Fractions and Mixed Numbers
1 Teaching objective(s)
Mississippi Framework- Grade 5
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
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
Prepared By: Harriette Roadman
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
intended to help relieve your anxiety and build your confidence in your
mathematics skills.
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
your classmates. Please read all course documents posted in Blackboard.
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
6.5 Applications of Quadratic Equations
6.6 Additional Applications of Quadratic Equations
6.7 Using a Graphing Calculator to Solve Equations and Absolute Values
6.8 Additional Factoring Practice
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
7.6 Additional Applications: Variation
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
10.1 Roots and Radicals
10.2 Rational Exponents
10.3 Arithmetic with Radicals
Chapter 11 Quadratic Equations
11.1 Quadratic Equations: Completing the Square
11.2 Quadratic Equations: The Quadratic Formula
11.3 Applications
11.4 Equations with Radicals
11.5 Equations in Quadratic Form
Chapter 12 Quadratic Functions and Conic Sections
12.1 Quadratic Functions: Parabolas
12.2 Quadratic and Other Inequalities
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.
To continue, ask yourself -
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.
To continue, ask yourself -
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.
To continue, ask yourself -
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.
To continue, ask yourself -
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 _____
---------------------------------------------------------------------------------------------------------------------------
YOUR TURN!!
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?
