of 12? _______
how many 3's are in the prime factorization of 30? _______
how many 3's are in the prime factorization of 54? _______

What is the MOST (M for Most and M for Multiple) number of 3's in any one of the numbers? _______ So this is how many 3's are in your LCMultiple.

how many 5's are in the prime factorization of 12? _______
how many 5's are in the prime factorization of 30? _______
how many 5's are in the prime factorization of 54? _______

What is the MOST (M for Most and M for Multiple) number of 5's in any one of the numbers? _______ So this is how many 5's are in your LCMultiple.

The LCM then is: ____ • ____ • ____ • _____ • ____ • ____ or _____

---------------------------------------------------------------------------------------------------------------------------

Find the GCF and LCM of 24, 36, and 90.

1. Find the prime factorization of each number.
2. Ask yourself the questions listed above for 2, 3 and 5.
3. Decide whether to use the Fewest number of times the factor appears or the Most number of times the factor appears.
4. What is the GCF and the LCM of these numbers?

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