Title: Simplifying Fractions/Equivalent Fractions
Annotation: This lesson is designed to teach students how to simplify fractions. The first part
of the lesson will be a hands-on activity and then the lesson will focus on computations. The
final part will be the use of a web site to allow students the opportunity to play a matching
game involving equivalent fractions.
Primary Learning Outcome: After completing this lesson, students will be comfortable with
seeing that when fractions are simplified they are also equivalent. After they have finished
any one of the four basic operations involving fractions, they should be able to answer
whether or not the fractional sums, differences, products, or quotients are in their simplest
form.
Assessed QCC 6.29; Students will be able construct visual models to represent parts of a
whole for fractions.
Assessed QCC 6.40; Students will be able to find the greatest common factor by using a list
of factors or by using prime factorization.
Standards: NCTM; Number and Operations.
Total Duration: One hundred ninety-five (195) minutes.
Materials and Equipment: 1. Chalkboard. 2. Overhead projector. 3. Bond paper. 4. Eegg
carton (one dozen) template paper. 5. Egg (one dozen) cartons. 6. Cotton pom-pom balls. 7.
Computers. 8. Student textbook Middle Grades Math, Course 1, published by Prentice Hall.
Technology Connection: Web Site URL- www.quia.com....Brainchild Personal Learning
System 100 (PLS). The PLS 100 is a portable computer. It is used with various cartridges.
The cartridge for this lesson is entitled Math Mechanics, Fractions.
Procedures: 1. Warm up with finding the perfect number. This activity is designed to initiate
the concept of factorization. The numbers to be factored are 8, 20, and 28. They will find
that: the sum of 8’s factors, excluding the 8, is 7; the sum of 20’s factors, excluding 20, is
22; and that the sum of 28’s factors, excluding 28 is 28. Therefore, 8 is a deficient number,
20 is an abundant number, and 28 is a perfect number.
2. The second warm-up is a paper folding activity. Students will do the classic
“hot dog fold” to identify halves, followed by the classic “hamburger fold” to identify
fourths, and finally another hamburger fold to show eighths. Students will be able to see the
equivalency of the fractional parts of the folded paper; that 2/4=1/2, that 4/8=1/2, and that
2/8=1/4. Additional equivalencies can be shown on these folds, or additional folds can be
made to show sixteenths, thirty-seconds etc.
3. Egg carton template paper will now be used to reinforce the concept of
equivalency and simplification. Students will be asked to place the number of dots in one of
the blank template patterns that matches a fractional part of twelve; then on an adjacent
template they will show an equivalent set of dots. Pom-pom balls and egg cartons will follow
this paper and pencil exercise using the following fractions.
2/12= 2 dots; 1/6=2 dots
2/6=4 dots; 1/3= 4 dots
12/12=12 dots no equivalent
3/12= 3 dots; 1/4=3 dots
3/6=6 dots; 1/2= 6 dots
4/12= 4 dots; 1/3=4 dots
4/6=8 dots; 2/3= 8 dots
6/12= 6 dots; 1/2=6 dots
1/12=1 dot
no equivalent
8/12= 8 dots; 2/3=8 dots
5/12=5 dots no equivalent
9/12= 9 dots; 3/4=9 dots
7/12=7 dots no equivalent
10/12= 10 dots; 5/6= 10 dots 11/12=11 dots no equivalent
Point out that the fractions with no equivalents are already simplified.
4. Students will now be taught how to calculate the greatest common factor (GCF) by
both listing the factors and by using prime factors.
A. 27: 1, 3, 9, 27.
45: 1, 3, 5, 9, 15, 45.
Nine is the largest common factor; therefore, the GCF of 27 and 45 is 9 using
the listing of factors method.
B. 27
45
X
X
3 9
5 9
X
X
3 3
3 3
The product of the common factors is 3x3=9. Therefore the GCF is 9 using the
prime factorization method.
5. Students will work the odd numbered problems on page 190 of the student textbook,
twelve problems.
6. Students will now be taught how to simplify fractions. They will be taught that
whenever the GCF is the number one, then the fraction is already simplified. Examples
follow: Write 20/28 in its simplest form. The GCF is 4 found by either method in paragraphs
4A or 4B above. Now divide the numerator and denominator by 4. The simplest form of
20/28 is 5/7. Write the fraction 4/9 in its simplest form. The fraction 4/9 is in its simplest
form because its GCF is 1.
7. Students will now work problems 30-41 on page 199 of the student textbook, 12
problems. They will evaluate their work with the attached rubric.
8. Students will move to the computer lab and log on the website Quia. Com. as noted in
the Technology Connection paragraph on page one; click on the Instructor Zone; click on
mathematics; scroll down to Game #13, Equivalent Fractions; click on the matching game;
play the game whose object is to challenge them to click on the squares that have equivalent
fractions. Once completing this game, students may change the size of the fractions in the
matching squares, and then play another game.
9. If the computers are not available for the entire class, then they will be issued the
Brainchild PLS 100 portable computer with cartridge in order to play a matching game of
equivalent fractions.
Assessment: Teacher observations, student rubric, quiz.
STUDENT RUBRIC
Evaluate your work by using a checkmark with the following scale:
Yes=I did the requirement, and I understood what I did.
No=I did the requirement, but I did not understand what I did.
Almost=I did the requirement, but I need more practice to fully understand what I did.
Not Applicable=I did not need to do this to solve the problem.
1. Did I use the listing of factors method correctly and list all of the factors of the numerator
and the denominator to find the GCF?
Yes___________
No___________ Almost_________
Not Applicable__________
2. Did I use the prime factor method correctly by multiplying the common prime factors to
find the GCF?
Yes____________
No___________
Almost__________
Not Applicable___________
Almost___________
Not Applicable__________
3. Did I find the GCF?
Yes___________
No___________
4. Did I divide the numerator by the GCF?
Yes___________
No___________
Almost___________
Not Applicable__________
5. Did I divide the denominator by the GCF?
Yes___________ No____________
Almost ___________ Not Applicable__________
6. Did I check to see if the GCF of the new simplified fraction was the number 1?
Yes____________ No_____________
Almost____________ Not Applicable
NAME________________________________________
DATE____________________
QUIZ
I. Find the GCF of the following fractions.
1. 4/12
GCF_______
2. 3/27
GCF_______
3. 4/9
GCF_______
II. Simplify the following fractions
4. 6/18=_______________
5. 8/24=_______________
6. 9/36=________________
7. 12/48=_______________
8. 5/16=_______________
9. 18/21=______________
III. Solve the following word problem.
10. A package of M&M’s candy contained 56 multi-colored pieces. If 16 of the pieces were
brown, then the fraction that represents the color brown in16/56. Is 16/56 in its simplest
form? Yes _____ No______. If your answer is no, then what is 16/56 in its simplest form?
________.